# Fortune's Formula

**Author:** William Poundstone
**Year:** 2005
**Pages:** 389

> Full text extracted from PDF for on-demand reference. Use grep/search to locate concepts.


## Page 2

Fortune's
Formula
THE
UNTOLD
STORY
OF
THE
SCIENTIFIC
BETTING
SYSTEM
THAT
BEAT
THE
CASINOS
AND
WALL
STREET
William
Poundstone
to
nil
ill
and
Wang
A division
of
Farrar, Straus and
Giroux
New
York


## Page 3

Hill and Wang
A divisionof
Farrar,
Straus and Giroux
19
Union
Square
West,
New
York
10003
Copyright
©
2005
by
William
Poundstone
All
rights
reserved
Distributed
in
Canada
by
Douglas
&
Mclntyre
Ltd.
Printed in the United States of America
Published
in 2005 byHilland
Wang
First
paperback
edition.
2006
The
Library
of
Congress
has
cataloged
the
hardcover
edition
as
follows:
Poundstone,
William.
Fortune's
formula
: the
untold
storyof the
scientific
betting
system
that
beat
the
casinos
and
Wall
Street
/
by
William
Poundstone.—
isted.
p.
cm.
Includes
bibliographical
references
and
index.
ISBN-IO:
0-8090-4<>37-7
(hardcover
:
alk.
paper)
ISBN-13:
978-O-8090-4637-9
(hardcover
:
alk.
paper)
1.
Gambling.
2.
Gambling—
History.
3.
Gambling-Mathematical
models.
4.
Shannon.
Claude
Elwood.
1916-
I.
Title.
HV6710.P68
200s
795'.oi'5i92—dc22
2005005725
Paperback
ISBN-13:
978-O-8090-4599-0
Paperback
ISBN-IO:
0-8090-4599-O
Designed
by
Robert
C.
Ohson
www.fsgbooks.com
3579
10
8642


## Page 4

To
Emily,
Alyssa,
and
Weston


## Page 5

Itsgettingso
a
businessman
can't
expect
no
return
from
a
fixed
fight.
Now,
if
you
can't
trust
a
fix,
what
can
you
trust?
—Joel
Coen
and
Ethan
Cocn,
Miller's
Crossing
Mathematicians
are
like
a
certain
type
of
Frenchmen:
when
you
talk
to
them
they
translate
it
into
their
own
language,
and
then
it
soon
turns
into
something
completely
different.
—Johann
Wolfgang
von
Goethe


## Page 6

CONTENTS
Prologue:
The
Wire
Service
PART
ONE:
ENTROPY
13
Claude
Shannon
•
Project
X •
Emmanuel
Kimmel
•
Edward
Thorp •
Toy
Room
•
Roulette
•
Gambler's
Ruin
•
Randomness,
Disorder,
Uncertainty
•
The
Bandwagon
•
John
Kelly.
Jr.
•
Private
Wire
•
Minus
Sign
PART TWO: BLACKJACK
79
Pearl
Necklace
• Reno • Wheel of Fortune • More
Trouble
Than
an
S18
Whore
•
The
Kelly
Criterion,
Under
the
Hood
•
Las
Vegas
• The
First
Sure
Winner
in
History
•
Deuce-Dealing
Dottie
•
Bicycle
Built
for
Two
PART
THREE:
ARBITRAGE
115
Paul Samuelson •
The
Random Walk Cosa
Nostra
•
This
Is
Not the
Time
to
Buy
Stocks
• IPO •
Bet
Your
Beliefs
•
Beat
the
Market
•
James
Regan
•
Resorts
International
• Michael Milken •
Robert
C.
Mcrton
•
Man
vs.
Machine
•
Why
Money
Managers
Are No
Good
• Enemies List •
Widows
and Orphans
IX


## Page 7

Contents
PART
FOUR:
ST.
PETERSBURG
WAGER
179
Daniel
Bernoulli
•
Nature's
Admonition
to
Avoid
the
Dice
•
Henry
Latane
•
The
Trouble
with
Markowitz
•
Shannon's
Demon
• The
Feud
•
Pinball
Machine
•
It's
a
Free
Country
•
Keeping
Up
with
the
Kellys
•
Though
Years
to
Act
Are
Long
•
All
Gambles
Are
Alike
• A
Tout
in a
Bad
Suit • MyAlien Cousin
PART
FIVE:
RICO
239
Ivan
Boesky
•
Rudolph
Giuliani
•
With
Tommy
Guns
Blazing
•
The
Parking
Lot
•
Welcome
to
the
World
of
Sleaze •
Ultimatum
•
Princeton-Newport
Partners,
1969-88 •
Terminator
• The
Only
Guy
on
Wall
Street
Who's
Not
a
Rat
PART
SIX:
BLOWING
UP
275
Martingale
Man
•
Kicking
and
Screaming
•
I've
Got a
Bad
Feeling
About
This
•
Thieves'
World
•
Fat
Tails
and
Frankenstein
•
Survival
Motive
• Eternal
Luck
•
Life's Rich Emotional Experiences
PART
SEVEN:
SIGNAL
AND
NOISE
3°5
Shannon's
Portfolio
•
Egotistical
Orangutans
•
Indica
tors
Project
•
Hong
Kong
Syndicate
•
The
Dark
Side
of
Infinity
Notes
331
Bibliography
357
Acknowledgments
3^9
Index
371


## Page 8

Prologue:
The
Wire
Service


## Page 9

The
STORY
starts
with
a
corrupt
telegraph
operator.
His
name
was John
Payne,
and he
worked
for Western Union's Cincinnati
office
in
the
early
1900s.
At
the
urging
of
one
of
its
largest
stock
holders.
Western
Union
took
a
moral
stand
against
the
evils
of
gam
bling.
It
adopted
a
policy
of
refusing
to
transmit
messages
reporting
horse
race
results.
Payne
quit
his
job
and
started
his
own
Payne
Telegraph
Service
of
Cincinnati.
The
new
service's
sole
purpose
was
to
report
racetrack results to bookies.
Payne
stationed an
employee
at the
local
racetrack.
The instant a
horse
crossed
the
finish
line,
the
employee
used
a
hand
mirror
to
flash
the
winner,
in
code,
to
another
employee
ina
nearby
tall
build
ing.
This
employee
telegraphed
the
results
to
pool
halls
all
over
Cincinnati,
on
leased
wires.
In our
age
of
omnipresent
live
sports
coverage,
the
value
of
Payne's
service
may
not be
apparent.
Without
the
telegraphed
re
sults,
it
could
take
minutes
for
news
of
winning
horses
to
reach
bookies.
All
sorts
of
shifty
practices
exploited
this
delay.
A
customer
who
learned
the
winner
before
the
bookmakers
did
could
place
bets
on a horse that had
already
won.
Payne's
service
ensured
that the
bookies
had
the
advantage.
When
a
customer
tried
to
place
a beton a
horse
that
had
already
won, the
bookie
would
know it and refuse the bet.
When
a
bettor
unknowingly
tried
to
place
a beton a
horse
that
had
already
lost.
. .
naturally,
the bookie
accepted
that bet.


## Page 10

fortune's
formula
It is the
American
dream to invent a
useful
new product or ser
vice
that
makes
a
fortune.
Withina
few
years,
the
Payne
wire
service
was
reporting
results
for
tracks
from
Saratoga
to
the
Midwest.
Local
crackdowns
on
gambling
only
boosted
business.
"It
is
my
intention
to
witness
the
sport
of
kings
without
the
vice
of
kings,"
decreed
Chicago
mayor
Carter
Harrison
II,
who
banned
all
racetrack
bet
ting
in
the
city.
Track
attendance
plummeted,
and
illegal
bookmak-
ing
flourished.
In
1907
a
particularly
violent
Chicago
gangster
named
Mont
Tennes
acquired
the
Illinois
franchise
for
Payne's
wire
service.
Tennes
discreetly
named
his
own
operation
the
General
News
Bu
reau.
The
franchise
cost
Tennes
S300
a
day.
He made that
back
many
times
over.
There
were
more
than
seven
hundred
bookie
joints
in
Chicago
alone,
and
Tennes
demanded
that
Illinois
bookies
pay
him
halftheir
daily
receipts.
Those
profits
were
the
envy
of
other
Chicago
gangsters.
In
July
through
September
of
1907,
six
bombs
exploded
at
Tennes's
home
or
places
of
business.
Tennes
survived
every
one
of
the
blasts.
The
reporter
who
informed
Tennes
of
the
sixth
bomb
asked
whether
he
had
any
idea
who
was
behind
it.
"Yes,
of
course
I
do,"
Tennes
an
swered,
"but I
am
not
going
to
tell
anyone
about
it,
am
I?
That
would be poor for
business."
Tennes
eventually
decided
he
didn't
need
Payne
and
squeezed
him out of
business.
Tennes's
General
News
Bureauexpandedsouth
to
New
Orleans
and
west
to
San
Francisco.
This
prosperity
drew
the
attention
of
federal
judge
Kenesaw
Mountain
Landis.
In
1916
Judge
Landis
launched a probe into
General
News Bureau. Clarence Darrow
represented
Tennes. He
advised
his client to take the Fifth Amendment.
Judge
Landis
ulti
mately
ruled
that
a
federal
judge
had
no
jurisdiction
over
local
antigambling
statutes.
In
1927
Tennes
decided
it
was
time to
retire.
He
issued
100
shares
of
stock in General News Bureau and sold them all. Tennes
died
peacefully
in
1941.
He
bequeathed
partof
his
fortune
to
Camp
Honor, a
character-building
summer camp for
wayward
boys.
General
News
Bureau's
largest
stockholder,
of 48
shares,
was


## Page 11

Prologue:
The
Wire
Service
Moses
("Moe")
Annenberg,
publisher
of the
Racing
Form.
Annenberg
was unapologetic about the
social
benefits of quick and accurate race
results.
"If people
wager
at a
racetrack
whyshould they be deprived
of the right to do so
away
from
a
track?"
he
asked.
"How many peo
ple can take time off from their jobs to go to a
track?"
Annenberg hired a crony named
James
Ragan
to run the wire
service.
By
that time, there were scores of competitors. Annenberg
and
Ragan
expanded by
buying
up the
smaller
wire
services
or run
ning them out of
business.
One manwith theguts to stand up to
Annenberg
and
Ragan
was
Irving
Wcxler,
a
bootlegger
and
owner
of the
Greater
New
York
News
Service.
After
Ragan
started a price war with Greater New
York
News,
Wcxler sent a team of thugs to
vandalize
Anncnberg's
New York headquarters.
Annenberg
knew
that
Wexlcr
was
tapping
into
General
News's
linesto get
race
results.
It
was
cheaper
than
paying
his
own
employ
ees
to report
from
each
racetrack.
So one
day
Annenberg
delayed
the race results on the portion of line that Wcxler
was
tapping.
An
nenberg
had
the
timely
results
phoned
to a
bunch
of
his
own
men,
who
placed
big
bets
on the
winning
horses
with
Wexler's
sub
scribers.
Wexler's
bookies,
gettingthe
delayed
results,
did not
know
that the
horses
had
already
won.
By
day's
end, they had
suffered
crippling
losses.
Annenberg's
men
went
to
each
of
Wexler's
subscribers
and
ex
plained
what
had
happened.
They
refunded
the
day's
losses,
advising
the
bookies
that
it
would
be wise to
switch
to
General
News
Bureau.
With
such
tactics.
Annenberg's
service—also
known
as "the
Trust"
or "the
Wire"—expanded
coast-to-coast,
to
Canada.
Mexico,
and Cuba. In
1934
Annenberg ditched his partners much as Tennes
had
done.
Annenberg
established
a
new,
rival
wire
service
called
Na
tionwide
News
Service.
Bookies
were
told
to
switch
carriers
or
else.
The
growth
of
General
News
Bureau
paralleled
that of the
Ameri
can
Telephone
and
Telegraph
Company.
In
1894
Alexander
Graham
Bell's
telephone
patents
expired.
Within
a
few
years,
over
6,000 lo-


## Page 12

FORTUNE
S
FORMULA
cal
telephone
companies
were
competing
for the
U.S.
market.
AT&T
acquired
or drove most of them out of
business.
Though
AT&T's
techniques
were more
gentlemanly
than
Annenberg's,
the
result was about the same. The government stepped in with an
antitrust suit. The
legal
action
was
settled in
1913
with an agreement
that AT&T permit competing phone companies to connect to its
long-distance
network.
In
1915
the first coast-to-coast telephone
line went into
operation.
The
following
year,
AT&T
was
added to
the
Dow
Jones
average.
With its
now-legal
monopoly
and
reliable
dividend. AT&T was reputed to be a favorite stock of widows and
orphans.
Few
of those
widows
and
orphans
realized
how
closely
the phone
company's
business
was
connected
to
bookmaking.
General
News
Bureau
did not own the
wires
connecting
every
racetrack
and
bookie joint. It
leased
lines
and equipment from
AT&T,
muchas to
day's
Internet
services
lease
cables
and
routers.
Both
telegraph
and
voice
lines
were
used.
As
the
system
grew
more
sophisticated,
voice
lines
provided
live
track
commentary.
AT&T's
attorneys
worried about this side of the business. An in-
house
legal
opinion
from
1924
read:
"These
applicants
[the
racing
wire
services]
must
know
that a
majority
of their
customers
are
bound
to
be
owners
of
poolrooms
and
bookmakers.
They
cannot
willfully
blind
themselves
to
these
facts
and,
in
fact,
set
up
their
ig
norance
of
what
everybody
knows
in order to
cooperate
with
law
breakers."
On
legal
advice,
AT&T
put an
escape
clause
in its contract with
the
wire
lessees.
The
clause
gave
the
phone
company
the
right
to
cancel
service
should
authorities
judge
the
lessee's
business
illegal.
AT&T
continued
to do
business
with
bookies—while
officially
it
could
claim
to be
shocked
that
gambling
was
going
on in its net
work.
By
the
mid-i930s,
Moe
Annenberg
was
AT&T's
fifth
largest
customer.
Annenberg's takeover
of
the wire service business infuriated the
other
stockholders
of
General
News
Bureau,
who
now
owned
shares


## Page 13

Prologue:
The
Wire
Service
in a company with
practically
no customers.
One
stockholder, Chi
cago
mobster
John
Lynch,
took
Annenberg
to court.
Annenberg
attorney
Weymouth
Kirkland
argued
that,
because
the wire service
was
patently
illegal,
the court had no
jurisdiction.
He cited a
1725
precedent in
which
an
English
judge
had
refused
to divide the loot
of two
disputing
highwaymen.
The court
accepted
Kirkland's
bold
defense.
Lynch
appealed to Al Capone's
mob.
He felt he might get a sym
pathetic ear as Capone (then in prison for tax
evasion)
had
already
made
unsuccessful
overturesto Annenbergabout acquiringthe wire
service.
Capone's
enforcer,
Frank
Nitti, told
James
Ragan
that if
he'd allyhimself with the Capone
mob,
Annenberg would be dead in
twenty-four
hours.
Ragan
said no. Annenberg skipped town for
Miami.
Negotia
tions
between
Annenberg
and
Capone's
people
dragged
on for a
couple of
years.
It
was
eventually
agreed
that Annenberg would pay
Capone's people Si
million
a year in protection
money,
but Annen
berg
would
retain
ownership
of the
wire
service.
Then, in
1939,
Annenberg
was
up on tax
evasion
charges.
In or
der to
prove
he
was
a
reformed
man,
he did the
unthinkable.
He
walked away from the wire service.
The
vacuum
created did not last
long.
The wire
service
was
quickly
reconstituted under the name of Continental
Press
Service.
James
Ragan
remained
at the
helm.
Again
the
Chicago
mob
approached
Ragan
about
taking
over.
Ragan
still
wasn't
interested.
To
protect
himself,
he
prepared
affi
davits
implicating
Frank
Nitti in the attempted murder of Annen
berg.
He let it be
known
that
should
anything
happen
to
him,
the
affidavits would go to the FBI.
The most
powerful
Italian
and
Jewish
mobsters
of the time were
allied in a national organization
cryptically
called
"the Combina
tion." The Combination decided it didn't need
Ragan.
It founded
its own wire service, Trans-American Publishing and News Service,
with the intention of putting
Continental
out of
business.
Trans-American was run by Ben
Siegel.
Better known as
"Bugsy,"
a name he
hated,
Siegel
was
a
New
Yorker
who had
moved
to the


## Page 14

FORTUNES
FORMULA
West Coast. Trans-American's territory included
Nevada—a
special
case,
since
gambling
was
legal
there.
Siegel
decided that
Nevada
bookies
should pay
more,
not
less.
He
reasoned
that casino book-
making
operations are a
way
to draw
people
into the
casinos
so that
they
will
play
the other
games.
Siegel
therefore
charged
the casino
bookies the usual subscription price plus a cut of their income—in
some
cases,
as much as
100
percent
of the
bookmaking
income.
On June 24, 1946, James Ragan stopped his car at a Chicago inter
section. A banana truck
full
of crates
pulled
up next to him. Some
one on the truck
pulled
up a
tarpaulin.
Two
shots rang out. One
mangled
Ragan's
arm and
shoulder.
Ragan
spent the next six
weeks
under
police
guard in a
Chicago
hospital.
Despitethat, someone ap
parently poisoned
Ragan
by putting mercuryin his
Coca-Colas,
or
his
catheter,
according
to
various
accounts.
With
Ragan
dead,
the
mob
seized
Continental
Press.
The
synergy
of
merging
Continental
Press
and
Trans-American
did not
escape
anyone.
It didn't
escape
Los
Angeles
bookies,
who
were compelled to subscribe to
both
wire services at Si50 a week
each.
But
Siegel
decided
that
Trans-American
was
really
his own
business,
not the
Combination's.
Siegel
was
building
the
Flamingo
hotel
and
casino
in
Las
Vegas.
It
had
cost
far
more
than
projected,
and
Siegel
owed
the
construction
company
S2
million.
Siegel
told
the
Combination's
"board
of
directors"
in
New
York
that they
could
have
the
Trans-American
wire
service
back
for
only
$2
million.
The
board's response was cool.
Siegel
later got word that the Combination had called
another
board of
directors
meeting
without
inviting
him.
That
was
a bad
sign.
Siegel
was
concerned
enough
to
track
down
the
exiled
Lucky
Luciano
in
Havana.
Siegel
insisted
he
needed
to
keep
the wireser
vice and its profits one more
year.
Luciano,
still one of the most
powerful
men
in the
Combination,
advised
Siegel
to
give
the
wire
serviceback
immediately.
One
implausibly
verbatim
contemporary account records Sie-


## Page 15

Prologue:
The
Wire
Service
gel's
reply
as:
"Go
to
hell
and
take
the
rest
of
those
bastards
along
with
you.
I'll
keep
the
goddamn
wire
as
longas I
want."
There had been a
rule
that no
board
member
got the death sen
tence.
The
Combination
broke
that
rule
for
the
first
time
with
Siegel.
On June 20,
1947,
an
unknown
gunman
took aim at
Siegel
through the
trellis
of a rose arbor in
Beverly
Hills.
He
fired
a
full
clip of steel-jacketed bullets from a .30 caliber army carbine. Most
missed.
The four that didn't were more than enough to do the
job.
Siegel's
right
eyeball
came to rest
fifteen
feet
away,
on the tile of a
dining room
floor.
A half hour before the
murder,
four toughs
assembled
in the
lobby of the
Flamingo.
At the appointed time, they
walked
over to
the managerand announced that they were taking
over.
The Com
bination took over
Siegel's
wire
service,
too.
The murder of
Ben
Siegel
was
a
costly
mistake.
A high-profileexe
cution in a
wealthy
Californiasuburb
showed
that organized crime
had reached all the
way
to the
Pacific.
It raised interest in the wire
service that the mob was so intent on
possessing.
Tennessee
senator Carey
Estes
Kefauvcr
branded Continental
Press
"Public
Enemy
Number One." "In my opinion," the senator
said, "the wire service keeps alive the
illegal
gambling empire which
in turn
bankrolls
a
variety
of other
criminal
activities
in
America."
Kefauver,
a
folks)-
man who liked to be photographed in a coon-
skin
cap,
organized
a
Special
Committee
to
Investigate
Organized
Crime in
Interstate
Commerce. The
Kefauvcr
committee's hearings
were
televised
and ran for
fifteen
months starting in
1950.
The Sen
ate committee traveled the nation, subpoenaing most of the coun
try's majororganizedcrime
figures.
Manyof them
managed
to be on
vacation
when the committee hit town.
Many
invoked
the Fifth
Amendment.
The
committee
sometimes got more
interesting
testi
mony from corrupt cops and
prosecutors.
A
Chicago
police captain
admitted
allowing
a
bookie
joint to
operate
while
he himself
amassed
a fortune bettingon
sports,
elections,
and the stock
market.


## Page 16

FORTUNE
S
FORMULA
Louisiana
police
explained
that they didn't
have
the heart to
close
down
illegal
casinos
that
employed
the
underprivileged.
The
high
point of the
investigation
came
in
March
1951,
when
the committee grilled the
powerful
crime
families
of New
York.
"How can we curb
gambling
in this
country?"
Senator
Kefauvcr
asked
New
York
mobster
Frank
Costello.
"Senator,"
Costcllo
answered,
"if you want to cut out
gambling
there's just two things you need to do. Burn the stables and shoot
the
horses."
Kefauver
demanded to know
where
Costello got the money to
buy three
buildings
on
Wall
Street. Costello said he borrowed it
from gamblers.
Costello had gotten his start
making
counterfeit
Kewpic
dolls
for
carnival
prizes.
From
that he had built a
gambling
empire that
extended south to Tropical
Park,
Miami.
The dapper Costcllo
agreed
to
testify'
on the condition that his
face
not be
televised.
When he
spoke,
the TV
cameras
cut to his
carefully
manicured
hands. Costello sounded
ill
at
case,
and his
graceful
gestures,
de
scribed as a "hand ballet,"were surreallydisconnected from his sta
tus as a major crime boss.
Possibly
the real mastermind behind the Combination was New
Jersey
gangster
Longy
Zwillman.
Interviewed
in
Washington,
Zwill-
man presented himselfas a
legitimate
businessman
who
was
baffled
as to
why
he had been
brought
before
this
particular
committee.
He
addressed
his interrogators as "sir" and
politely
requested that the
photographers
stop
using
flashbulbs.
"I
feel
like
I'm
getting
shot,"
he told Senator
Kefauver.
The line got a big
laugh.
The
senators
were
attempting
to establish that an
intercon
nected
social
network
of
career
criminals
ran
a
wire
service
for
bookies,
as
well
as
gambling,
prostitution,
loan-sharking,
and
rackets
throughout the country. As much as
possible,
the mobsters denied
knowing
each
other.
Zwillman
admitted
knowing
Costello,
slightly.
"In the old
days,
I met
everybody,"
Zwillman
said.
"Every
place
you
went, you
met
somebody."
Zwillman's
business
associate
in New
Jersey
was
Willie Morctti.
Morctti
was
as short (just over
five
feet)
and
loud
as
Zwillman
was
10


## Page 17

Prologue:
The
Wire
Service
tall
and
quiet.
Moretti
dressed
like
a
gangster,
down
to the om
nipresent
diamond
stickpin.
He
was
a
great
lover
of
women,
the
darker
their
skin
the
better.
Long
ago,
Moretti
had
contracted
syphilis.
He neverhad it treated and
was
entering the
disease's
ter
minal
stages.
At
first
this hadn't been a
problem
for
Zwillman.
His
business
was
builton
intimidation.
It
was
not
such
a bad thingto
have
a part
ner
who
was
not
only
violent
and
impulsive
but
also
losing
his
mind.
Moretti
became
a
problem
in the
Kefauvcr
hearings.
Testifying
before
the
committee,
Moretti
freely
admitted
knowing
Frank
Cos
tello.
He
said
he
knew
every
other
big-name
mob
figure
in the
whole country. They were "well-charactered men" he had met at
racetracks.
Moretti
described
himself as a
professional
gambler.
He had
made S25,ooo by betting on a
race—the
1948
presidential
race.
He
picked Truman to win.
The
senators put it to Moretti that his business interests were
mob-infiltrated
rackets.
"Everything
is a
racket
today,"
Morctti
replied. As he left the stand, he invited the senators to come visit
him at his home on the
Jersey
shore. Moretti quicklybecame one of
the first celebrities of reality TV. He prolonged his fifteen minutes
of fameby
giving
off-the-cuff
interviews
to reporters.
This
was
too
much
for Vito
Gcnovcse.
From
1949
Genovese
had
been the leader of the Cosa
Nostra.
Genovese
began spreading ru
morsof Moretti's mental deterioration. If Moretti
was
mouthing off
now,
what would he
say
as the rest of his brain rotted
away?
Gen
ovese
called
a meeting of the Combination. They decided that it
was,
regrettably,
time to
kill
another board
member.
On October 4,
1951,
Moretti was shot twice in the forehead at his hangout, Joe's El
bow Room in Cliffside, New
Jersey.
In its final
report,
Kefauver's
committee
traced much
American
organized crime to the
age-old
Sicilian
criminal
brotherhood, the
Mafia.
However,
Kefauvcr
concluded that the most powerful crime
figure
in America
was
not
Italian.
He
was
Longy
Zwillman,
a
Jew.
The
Kefauvcr
hearings
were,
all
things
considered,
effective.
Through them
America
learned of the extent of organized crime
II


## Page 18

FORTUNE'S
FORMULA
and
was
galvanized
into
action.
Public
sentiment
turned
against
gambling.
The
Senate
hearings
were
credited
with
the
defeat
of
proposals
to
legalize
gambling
in
California,
Massachusetts,
Ari
zona,
and
Montana.
Kefauver
recommended
a ban on the
trans
mission
of interstate
gambling
results.
Congress
quickly
passed
the
legislation.
The surprising thing is that it
worked.
The
legal
pressure put
the mob's wire
service
out of
business.
Maybe
the
crackdown
worked because, at the dawn of the television
age,
the wire service
was
already
technologically
obsolescent.
After
fifty
years,
Payne's
profitableidea cameto an abrupt end.
This book is about a curious
legacy
of that long-ago wire
service.
Twelve
miles to the southwest of the West Orange, New
Jersey,
mansion that Zwillman bought with mob
money,
American Tele
phone and
Telegraph
built a
scientific
think tank with its own mo
nopolistic
riches.
In
1956
a youngscientist pondering his employer's
ambivalent
relationship
with
bookmaking
devised
the most
success-
fill
gambling
system
of
all
time.
12


## Page 20

Claude
Shannon
Life
is a
gamble.
There are
few
sure
things,
least
of
all
in the
competitive
world
of
academic
recruitment.
Claude
Shannon
was as
close
to a
sure
thing
as
existed.
That
is
why
the
Massachusetts
Insti
tute
of
Technology
was
prepared
to
do
what
was
necessary
to
lure
Shannon
away
from
AT&T's
Bell
Labs,
and
why
the
institute
was
delighted
when
Shannon
became
a
visiting
professor
in
1956.
Shannon
had
done
what
practically
no one
else
had
done
since
the
Renaissance.
He
had
single-handedly
invented
an
important
new
science.
Shannon's
information
theory
isan
abstract
science
of
communication
that
lies
behind
computers,
the Internet, and
all
digital
media.
"It's
said
that
it
is
one
of
the
few
times
in
history
where
somebody
founded
the
field,
asked
all
the
right
questions,
and proved most of them and answered them all at once," noted
Cornell's
Toby
Berger.
"The
moment
I
met
him,
Shannon
became
my
model
for
what
a
scientist
should
be,"
said
MIT's
Marvin
Minsk)'.
"Whatever
came
up,
he
engaged
it
with
joy,
and
attacked
it
with
some
surprising
re
source—which
might
be
some
new
kind
of
technical
concept—or
a
hammer
and
saw
with
some
scraps
of
wood."
There
were
many
at
Bell
Labs
and
MIT
who
compared
Shan
non's
insight
to
Einstein's.
Others
found
that
comparison
unfair—
unfair
to
Shannon.
Einstein's
work
had
had
virtually
no
effect
on the
life
of the
average
human
being.
The
consequences
of
Shannon's
work
were
already
being
felt
in
the
1950s.
In
our
digital
age,
people
15


## Page 21

FORTUNE
S
FORMULA
asked
to
characterize
Shannon's
achievement
arc apt to be at a
loss
for
words.
"It's
like
saying
how
much
influence
the
inventor
of the
alphabet
has
had
on
literature,"
protested
USC's
Solomon
W.
Golomb.
It
was
Shannon who had the idea that computers should com
pute
using
the
now-familiar
binary
digits,
o's
and
i's.
He
described
how
these
binary
numbers
could
be
represented
in
electric
circuits.
A
wire
with an
electrical
impulse
represents
I, and a wire without
an
impulse
represents
O.
This
minimal
code
may
convey
words,
pictures,
audio,
video,
or
any
other
information.
Shannon
may
be
counted
among
the
two
or
three
primary
inventors
of
the
electronic
digital
computer.
But
this
was
not
Shannon's
greatest
accomplish
ment.
Shannon's
supreme
opus,
information
theory,
turned
out to
be
one of
those
all-encompassing
ideas
that
sweep
up
everything
in
history's
path.
In the
1960s,
1970s,
and
1980s,
scarcely
a
year
went
by
without
a
digital
"trend"
that
made
Claude
Shannon
more
rele
vant than
ever.
The
transistor,
the
integrated
circuit,
mainframe
computers,
satellite
communications,
personal
computers,
fiber
optic
cable,
FIDTV,
mobile
phones,
virtual
reality,
DNA
sequenc
ing:
In
the
nuts-and-bolts
sense,
Shannon
had
little
or
nothing
to
do with these
inventions.
From a broader
perspective,
the whole
wired, and wireless, world was Shannon's
legacy.
It
was
this
expansive
view
that
was
adopted
by
the
army
of
jour
nalists
and
pundits
trying
to
make
sense
of the
digital
juggernaut.
Shannon's
reputation
burgeoned.
Largely
on
the
strength
of
his
groundbreaking
1948
paper
establishing
information
theory,
Shan
non
collected
honorary
degrees
for the rest of his
life.
He kept the
gowns
on a
revolving
dry
cleaner's
rack
he
built
in
his
house.
Shan
non
was
a
hero
to the
space
age
and to the
cyberpunk
age.
The
digital
revolution
made
Shannon's
once-arcane
bits
and
bytes
as
fa
miliar
to any
household
as
watts
and
calories.
But
ifa
journalist
or
visitor
asked
what
Shannon
had
been
up to
lately,
answers
were
often
elusive.
"He
wrote
beautiful
papers—when
he
wrote,"
explained
MIT's
Robert
Fano,
a
longtime
friend.
"And
he
gave
beautiful
talks—when
he
gave
a
talk.
But
he
hated
to
do
it."
16


## Page 22

Entropy
In
1958
Shannon
accepted
a
permanent
appointment
as
profes
sor
of
communication
sciences and
mathematics
at MIT.
Almost
from
his
arrival,
"Shannon
became
less
active
in
appearances
and
in
announcing
new results," recalled
MIT's
famed
economist
Paul
Samuelson.
In
fact
Shannon
taught
at MIT
for
only
a
few
semes
ters.
"Claude's
vision
of
teaching
was
to
give
a
series
of
talks
on
re
search
that no
one
else
knew
about,"
explained
MIT
information
theorist
Peter
Elias.
"But
that
pace
was
very
demanding;
in
effect,
he
wascoming up with a
research
paper
every
week."
So
after
a
few
semesters
Shannon
informed
the
university
that
he
didn't
want
to
teach
anymore.
MIT
had
no
problem
with
that.
The
university
is
oneof the
world's
great
research
institutions.
Shannon
wasn't
publishing
much
research,
though.
While
his
Bell
Labs
colleague
John
Nash
may
have
had
a
beautiful
mind,
Shannon
"had
a
very
peculiar
sort
of
mind,"
said
David
Slepian.
Shannon's
genius
was
like
Leonardo's,
skipping
restlessly
from
one
project
to
another,
leaving
few
finished.
Shannon
was
a
perfection
ist
who
did not
like
to
publish
unless
every
question
had
been
answeredand even the prose
was
flawless.
Before
he'd
moved
to
MIT,
Shannon
had
published
seventy-
eight
scientific
articles.
From
1958
through
1974,
he
published
only
nine
articles.
In the
following
decade,
before
Alzheimer's
disease
ended
his
career
all
too
decisively,
the
total
published
output
of
Claude
Shannon
consisted
of a
single
article.
It
was
on
juggling.
Shannon
also
worked
on an
article,
never
published,
on
Rubik's
cube.
The
open
secret
at MIT
was
that one of the
greatest
minds
of
the
twentieth
century
had
all
but
stopped
doing
research—to
play
with
toys.
"Some
wondered
whether
he
was
depressed,"
said
-Paul
Samuelson.
Others
saw
it
as
part of
an
almost
pathologically
self-
effacing
personality.
"One
unfamiliar
with
the
man
might
easily
assume
that
anyone
who
had
made
such
an
enormous
impact
must
have
been
a
pro
moter with a
supcrsalesman-like
personality,"
said
mathematician
Elwyn
Berlekamp.
"But such
was
not the
case."
Shannon
was
a
shy,
courteous
man,
seemingly
without
envy.
17


## Page 23

FORTUNE
S
FORMULA
spite,
or
ambition.
Just
about
everyone
who
knew
Shannon
at
all
liked him. He was
five
feet ten, of thinnish good looks and natty
dress.
In
late
middle
age
he
grew
a
neat
beard
that
made
him
look
even more
distinguished.
Shannon
enjoyed
Dixieland
music.
He
could
juggle
four
balls
at
once.
He
regretted
that
his
hands
were
slightly
smaller
than
average;
otherwise
he
might
have
managed
five.
Shannon
described
himself
as an
atheist
and
was
outwardly
apolitical.
The
only
evidence
of
political
sentiment
I
found
in
his
papers,
aside
from
the
fact
of
his
defense
work,
was
a
humorous
poem
he wrote on the
Watergate
scandal.
Shannon
spent
much
of
his
time
with
pencil
in
hand.
He
filled
sheets
of
paper
with
mathematical
equations,
circuit
diagrams,
drafts
of
speeches
he
would
give
or
papers
he
would
never
publish,
possible
rhymes
for
humorous
verse,
and
eccentric
memoranda
to
himself.
One
of
the
memos
is a list
of
"Sometime
Passions."
It in
cludes
chess,
unicycles,
juggling,
the
stock
market,
genealogy,
run
ning,
musical
instruments,
jazz,
and
"Descent
to
the
demi-monde."
The
latter
is
tantalizingly
unexplained.
In
one
interview,
Shannon
spoke
affectionately
of
seeing
the
dancers
in
the
burlesque
theater
as
a
young
man.
At
Bell
Labs
Shannon had been
famous
for riding a
unicycle
down the corridors.
Characteristically,
Claude was not
content
just
to
ride
the
unicycle.
Fie
had
to
master
it
with
the
cerebrum
as
well
as the
cerebellum,
to
devise
a theory of
unicycle
riding.
Fie
won
dered
how
small
a
unicycle
could
be
and
still
be
ridcablc.
To
find
out, he constructed a
succession
of ever-tinier
unicycles.
The
small
est
was
about
eighteen
inches
high.
No
one
could
ride
it.
Fie
built
another
unicycle
whose
wheel
was
purposely
unbalanced
to
provide
an
extra
challenge.
An
accomplishment
that
Shannon
spoke
of
with
satisfaction
was
riding
a
unicycle
down
the
halls
of
Bell
Labs
while
juggling.
Shannon
was
born in
Petoskcy,
Michigan,
on April 30,
1916.
He
grew
up
in
nearby
Gaylord,
then
a
town
of
barely
3,000
people
near
18


## Page 24

Entropy
the
upper
tip
of
Michigan's
mitten.
It
was
small
enough
that
walking
a
few
blocks
would
take
the
stroller
out
into
the
country.
Shannon's
father,
also
named
Claude
Elwood
Shannon,
had
been
a
traveling
salesman,
furniture
dealer,
and
undertaker
before
becoming
a
pro
bate
judge.
He
dabbled
in
real
estate,
building
the
"Shannon
Block"
of
office
buildings
on
Gaylord's
Main
Street.
In
1909
the elder
Shannon
married
the
town's
high
school
principal,
Mabel
Wolf.
Judge
Shannon
turned
fifty-four
the
year
his
son
was
born.
He
was
a
remote
father
who
dutifully
supplied
his
son
with
Erector
sets
and
radio
kits.
There
was
inventing
in the
family
blood.
Thomas
Edison
was
a
distant
relation.
Shannon's
grandfather
was
a
farmer-inventor
who
designed
an
automatic
washing
machine.
Claude
built
things
with
his
hands,
almost
compulsively,
from
youth
to
old
age.
One
project
was
a
telegraph
set to tapout
messages
to a
boyhood
friend.
The
friend's
house
was
halfa
mile
away.
Shannon
couldn't
afford
that lengthof
wire.
Then one
day
he
realized
that there were
fences
marking
the
property
lines.
The
fences
were
made
of barbed
wire.
Shannon
connected
telegraph
keys
to
each
end of the
wire
fence.
It
worked.
This
ability
to
see
clean
and
elegant
solutions
to
complex
problems
distinguished
Shannon
throughout
his
life.
Shannon
earned
money
as a
messenger
boy
for
Western
Union.
In
1936
he
completed
his
bachelor
of
science
at the
University
of
Michigan. He had little notion of what he wanted to do next. He
happened
to
see
a
postcard
on the
wall
saying
that the
Massachu
setts Institute of
Technology
needed someone to maintain its new
computer,
the
Differential
Analyzer.
Shannon
applied
for
the
job.
He met with the
machine's
designer,
Vannevar
Bush.
Bush
was
the head of MIT's
engineering
department,
a
bespectacled
vision
ary
rarely
seen
without
a
pipe.
Bush
advised
presidents
on the
glori
ous
future
of
technology.
One of
his
favorite
epigrams
was
"It is
earlier
than
we
think."
Bush's
Differential
Analyzer
was
the most
famous
computer of
its
time.
It
was
about
the
size
of a
two-car
garage.
Electrically
pow
ered,
it
was
fundamentally
mechanical,
a
maze
of
gears,
motors.
19


## Page 25

FORTUNE
S
FORMULA
drive
belts,
and
shafts.
The
positions
of
gears
and
shafts
represented
numbers.
Whenever
a
new
problem
was
to be
solved,
mechanical
linkages
had
to
be
disassembled
and
rebuilt
by
hand.
Gears
had
to
be
lubricated,
and their
ratios
adjusted
to
precise
values.
This
was
Shannon's
job.
It
was
several
days
of
grunt
work
to set
up
an
equa
tion and several more for the machine to solve it. When
finished,
the
machine
plotted
a
graph
by
dragging
a
pen
across
a
sheet
of
paper
fixed
to a
drafting
board.
Shannon understood that the Differential Analyzerwas two ma
chines
in one. It
was
a
mechanical
computer
regulated
byan
electri
cal
computer.
Thinking
about
the
machine
convinced
Shannon
that
electrical
circuits
could
compute
more
efficiently
than
mechanical
linkages.
Shannon
envisioned
an
ideal
computer
in
which
numbers
would
be
represented
by
states
of
electrical
circuits.
There
would
be
nothingto
lubricate
and a lot
less
to
break.
As
an
undergraduate.
Shannon
had
learned
Boolean
algebra,
an
unusual
subject
for
engineers.
Boolean
algebra
deals
in
simple
no
tionslikeTRUE or
FALSE
and
logical
relationships
such
as AND,
OR, NOT, and
IF.
Any
logical
relationship
may
be put
together
from a combination of these
elements.
Shannon posed himself the
problem
of
encoding
each
of
these
logical
ideas
in
an
electrical
cir
cuit.
To
his
delight,
he
succeeded.
In
effect,
he
proved
that an
elec
tronic
digital
computer
could
compute
anything.
Shannon
promptly
published
this
idea
in
1937
(he
would
not,
in
subsequent
years,
be
known
for
promptly
publishing
anything).
It
hasbeen
claimed
that this
was
the mostimportant
master's
thesis
of
all
time.
Vannevar
Bush
was
so
impressed
that he
insisted
that the
mathematics
department
accept
Shannon
for
his
doctoral
work.
The
result was too momentous to be "mere" electrical engineering.
Bush's
mercurial
colleague
Norbcrt Wiener
was
equally
im
pressed.
(When
Wiener
got
upset
with
someone,
which
was
often,
he sometimes wrote an
unflattering
caricature
of the person into a
private,
forever-unpublished
novel.
Bush
was
the
villain
of
one
of
these
novels.)
Wiener
realized
the
superiority
of
Shannon's
digital
computation
to
that
in
Bush's
analog
computer.
With
these
two
fa-
20


## Page 26

Entropy
mous
scientists
behind
him.
Shannon
was
a
budding
intellectual
celebrity
at
age
twenty-one.
"Apparently,
Shannon
is
a
genius,"
Bush
wrote
in
1939.
Yet
Bush
worried
about
Shannon.
Claude
is
"a
decidedly
unconventional
type
of
youngster."
Bush
warned
one
colleague.
"He
is
a
very
shy
and
re
tiring
sort
of
individual,
exceedingly
modest,
and
who
would
readily
be
thrown
off
the
track."
Bush
believed
Shannon
to
be
an
almost
universal
genius,
whose
talents
might
be
channeled
in
any
direction.
Bush
feared
that
Shan
non
was
unable
to
guide
his
own
career.
There
is
some
irony
in
that,
for
Bush,
the
grandson
of a
sea
captain,
was
loath
to
take
direction
from
anyone.
Bush
appointed
himself
Shannon's
mentor.
His
first
and
only-
major
career
decision
for
Shannon
was
a
bizarre
one.
He
suggested
that
Shannon
do
his
doctoral
dissertation
on
genetics.
That may not seem so odd
now,
with "DNA is information" be
inga
cliche.
No one
thought
in
those
terms
then.
DNA's
structure
was
a
mystery.
More
to
the
point,
Shannon
knew
nothing
about
ge
netics.
Shannon
did
a
little
reading.
Working
alone,
he
quickly
pro
duced
a
rough
draft
ofa
paper.
Without
Shannon's
knowledge.
Bush
passed
it
on
to
some
geneticists.
All
agreed
it
was
a
major
advance.
That
settled
the
matter.
Bush
arranged
a
summer
fellowship
for
Shannon
with
Barbara
Burks,
who
ran
the
Eugenics
Record
Office
at
Cold
Spring
Flarbor,
on
Long
Island.
This
was
one of the
last
outposts
of
the
dying
eugenics
movement.
The
significance
for
Shannon
was
that
it
had
some
of
the
most
extensive
records
any
where
on
inheritance.
For
years
the
eugenics
organization
had,
for
instance,
sent
researchers to circus sideshows to interview the dwarfs
and
sketch
pedigrees
on the
backs
of
performers'
business
cards.
The
Eugenics
Record
Office
had
records
purporting
to
describe
the
transmission
of
such
attributes
as
hair
color,
hemophilia,
feeble
mindedness,
and
love
of
the
sea.
21


## Page 27

fortune's
formula
While
at
Cold
Spring
Flarbor,
Shannon
recognized
a
mathemat
ical
connection
between
Mendelian
inheritance
and
Einstein's
rela
tivity^).
This
startling
insight
became
the
basis
of
his
dissertation,
titled
"Algebra
for
Theoretical
Genetics."
Nearly
everyone
who
read
the
dissertation
thought
it
brilliant.
Precious
few
people
did
read
it.
Upon
completion
of
his
Ph.D.,
Shannon
dropped
genetics
like
a
bad
habit.
His
results
were
never
published
ina
journal,
despite
his
and
Bush's
intentions
to do
so.
The
most
important
of
Shannon's
results
were
rediscovered
by
geneticists
five
to ten
years
later.
In October
1939
Shannon
met a
Radcliffe
coed,
Norma
Levor,
at an
MIT
party.
Levor
remembers
Shannon
as
"a
very
cute
guy"
standing
ina
doorway,
strangely
aloof.
She
got
his
attention
by
throwing
pop
cornat
him.
They
spoke
and
were
soon
dating.
Norma
was
nineteen
years
old
and
beautiful,
the
daughter
ofa
wealthy,
highly
assimilated
Jewish
family
in
New
York.
Radcliffe
girls
were
not
then
allowed
to
bring
boys
into
their
rooms.
Norma
and
Claude's
unlikely
trysting
spot
was
the
Differential
Analyzer
room.
On
January
10,
1940,
Claude
and Norma
were
married
bya
justice
of the
peace
in
Boston.
They
drove
to
New
Hampshire
for
a
honeymoon.
When
Shannon
went
to
register
at
the
hotel,
he
was
told:
"You
people
wouldn't
be
happy
here."
Claude
had
"Christ-like"
features,
recalled
Norma,
which
must
have
convinced
the
innkeeper
he
was
Jewish.
They
drove
elsewhere.
In
March,
Shannon
wrote
Bush
and
belatedly
informed
him
of
the
marriage.
He
said
they
had
moved
into
a
house
in
Cambridge,
and his life had been unsettled.The sameletter
describes
a new idea
Shannon
was
working
on:
a better
way
of
designing
lenses.
"Do
you
think it
would
be
worthwhile
to attempt to
work
this
out?"
Shannon
asked
Bush.
He
mentioned
that Thornton
Fry
of
Bell
Labs
had of
fered
him
a
job.
"I
am
not
at
all
sure
that
sort
of
work
would
appeal
to
me,"
Shannon wrote, "for there is bound to be some restraint in
an
industrial
organization
as
to
type
of
research
pursued."
AT&T
was
moving
most
of its
research
from
Manhattan
to an
expanded
suburban
outpost
in
Murray
Hill,
New
Jersey.
Shannon
22


## Page 28

Entropy
spent
the
summer
working
at
Bell
Labs'
Greenwich
Village
site.
Norma
remembers
this
as
the
happiest
part
of
their
brief
marriage.
Sheand
Claude
frequented
the
jazz
clubs.
Their next
move
was
to
the
Institute
for
Advanced
Study
at
Princeton.
This
was
the
home
of
Einstein,
Godcl,
and
von
Neumann.
Shannon
began
what
was
to
be
a
year
of
postdoctoral
work
under
mathematician
and
physicist
Hermann
Weyl.
He
worked
on
topology.
Nothing
came
of
it.
Shannon
left
abruptly
to
work
with
math
ematician
Warren
Weaver
of
the U.S.
Office
of
Scientific
Research
and
Development.
Shannon
helped
calculate
gunfire
trajectories
for
the
military.
Weaver
praised
his
work;
then
this
too
was
cut
short.
Shannon's
marriage
was
breaking
up.
Norma
saw
a
disturbing
change
in
Claude
when
they
moved
to
Princeton.
His
shyness
deepened
into
an
almost
pathological
reclu-
siveness.
The
institute's scholars are allowed to set their own hours
and to
work
where
they
like.
Shannon
chose
to
work
at
home.
"He
gotsohedidn't
want
to
see
anyone
anymore,"
said
Norma.
She
tried
to
convince
Claude
to
seek
psychiatric
help.
He
refused.
During
one
violent
argument,
Norma
ran
all
the
way
to
Princeton
Junction
and
took the train into Manhattan. She never returned to Claude or to
Princeton.
Claude was devastated. Weaver wrote Bush that "for a time it
looked
as
though
he
might
completely
crack
up
nervously
and
emo
tionally."
In
the
midst
of
Shannon's
personal
crisis,
Thornton
Fry
renewed
his
offer
of a
job
at
Bell
Labs.
This
time
Shannon
accepted.
And
once
again,
Shannon
turned
his
polymorphic
genius
to
something
completely different.
23


## Page 29

FORTUNE
S
FORMULA
*
Project
X
It
WAS
CALLED
PROJECT
X.
Declassified
only in 1976, it was a
joint
effort
of
Bell
Labs
and
Britain's
Government
Code
and
Ci
pher
School
at
Bletchley
Park,
north
of
London.
It
had
a
scientific
pedigree
rivaling
that
of
the
Manhattan
Project,
for
the
British-
American
team
included
not
only
Shannon
but
also
Alan
Turing.
They
were
building
a
system
known
as
SIGSALY.
That
was
not
an
acronym,
just
a
random
string
of
letters
to
confuse
the
Germans,
should they learn of it.
SIGSALY
was
the
first
digitally
scrambled,
wireless
phone.
Each
SIGSALY
terminal
was
a
room-sized,
55-toncomputer with an iso
lation
booth
for the user and an
air-conditioning
system to
prevent
its
banks
of
vacuum
tubes
from
melting
down.
It
was
a
way
for Al
lied
leaders
to
talk
openly,
confident
that the
enemy
could
not
eavesdrop.
The
Allies
built
one
SIGSALY
at
the
Pentagon
for
Roo
sevelt and another in the basement of
Selfridges
department store
for
Churchill.
Others
were
established
for Field Marshal
Mont
gomery
in
North
Africa
and
General
MacArthur
in
Guam.
SIGSALY
used
the
only
cryptographic
system
that is
known
to
be
uncrackable,
the
"onetime
pad."
In a
onetime
pad,
the
"key"
used
for
scrambling
and
decoding
a
message
is
random.
Traditionally,
this
key
consisted
ofa
block
of
random
letters
or
numbers
ona
pad
of
paper.
The
encoded
message
therefore
is
random
and
contains
none
of the
telltale
patterns
by
which
cryptograms
can
be
deciphered.
The
problem
with
the
onetime
pad
is
that
the
key
must
be
delivered
by
courier
to
everyone
using
the
system,
a
challenge
in
wartime.
24


## Page 30

Entropy
SIGSALY
encoded
voice
rather
than
a
written
message.
Its
key
was
a
vinyl
LP
record
of
random
"white
noise."
"Adding"
this
noise
to
Roosevelt's
voice
produced
an
indecipherable
hiss.
The
only
way
to
recover
Roosevelt's
words
was
to
"subtract"
the
same
key
noise
from
an
identical
vinyl
record.
After
pressing
the
exact
number
of
key
records
needed,
the
master
was
destroyed
and
the
LPs
distrib
uted
by
trusted
couriers
to
the
SIGSALY
terminals.
It
was
vitally
important
that
the
SIGSALY
phonographs
play
at
precisely
the
same
speed
and
in
sync.
Were
one
phonograph
slightly
off,
theout
put
was
abruptly
replaced
by
noise.
Alan
Turing
cracked
the
German
"Enigma"
cipher,
allowing
the
Allies
to
eavesdrop
on
the
German
command's
messages.
The
point
of
SIGSALY was to ensure that the Germans couldn't do the same.
Part
of
Shannon's
job
was
to
prove
that the
system
was
indeed
im
possible
for
anyone
lacking
a
key
to
crack.
Without
that
mathemat
ical
assurance,
the
Allied
commanders
could
not
have
spoken
freely.
SIGSALY
put
several
otherof
Shannon's
ideas
into
practice
for the
first
time,
among
them
some
relating
to
pulse
code
modulation.
AT&T
patented and
commercialized
many
of
Shannon's
ideas
in
the postwar
years.
Shannon
later
said
that
thinking
about
how
to
conceal
messages
with
random
noise
motivated
some
of
the
insights
of
information
theory.
"A
secrecy
system
is
almost
identical
with
a
noisy
communi
cations
system,"
he
claimed.
The
two
lines
of
inquiry
"were
so
close
together you couldn't separate
them."
In
1943
Alan
Turing
visited
Bell
Labs'
New
York
offices.
Turing
and
Shannon
spoke
daily
in the lab
cafeteria.
Shannon
informed
Turing
that he
was
working
on
a'way
of
measuring
information.
He
used a
unit
called the
bit.
Shannon
credited
that
name to
another
Bell
Labs
mathematician,
John
Tukey.
Tukey's
bit
was
short
for
"binary
digit."
Shannon
puta
subtly
dif
ferent spin on the
idea.
The bit, as Shannon defined it, was the
amount
of
information
needed
to
distinguish
between
two
equally
likelyoutcomes.
25


## Page 31

FORTUNE'S
FORMULA
Turing
told
Shannon
that
he
had
come
up
with
an
idea
for
aunit
called the
ban.
This
was the
amount
of
evidence
that
made a guess
ten
times
more
likely
to be
true.
The
British
cryptographers
used
that
term,
half
seriously,
in
decrypting
Enigma
ciphers.
The
"ban"
part
came
from
Banbury,
the
town
where
the
cryptographic
team's
scratch
paper
was
manufactured.
It
was
the bit, not the
ban,
that
changed
the
world.
The
defining
year
for
that
change
was
1948.
Shannon
remained
with
Bell
Labs
after
the
war.
One
day
he
spotted
a
strange
object
on
the
desk
of
another
researcher
and
asked
what
it was.
"It's
a
solid-state
amplifier,"
William
Shocklcy
told
him.
It
was
the
first
transistor.
Shockley
told
Shannon
that the
amplifier
could
do
anything
a
vacuum
tube
could.
It was small. Shannon learned that the new device worked by
having
different
materials
in
contact
with
each
other.
It
could
be
made
as
small
as
desired
as
long
as
the
different
materials
touched.
The transistor was the hardware that would make so many appli
cations
of
Shannon's
theory
a
reality.
This
incident
would
have
been
in late
1947
or
early
1948,
before
Bell
Labs
unveiled
the
transistor
on
June
30—and
just
about
the
time
Shannon's
classic
paper
on in
formation theory
appeared.
There is minor
scandal
associated
with that
paper.
Shannon
pub
lished
"A
Mathematical
Theory of
Communication"
in a 1948 issue
of
the
Bell
System
Technical
Journal.
He
was
then
thirty-two
years
old.
Most of the work had been done
years
earlier,
from
about
1939
to
1943.
Shannon
told
few
people
what
he
was
doing.
He
habitually
worked
with
his
office
door
closed.
As
Bell
Labs
people
gradually
learned
of
this
work,
they
were
as
tonished that Shannon had
devised
such an important result and
then
sat on it. In what
amounted
to a scientific
intervention,
friends
goaded
Shannon
to
publish
the
theory.
Shannon
recalled
the
process
of
writing
the
1948
paper
as
painful.
He
insisted
that
he
had
devel
oped
the
theory
outof
pure
curiosity,
rather
than
a
desire
to
advance
technology or his career.
26


## Page 32

Entropy
The
year
1948
was
also
a
turning
point
in
Shannon's
personal
life.
Shannon
would
often go into the
office
of
John
Pierce
to
chat.
Pierce was working on radar and was known as an avid science
fiction
fan.
Through these
visits.
Shannon
met
Pierce's
assistant,
Maty
Elizabeth
Moore.
"Betty"
Moore
had
been
in
the
math
group's
computing
pool,
performing
calculations
on
old-fashioned
desk
top
calculating
machines.
Moore
was
bright
and
had
a
Rosie-the-
Riveter
knack
for
making
things.
She
was
able
to
work
a
drill
press
and
lathe
in the
lab's
machine
shop.
She
was
attractive
and
one of
only
three
female
employees
there.
("One
was
married,
and
the
other
was
in her
fifties,"
Betty
recalls.)
She
and
Claude
had
their
first
date
in
December
1948.
On
March
27
the
following
year
they
married.
Shannon
began
teaching
at MIT
in
the
spring
1956
semester.
This
started
as
a
temporary
assignment,
and
at
least
one
friend
at
Bell
Labs
(John
Riordan)
understood
the
teaching
as
having
an
ul
terior
motive.
It
was
supposedto
allow
Shannon the free time to be
gin
writing
a
long-anticipated
book
on
information
theory.
"I am
having
a
very
enjoyable
time here at
M.I.T.,"
Shannon
wrote
his
Bell
Labs
boss,
Hendrik
Bode.
"The
seminar
is
going
very
well
but
involves
a
good
deal
of
work.
I
had
at
first
hoped
to
have
a
rather
cozy
little
group
of
about
eight
or ten
advanced
students,
but
the
first
day,
forty
people
showed
up,
including
faculty
members
from M.I.T.,
some
from
Harvard
..."
After
just
a
few
months
at
MIT
Shannon
wrote
Bode
to
resign
from
his
post
at
Bell
Labs.
He
was
taking
a
professorship
at
MIT.
He
found
that he and
Betty
liked
the
intellectual
and
cultural
lifeof
Cambridge,
so
worldly
next
to
the
New
Jersey
suburbs.
"Foreign
visitors
often
spend
a
day
at
Bell
Laboratories
but
spend
six
months
at
M.I.T.,"
Shannon
explained
to
Bode.
"This
gives
opportunities
for
real
interchange
of
ideas.
When
all
the
advantages
and
disadvan
tages are added up, it seems to me that
Bell
Labs and academic life
are
roughly
on a
par,
but
having
spent
fifteen
years
at
Bell
Labs
I
felt
myself
getting
a
little
stale
and
unproductive
and
a
change
of
scene
and of
colleagues
is
very
stimulating."
Shannon
had
approached
MIT
about
a
permanent
job,
not the
27


## Page 33

FORTUNE'S
FORMULA
other
way
around.
Money
was
not
the
issue.
Bell
Labs
offered
a
"flattering"
raise.
Shannon
turned
it
down
(he
retained
an
affiliation
with
Bell
Labs
through
1972).
His
initial
salary
at MIT
was
$17,000
a
year.
Shannon
enjoyed
the
stimulation
of MIT in
limited
doses.
Fie
did
his
best
work
alone.
He
had
perhaps
underestimated
the
volume
of
distraction
confronting
a
living
legend
at a
large
urban
university.
Shannon
"started
disappearing
from
the
scene,"
recalled
Robert
Fano.
"He kind of faded
away,
Claude."
Shannon
took
few
Ph.D.
students.
They often had to meet him
at
his
home
in
order
to get
advice.
One
student,
William
Suther
land,
remembers
walking
inon
Shannon's
oboe
practice
more
than
once.
"He
slept
when
he
felt
like
sleeping,"
said
Betty,
and
would
spend
hours
at the
kitchen
table
thinking.
Shannon's
careeras
publishing
scientist
was
just about
over.
He
never
completed
the
book
he
spoke
of.
Shannon's
papers
at
the
Li
brary
of
Congress
include
nothing
more
than
a
few
handwritten
notes that
may
have
related
to this
project.
Artificial
intelligence
pioneer
Marvin
Minsk)'
speculated
that
Shannon
stopped
working
on
information
because
he
felt
he
had
proven
almost
everything
worth
proving.
The
self-contained
per
fection
of
Shannon's
early
work
was
unsurpassable.
Fano
mentioned
an
uncanny
phenomenon.
With
rare
exceptions,
it
seemed
that
whenever
an information theorist mentioned a current problem to
Shannon,
(a)
Shannon
was
aware
of
the
problem,
and
(b)
Shannon
had
already
solved
it,but
hadn't
gotten
around
to
publishing
it.
"I
just
developed
different
interests,"
Shannon
said
of
his
near-
abandonment of the
field
he
created.
"As
life goes on, you change
your direction."
One of these interests
was
artificial
intelligence.
Shannon orga
nized
the
first
major
academic
conference
on the
subject,
held
at
Dartmouth in
1956.
Shannon's
stature
contributed
to
making
the
field
respectable.
Some
of
the
devices
Shannon
built,
including
an
early
chess-playing
computer
and
the
so-called
outguessing
ma-
28


## Page 34

Entropy
chine,
figure
prominently
in
the
early
history
of
machine
learning.
Shannon
was
an
articulate
advocate,
visionary
enough
to
see
what
fantastic
things
were
possible
and
practical
enough
to
appreciate
that they
were
not
going
to
happen
in
his
lifetime.
He had a talent
for
parrying
the
inevitable
ham-handed
questions.
Q_Will
robots
be
complex
enough
to
be
friends
of
people,
do
you think?
A.
I
think
so.
But
it's
quite
a
distance
away.
G\_Can
you
imagine
a robot
President
of the United
States?
A.
Could
be.
1
think
by
then
you
wouldn't
speak
of the
United
States
any
more.
It
would
bea
totally
different
organization.
Letters,
papers,
and
phone
calls,
many
from
world-renowned
scientists,
poured
into
Shannon's
office.
They
wanted
Shannon
to
review
a
paper
or
contribute
one;
give
a
talk,
an
opinion,
a
recom
mendation.
Shannon
turned
down
an
increasing
share
of
these
re
quests.
As
Shannon's
name
became
known
to a
broad
public,
he
began
receiving
letters
from
schoolchildren
building
science
proj
ects
and
crackpots
building
paranoid
complexes
about
scientists,
computers,
or the
phone
company
("Dear
Sir,"
begins
one
letter,
"Your
mechanical
robot
Bel,
the
idol
[Daniel
14]
in the
Bible,
is
a
mechanical
monstrosity...
You
are
making
a
traitor
outofthe
Pres
ident
of
the
U.S.
and
the
F.B.I,
by
letting
your
robot
deceive
you.
I
have
threatened
to
sue
the
N.Y.
Telephone
Co.
of
N.Y.
City,
and
I
will,
if
you
don't
wake
up").
From
time
to
time
the
CIA
and
other
agencies
turned
to
Shan
non
when
challenging
cryptographic
problems
arose,
only
to
be
informed
politely
of
Shannon's
retirement.
"We
really
are
not
ap
proaching
you
accidentally,"
read
a
1983
letter
from
the
CIA's
Philip
H.
McCallum.
"We
need
an
excellent
original
thinker,
and
at the
risk
of
kowtowing,
find
that
you
are
still
the bestforwhat
we
have
in
mind
.. .
Although
we
understand
that
you
do
not
need
the
money
we would still payyou a
fee."
Shannon
did
not
like
to
answer
a
letter
until
he
had
composed
the
perfect
reply.
Since
it
took
a
while
to
create
a
perfect
reply,
29


## Page 35

FORTUNE'S
FORMULA
Shannon
dealt
with
correspondence
by
shuffling
it
from
folder
to
folder.
On
these folders he would write labels like
"Letters
I've pro
crastinated
on
answering
for
too
long."
These
letters
are
now
neatly
boxed
with
Shannon's
papers
at
the
Library
of
Congress,
many
still
awaiting
answers.
Shannon
was
yet
in
his
forties
when
he
took
what
amounted
to
an
early,
unofficial
retirement.
Thereafter
Shannon
was
MIT's
Bartlcby,
whose
characteristic
reply
was
"I
would
prefer
not
to"—
clerk
of
his
own
private
dead-letter
office.
Emmanuel
Kimmel
Emmanuel
Kimmel
inhabited
a
different
America
from
that of
Claude
Shannon.
Kimmel
must
have
been born around
1898—even
his
son
isn't
sure
of
the
exact
year.
One
unconfirmable
story
has
it
that
the
young
"Manny"
Kimmel
was
kidnapped
on
board
a
ship
and
never
saw
his
parents
again.
Fie
jumped
ship
in
the
Orient and
found
workon a cattle
boat,
shoveling
steaming
piles
of
manure
into
the
tropic
sea.
Somehow
Kimmel
made
his
way
back
to
the
States.
He
spent
his
late
youth
on
Prince
Street
in
the
Jewish
section of Newark. There he befriended "Der
Langer."
Der
Langer
("the
Tall
One")
stood
about
six
feet
two.
He
tow
ered
like
a
god
over
Kimmel
and
most
of
the
Eastern
European
immigrants.
The
community
regarded
him
almost
as
a
god.
Occa
sionally
bands
of
Irish
kids
would
harass
the
merchants
on
Prince
Street,
upsetting
pushcarts
and
swiping
yarmulkes
as
trophies.
30


## Page 36

Entropy
When
that
happened,
people
would
call
for
Der
Langer.
Der
Langer
and
his
gang
would
appear
on
the
scene
within
minutes
and
beat
up
the
Irish
kids.
As Der Langer matured, he moved in broader circles of business
where
people
did not
always
speak
good
Yiddish.
He
shortened
his
boyhood
nickname
to
"Longy"—Abner
"Longy"
Zwillman.
From what he saw of America, Zwillman concluded that there
were
two
ways
to
make
real
money.
One
was
politics,
and the other
was
gambling.
Zwillman
decided
to
go
into
gambling.
Manny
Kim
mel
followed
him.
Their
business
was
the
numbers
or
policy
racket,
a
form
of
illegal
gambling that flourished before state lotteries existed. Customers
bet
pocket
change
on a
three-digit
number.
Each
day,
one
of
the
1,000
possible
three-digit
numbers
came
up.
A
lucky
bettor
who
picked
correctly
got
back
600
times
his
or
her
wager.
Zwillman
and
company's
cut
was
S400
outof
every
Si.ooo
wagered.
At
that
time,
the
daily
number
was
chosen
by
the
number
op
eration
itself—more
or
less
randomly
An
associate
of
Zwillman's
named
"Doc"
Stacher
observed
that the
less
random
the
numbers,
the
more
profit
the
operation
might
make.
In
1919,
on
Stachcr's
suggestion,
Zwillman
instituted
a
new
procedure.
After
gathering
all
the
day's
bets, his crew
would
determine
which
number had the
least
money
riding
on
it.
That
became
the
winning
number.
On
those
terms,
turning
a
profit
was
easy.
The
hard
part
was
dealing with
rival
mobs
and the
law.
Zwillman
was considered a
master
at
both.
A
minor
thug
named
Leo
Kaplus
began
roughing
up
Zwillman's
numbers
runners.
He
was
given
a
warning.
Kaplus
re
sponded
that he'd kick Zwillman in the balls to teach him a lesson.
Zwillman
insisted
on
handling
the
insult
personally.
He
tracked
Kaplus to a Newark bar and shot him once in the testicles.
Kaplus
was
rushed
to the
emergency
room
at
Beth
Israel
Hos
pital. A surgeon
removed
the
bullet.
Then one of
Zwillman's
men
showed up and demanded the bullet for
evidence.
The doctor
handed
it
over.
The
gangster
did
need
the
bullet
for
evidence,
as it
was
the
only
thing
connecting
Zwillman
to
the
shooting.
31


## Page 37

'
FORTUNE'S
FORMULA
In
1920
the
U.S.
Congress
handed
Zwillman
and
Kimmel
a
big
ger
moneymaker
than
the
numbers
racket.
It
was
the
Volstead
Act,
prohibiting
the
sale
of
alcohol.
Zwillman
turned
bootlegger,
and
Kimmel,
who
owned
garages
in
Newark,
leased
them
to
Zwillman
for
storing
the
contraband.
It
was
estimated
that
Zwillman's
crew
imported
40
percent
of
all
the
liquor
brought
into
the
United
States
from
Canada
during
Prohibition.
Zwillman
made
at
least
S20
mil
lion
off
this trade in the next decade. He did not pay taxes.
This
bootlegging
wealth
earned
Zwillman
the tag
"the
New
Jer
sey
Al
Capone."
That
must
have
rankled.
Brutal
as
he
was,
there
was
a side to
Zwillman
lacking
in
Capone.
Zwillman
was
a
connoisseur
of
art,
books,
and
opera.
He
dressed
soberly
and
made
a
point
of
driving
American-built
Chryslers
and
Buicks,
not
the
latest
models.
Readers
of
gossip
columns
knew
Zwillman
as
the
sugar
daddy
of
actress
Jean
Harlow.
It
was
Zwillman
who
lentor
bribed
Columbia
Pictures'
Harry
Cohn
a
reported
S500,ooo
to
secure
a
two-picture
deal for the then-unknown
Harlow.
Harlow went on to playa gang
ster's
moll
in
Public
Enemy
(1931).
Zwillman
adored
the
platinum
blonde for the rest of her short
life.
He grieved as Jeanette Mac-
Donald
and
Nelson
Eddy
sang
"Oh,
Sweet
Mystery
of
Life"
at her
funeral.
Manny
Kimmel
shared
some
of
Zwillman's
business
sense.
He
saw
that
cars
were
becoming
popular
with
the
middle
and
working
classes.
In
Newark,
these
people
lived
in
apartments
or
row
houses
with
neither
garage
nor
space
for
adding
one.
Kimmel
therefore
in
vested
in
garages
and
parking
lots.
The
story
goes
that
Kimmel
was
once
in
a
high-stakes
game
of
craps.
His
opponent
ran
out
of
money
and
put
up
a
parking
lot
he
owned
as
collateral.
He must not
have
made
his
point.
Kimmel
ended
up
owning
the
parking
lot,
on
Kinney
Street
in
Newark.
Over
time,
Kimmel
acquired
other
parking
lots,
finding
them
a
perfect
front for gambling operations.
Gambling
was
Kimmel's
vocation
and
avocation.
He
moved
into
bookmaking.
a
cash
business
requiring
careful
money
management.
32


## Page 38

Entropy
Kimmel
sometimes
mortgaged
the
parking
lots
when
he
needed
quick
money
to
pay
off
bets.
He
was
famous
as
a
proposition
man.
He
would
bet
on
anything,
at
any
time,
as
long
as
the
odds
were
to
his
liking.
Kimmel
taught
himself
calculus,
trigonometry
and
proba
bility
theory,
or said he had. Within his brain
was
a combination of
street
smarts
and
autodidact
book
learning
that
could
swiftly
ana
lyze
propositions.
He
memorized
sucker bets. One of his
favorites
was
betting
that
two
people
ina
group
would
have
the
same
birth
day.
Kimmel's
victims
would
take
even
money.
Kimmel
knew
he
had
an
edge
whenever
there
were
more
than
twenty-two
people.
Kimmel's
edge
was
not
always
strictly
mathematical
and not al
ways
strictly
ethical.
He
would
place
two
sugar
cubes
on a
lunch
counter and bet on
which
a
buzzing
fly
would
land on
first.
The
trick
was
to
doctor
one
cube
with
a
drop
of DDT
and
bet on the
other
cube.
Italian
mobsters
had
long
operated
illegal
gambling
houses
in
Manhattan
and
Brooklyn.
They
paid
off
New
York
cops
as
a
busi
ness
expense.
In the
late
1920s,
New
York
City
cracked
down
on
gambling.
It
became
clear
that
bribery
would
no
longer
work.
The
Italians
contemplated
moving
the
casinos
across
the
Hudson
to
New
Jersey.
New Jersey gangster Willie Moretti recommended that the Ital
ians
go into
business
with
Longy
Zwillman.
Moretti
knew
that
Zwillman's
control
of
New
Jersey
politicians
would
be
invaluable.
Moretti
brokered
a
meeting
between
Zwillman
and
a
group
thatin
cluded
Lucky
Luciano
and
Joe
Adonis.
They
agreed
to
become
part
ners in a string of New
Jersey
casinos.
The
plan
required
a
way
of
getting
customers
from
New
York
to
the
casinos
and
back.
For that,
Joe
Adonis
ran a
limousine
service.
The
New
York
terminus
was
a
place
where
people
could
come
and
go
at
all
hours
without
being
noticed:
Manny
Kimmel's
parking
lot
at
Broadway
and
Fifty-first
Street.
Zwillman foresaw that
Prohibition
wouldn't
last. He believed
that
businessmen
such
as
himself
ought
to
plan
for
a
future
beyond
boot-
33


## Page 39

FORTUNES
FORMULA
legging.
Fie
spoke
of
creating
a
trade
organization
along
the
lines
of
the National Association of
Manufacturers.
They would split the
territory,
stop
fighting
among
themselves,
and
plan
their
next
move.
To
this
end,
Zwillman
organized
a
national
convention
of
crime
in
Atlantic
City.
It
began
on
May
14,
1929.
It
was
supposed
to
take
place
at
the
Breakers,
a
hotel
known
for
renting
only
to
WASPs.
Reservations were made under suitable
pseudonyms.
Every
major
crime
figure
from
Al
Capone
to
Dutch
Schultz
showed
up.
When
the
Breakers
staff
recognized
the
notorious
men
checking
in,
they
announced
that
all the hotel's rooms were taken.
The
mobsters
rented a caravan of limousines and went to the nearby Ritz.
This
meeting
marked
the start of the
Combination—or
as
the
press
sometimes
called
it,
"Murder,
Inc."
The
Combination
pat
terned
itselfafteran
American
corporation,
down
to
having
a
board
of
directors.
The
most
powerful
figures
were
the
"Big
Six"—Zwill
man
in
New
Jersey,
Lucky
Luciano,
Meyer
Lansky,
Frank
Costello,
and
Joe
Adonis
in
New
York,
and
Ben
Siegel
on the
West
Coast.
Zwillman's
message
at the Atlantic City convention
was
to
go
legitimate.
Organized
crime
needed
to
diversify
to
invest
its
profits
in
legitimate
businesses.
It
would
be
a
way
of
hedging
their
bets
against
the end
of
Prohibition. It would also make mobsters less vulnerable
to
prosecution.
They
would
have
some
legitimate
income
to
report
on
their
taxes.
The
flow
of
mob
money
into
small
legal
businesses
was
already
happening.
In
1930
investigators
reported
that
racketeers
had
taken
over
fifty
industries
and
commodities
in
New
York
City.
They
in
cluded furriers, laundries, kosher
chickens,
tailors, construction, fu
neral
parlors,
parking
lots,
miniature
golf
courses,
artichokes,
and
grapes.
Once
the
racketeers
controlled
a
particular
industry,
they
could
raise
prices.
It
was
capitalism
without
competition.
Zwillman himself came to own or control two steel companies, a
couple
of
small
motion
picture
production
companies,
the
GMC
truck
dealership
for
Newark,
the
Hudson
&
Manhattan
Railroad
(this
would
later
be
bought
by
the
Port
Authority
and
renamed
PATFI),
and
companies
involved
in
cigarette
vending
machines,
jukeboxes,
and
apartment
laundry
machines.
Zwillman
was
a
major
34


## Page 40

Entropy
investor
in
Ben
Siegel's
Flamingo
and
other
Las
Vegas
casinos;
also
in
Manhattan's
Sherry
Netherlands
hotel
and
in
sumptuous
illegal
casinos
in
places
like
Miami
Beach
and
Saratoga.
Fie
had
slot
ma
chines
hidden
in
back
rooms.
These
were
popular
with
children,
and
Zwillman's
mob
made
sure
the
youngsters
had
little
stools
to
help
them
reach the
handles.
Zwillman
was said to have an
interest
in
Moe
Annenberg's
General
News
Bureau.
Possibly
Zwillman's
most
peculiar
investment
was
another
type
of
wire
service
entirely.
It
was
a
company
that ran
wires
to
wealthy
subscribers'
homes.
The
wires
carried
opera
and
other
soothing
music.
The
firm
prospered
only
when
it
offered
its
service
for
stores,
offices,
and
elevators.
In
1954
the
Chicago
Crime
Commission
concluded
that
the
Muzak
Corpo
ration
was
controlled
by
the
notorious
Longy
Zwillman.
Zwillman
said he
was
merely
a
stockholder.
During
Prohibition,
someone
hijacked
a
shipment
of
Flaig
&
Haig
scotch
whiskey
outside
Brockton,
Massachusetts.
The scotch be
longed
to
Joseph
Kennedy.
Kennedy
had
made
his
first
fortune
through
insider
trading
and
his
second
through
bootlegging.
Ken
nedy
believed
there
was
only
one
person
capable
of the
heist—his
archrival,
Longy
Zwillman.
Kennedy
"said
he'd
get
Longy
if it
was
the
last
thing
he
did,"
ac
cording
to
one
of
Zwillman's
partners.
To
his
dying
day,
Zwillman
swore
he
knew
nothing
about
the
missing
scotch.
With the
logic
of a
narcissist,
Zwillman
blamed much of his sub
sequent
troubles
with
the
U.S.
government
on
this
old
grudge.
Kennedy
pushed
his
sons
into
political
careers.
One of them,
Robert,
was
a
minor
Senate
aide
assisting
in the
Kefauver
hearings.
Zwillman
told
friends
that
Bobby
Kennedy
was
settling
a
score
for
the
old
man.
The
Senate
hearings
were
only
the
beginning.
The
post-
Kefauver
wave
of
enforcement
put the
squeeze
on
Zwillman's
num
bers
racket,
floating
card
games,
casinos,
and slot
machines.
On
June 10, 1952, the IRS
sent
letters to Zwillman, Costello, Adonis,
and
the
late
Willie
Moretti.
The
agency
was
investigating
their in-
35


## Page 41

FORTUNES
FORMULA
come
taxes.
Zwillman
had been smart enough to report a share of
his more
legitimate
income.
Even
so,
U.S.
Attorney
Grovcr
Richman
filed
nearly
a
million
dollars'
worth of tax
liens
against
Zwillman
and
family.
Richman
was
trying
to
freeze
Zwillman's
assets,
and thus
put
him
out of
business,
while
the
IRS
built
its
case
against
him.
Zwillman's
attorneys
complained
that the
government
was
punish
ing their client before a
trial.
In 1954 Joe Adonis went on trial for racketeering. Adonis was
not his
original
name.
He felthe
was
too
good-looking
for the com
monplace
name
(Joseph
Doto)
he
had
been
born
with.
After the
verdict, Adonis decided he was too good-looking for prison. He
chose
to be deported to
Italy.
That left the
Zwillman
mob with one
less
powerful
ally
in New
York.
A
few
years
later,
they lost
Frank
Costello.
This
came
about
partly
as
a
consequence
of an
old
insult.
At
one
meeting
of the
Combination, Costcllo ran over a list of criminals to be brought
into the
organization.
Most
of the
names
were
Jewish.
Vito
Gen
ovese
complained
that
Costello
was
trying
to bring in a
bunch
of
"hcbes."
This was within earshot of Zwillman and Meyer
Lansky.
Gen
ovese
was
Luciano's
employee;
it
was
his
place
to
silence
him. In
stead Costello spoke
up.
"Take
it
easy,
Don
Vitone,"
he reportedly
said,
"you're
nothing but a
fucking
foreigner
yourself."
He meant
that
Genovese
was
from
Naples,
not
Sicily.
"Don
Vitone"
was
also
an insult. Genovese was
not
a don; he was just there to carry Lu
ciano's
coat.
Genovese never forgot the incident. In
1957
Genovese put out a
contract on Costcllo's
life.
On
May
2 an obese gunman extracted
himself from a
double-parked
Cadillac
and
ambushed
Costello in
the
foyer
of his apartment
building,
the
Majestic
at
Seventy-second
Street and Central Park West. "This is for you,
Frank!"
the hitman
said as he pulled the trigger.
Costello took the bullet,
nonfatally.
He also took the hint. He
opted for
early
retirement.
This
consolidated
the
power
of
Vito
Genovese,
who
did
not
like Jews.
After the Central
Park
West
shooting,
doctors at
Roosevelt
Hos-
36


## Page 42

Entropy
pital
dressed
Costcllo's
superficial
head
wound
as
police
rummaged
through
his
personal
effects.
In
one
pocket
of
Costcllo's
suit
they
found
a
handwritten
note
giving
"gross
casino
wins
as of
4/27/57"
for the
Tropicana
Flotel,
Las
Vegas.
That
hotel's
gambling
license
had been
issued
to
supposedly
legitimate
businessmen
with no ties
to
organized
crime.
Costello
told
police
he
had
no
idea
how
the
note had ended up in his pocket.
Zwillman
came to trial on tax
charges
in
1956.
IRS agents had
made
a
painstaking
analysis
of
Zwillman's
expenditures.
They
were
able
to
show
that he spent far morethan the
income
he
reported.
Zwillman's
attorney
advanced
the theorythat his client
was
sup
plementing
his
lifestyle
by
dipping
into
a
cash
hoard
of
bootlegging
profits.
This
cash
was
now
beyond
the statuteof
limitations.
The
jury
deadlocked,
and
Zwillman
was
a
free
man.
But
in
Janu
ary
1959
an
FBI
bug
revealed
that
Zwillman
had
bribed
two
of
the
jurors.
Agents
arrested
the
two
henchmen
directly
responsible,
and
J.
Edgar
Floovcr
himself
announced
the
news.
It
was
plain
that
pros
ecutors would be
revisiting
the
Zwillman
tax
case.
Sometime after 2
a.m.
on the morning of
February
26,
1959.
Zwillman
left his wife in bed
and
descended
to the
basement
of
his
twenty-room
home
at 50
Beverly
Road,
West
Orange,
New
Jersey.
He
hung
himself
with
a
plastic
electrical
cord.
Police
found
twenty-
one
tablets
of a
tranquilizer
in
his
dressing
gown
and a
half-empty
bottle of
Kentucky
bourbon
on a
nearby
table.
Inevitably,
it
was
theorized
that
someone
else
killed
Zwillman
and
made
it
look
like
suicide.
Arguing
against
this
arc
friends'
state
ments that
Zwillman
had been
depressed
in the
days
leading
up to
his
death.
The
peculiar
accommodation
that
Zwillman
had
come
to
with American
society'
was crumbling.
Zwillman's
death left
Manny
Kimmel
holding
a
portfolio
of
businesses,
some
legitimate
and
some
not,
some
owned
by
Kimmel
and
others
apparently
in
partnership
with
Zwillman's
estate
and/or
still
other
murky
entities.
Kimmel
had
an
idea
for
parlaying
this
wealth.
It
was
going
to be
the
biggest
gamble
of
his
life.
It
involved
the
stock
market.
37


## Page 43

FORTUNE
S
FORMULA
Edward
Thorp
One
friend
described
Edward
Oakley Thorp as "the most
precise man I have ever met." This zeal for
measurement
was evi
dent
from
earliest
youth.
It hasbeen
claimed
that
mathematical
tal
ent
is,
ironically,
linked
with
a
child
being
slow
to
speak.
Ed
Thorp
was
born in
Chicago
on
August
14,
1932,
and did not utter his
first
words
until
he
was
nearly
three.
The Thorp
family
was
at a
Mont
gomery
Ward
department
store
when
a
group
of
people
stepped
out
of an
elevator.
"Where's
the man
gone?"
someone
asked.
"Oh, he's gone to buy a
shirt,"
Ed
said.
From that moment, Ed
conversed almost like an adult. Six
months
after
that
first
sentence,
Ed
knew
how
to
count
to a
million.
He
could
read
and
had
a
near-
photographic
memory.
At
the
age
of
five,
Ed
was
challenged
to
name
the
kings
and
queens
of
England.
"Egbert,
802
to
839,"
he
began.
"Ethclwulf,
839 to
857;
Ethelbald,
857 to 860
..."
He continued
without interruption or error, up to "Queen
Victoria,
I know when
her
reign
began
but I don't know when it
ended."
The book from
which
Ed
had
learned
this
was
Charles
Dickens's
A
Child's
History
of
England.
Dickens
had
no
way
of
knowing
that
Victoria
would
die
in
1901.
Thorp's father
was
an
army
officer
who had returned to
civilian
life
as the
American
economy
collapsed
into
depression.
He had to
take
a job as a bank
guard.
He
plied
his
gifted
son with math and
reading
primers,
telling
Ed
(and
himself)
that
education
was
the
key to success in America.
Growing
up in
hard
times,
Ed
turned
his
wits
to
making
money.
38


## Page 44

Entropy
Fie
bet a grocerhe
could
total
customers'
bills
in hishead
faster
than
the grocer could using an adding
machine.
Ed won, earning ice
cream cones for his
performance.
FIc
would buya packof
Kool-Aid
for
five
cents and
sell
the
mixed
beverage
to hot WPA
workers
for
one cent a
glass.
Ed
could
get
six
glasses
from
a
pack
for a penny
profit.
An older
cousin
took
Ed
to a
gas
station
where
gangsters
had
placed
illegal
slot
machines
in the
rcstrooms.
Ed
learned
howto jig
gle
the
handles
so the
machines
would
pay
off
when
they
weren't
supposed to.
Ed's
life
changed
when
his
family
moved
to
Los
Angeles
to
take
jobs
in
wartime
defense
plants.
With
both
parents
working,
Ed
and
his
younger
brother,
James,
were
latchkey
kids.
Ed
would
go to the
public
library
to
self-administer
IQjrests.
He
usually
scored
170
to
200. The
absence
of
parental
supervision
facilitated
an interest in
blowing
things
up.
Ed
whacked
homemade
nitrocellulose
with
a
sledgehammer
to
blow
holes
inthe
sidewalk.
He
built
pipe
bombs
to
blow craters in the
cliffs
of
Palos
Verde
and a gunpowder-propelled
"rocket-car."
By
mixing
ammonia
water
with
iodine
crystals,
he
made
an
incredibly
sensitive
explosive
called
ammonium
iodide.
He
painted
this
onto
the
bottom
ofa
hemispherical
metal
bowl,
then
set the
bowl
on the
ground.
The
explosive
became
active
asit
dried.
The
weight
of a
fly
landing
on the
prepared
bowl
would
trigger
a
small explosion.
In
spring
1955
Thorp
was
a
physics
graduate
student
at
UCLA.
He
made
doona
budget
ofSiooa
month.
To
subsist
on
that,
he
lived
in
the
student-run
cooperative
in
Robinson
Hall.
Known
asthe
"Glass
House,"
Robinson
Hall
was
designed
by
Richard
Neutra in the
1930s.
The rent
was
S50
a
month
plus
four
hours
of
work
per
week.
Since
time
was
money.
Thorpputin
fifty
to
sixty
hours
a
week
of
classes
and
study.
He
read
books
on
psychology
for
tips
on
how
to
learn
faster.
The
books
recommended
taking
a break
every
nowand
then.
Study
an
hour,
then
take
a
ten-minute
break
to eator run er
rands.
Following
this
advice
one
Sunday
afternoon.
Thorp
attended
a faculty tea.
39


## Page 45

FORTUNE
S
FORMULA
Assunlight streamed in through Neutra'splate
glass,
the conver
sation turned to
ways
to make easy
money.
Someone mentioned
roulette.
The group
was
unanimous
in the
conviction
that
gam
bling
systems
are
worthless.
The
discussion
had to do with
physics.
Arc roulette
wheels
so perfect that predicting
likely
numbers is im
possible?
The
group
was
of
two
opinions.
Some
felt
that
nothing
in the
world
is
perfect,
not
even
perfectly
random.
Therefore,
every
rou
lette
wheel
must
have
slight
physical
defects
that
cause
it to
favor
some
numbers.
It
might
be
possible
to
identify
these
favored
num
bers
and
bet
on
them.
The
other
group countered that roulette wheels are manufac
tured to
exacting
specifications
for just this
reason.
Thorp
had
the
most
original
argument.
He
said
you
could
make
money
either
way.
If the
wheels
are
physically
perfect,
simple
physics
can predict
where
the
ball
is
going
to
go.
If the
wheels
have
flaws,
someof the
numbers
ought to be
favored.
Thorp did
some
further
investigation
on
his
own.
He learned
that
casinos
accept
bets
for
a
couple
of
seconds
after
the
croupier
re
leases
the
white
ball.
The
reason
is
that
the
ball
takes
a
fairly
long
time
to
come
to
rest.
Anytime
the
croupier
is not
accepting
new
bets, the
casino
is not
making
money.
Thorp
fantasized
about
building
a
portable
electronic
device
to
predict
the
winning
numbers.
It
would
be
fast
enough
to
make
a
prediction
in
the
couple
of
seconds
in
which
wagers
are
permitted
after the
ball
is
cast.
Thorp
sketched
out an
orchestrated
attackon
Las
Vegas.
One member of his entourage
would
stand next to the
wheel, operating the prediction
device.
The device would radio its
predictions
to
another
person
at the
same
table.
This
person,
seated
where
he
did
not
have
a
good
view
ofthe
wheel,
would
pay
no
atten
tion to the
wheel
ashe
casually
placed
last-second
wagers.
Every
now
and
then
one
of
these
two
people
would
get up
and
walk
to
another
table—for
there
would
bea
whole
army
of
confed
erates,
half
with
the
devices
and
half
placing
bets.
They
could
come
and go at random.
Thorp
bought
a
cheap
roulette
wheel.
He put a
stopwatch
next
40


## Page 46

Entropy
to it and
filmed
it in motion. After
examining
the
film
frame by
frame.
Thorp
concluded that the toy wheelwas too erratic to permit
a prediction.
During
Christmas
break of
1958.
Ed
and his
wife,
Vivian,
took a
trip to
Las
Vegas.
Vivian
Sinetar
was
a slender
English
major.
Her
parents had
questioned
the earning
potential
of a
physics
Ph.D.
who had shown more talent for thrift than for
making
money.
Ed
told
Vivian
that
Las
Vegas
was
a great
place
for a bargain-priced
vacation.
He wanted to get a
look
at the
casino
roulette
wheels
in
action.
Just
before
this
trip,
a
friend
gave
Thorpan
article
from
the
Journal
of
the
American
Statistical
Association.
It
was
an
analysis
of the game of
blackjack.
Until the computer
age,
it
was
impractical
to
calculate
the
exact
probabilities
in
blackjack
and
many
other card
games.
There arc an
astronomical
number
of
possible
arrangements
of a
deck
of
fifty-
two cards. Unlike in the
case
of roulette, the
blackjack
playerhasde
cisions
to
make.
The odds in
blackjack
therefore depend on what
strategy
the
player
uses.
In
1958
no
one
knew
what
strategy
was
best.
Casinos
simply
knew
from
experience
that
they
made
an
excellent
profit.
The
journal
article
was
by
mathematician
Roger
Baldwin
and
three
associates
at the
U.S.
Army's
Aberdeen
Proving
Ground.
They
had
analyzed
blackjack
with
army
"computers,"
a
term
that
still
meant
adding
machines
or the
people
operating
them.
Baldwin's
team
spent
nearly
three
years
pecking
away
at
calculators
in order to
devise
an
optimum
blackjack
strategy.
Their
conclusion
was
that the
house
edge
was
just 0.62
percent
when
a
player
used
their
optimal
strategy.
Thorp
computed
that
he
could
play
all
day,
placing
one
thousand Si bets, and it would "cost"him only S6, on the
average.
Relatively
speaking,
a 0.62
house
edge
is
great.
The
house
advan
tage
in
American
roulette
is
usually
5.26
percent.
Forslot
machines,
it
runs
10 to 20
percent.
Writers
on
blackjack
had
previously
claimed
a house
advantage
of 2 or 3
percent.
No one had
really
un-
41


## Page 47

FORTUNE
S
FORMULA
dcrstood the
game.
The
Baldwin
group's
strategydiffered
from
the
intuitive one that
"good"
blackjack
players
had been
using.
Thorp, who had never
played
blackjack,
wanted to try the
Bald
win
strategy.
Fiecopied the
article's
strategychart onto a
small
card.
When he got to Las
Vegas,
he bought ten silver dollars and sat down
at a blackjack table.
Las
Vegas
people then considered
blackjack—also
known as
twenty-one—to
be a
woman's
game,
offered
to
give
wives
some
thingto do
while
their
men
played
craps.
The
game
moved
quickly.
Thorp had to look up
every
decision
on his
card.
The dealer and
players
wanted
to
know
what
he
was
looking
at in
his
palm
and
why
he
was
taking
so
long.
When
he told
them,
they
thought
it
was
funny.
Thorp's
pile
of
silver
dollars
shrank,
but the
mockers
were
losing
faster.
At the end of halfan
hour.
Thorp
quit.
He
was
downto
S1.50.
This
experience
preyed
on
Thorp's
mind
in the
following
months.
lie
saw
a
way
to
improve
the
strategy.
It restedon the fact
that the
chances
of
drawing
particular
cards
are
not
completely
in
dependent
from hand to hand.
You
might for instancesec three
aces
played
in one deal.
Aces
are
good
for the
player.
The
dealer
discards
the
played
cards
and,
as
suming
she's
got
enough
cards
to goon
without
shuffling,
deals
the
next
hands
from
the
remainder
of the
deck.
Since
you've
already
seen three aces
played,
you know that there can at most be one ace
in
the
new
hands.
You
could
use
that
information
to
adjust
your
strategy
and/or the
size
of
your
bet.
This
had
not
been
considered
in
the
Baldwin
group's
study.
They
had
pretended
that the
chance
of
drawing
any
card
is
fixed
at
exactly
1in 52, in every hand dealt.
Thorp
grew
so
convinced
that
he
could
beat
blackjack
that
his
roulette
idea
went
on the back
burner.
lie
wrote
Baldwin
to ask
if
he
could
see
the
group's
original
computations.
In
spring
1959
Bald
win sent a cardboard box
full
of the
group's
notebooks.
That
year.
Thorp
began a job as a mathematics
instructor
at
MIT.
He
went
to
Massachusetts,
alone, in June, for a
summer
re-
42


## Page 48

Entropy
search project. Thorp spent the humid
Boston
nights in his new
office,
hammering
on a
desk
calculator
and
slapping
the omni
present mosquitoes. He was working on the
blackjack
system. After
a
couple
of
weeks,
he
concluded
that the
problem
was
too big to
solve
by
hand.
Then he
realized
that he
might
be
able
to do the
computations on
MIT's
mainframe computer. It was an IBM 704,
a
real,
programmable,
electronic
computer.
It had some free time
during
the
summer
break.
Thorp taught himself FORTRAN, the
venerable
programming
language,
and
programmed
the computer
himself.
Fliscomputations
told him that the
five
cards
make
a
bigger
difference to the house
advantage
than
any
other
rank.
The
fives
are bad for the
player
and
good
for the
house.
By
simply
keeping
track
of
how
many
fives
have
been
played,
the
player
could
judge
whether the remainder of the
deck
was
favorable
or
not.
Thorp decided to
publish
the
system.
He determined that the
most
prestigious
journal
that
might
take
the article
was
The
Proceed
ings
of
the
National
Academy
of
Sciences.
But
articles
had to be submitted
by a National
Academy
member.
There
was
onlyone
academy
member
at MIT who
was
a mathe
matician.
That
was the famous Claude Shannon.
Thorp
called Shan
non's secretaryand made an appointment to meet him.
It
was
a
chilly
afternoon in Novemberi960.
Before
Thorp went in,
the
secretary
warned
him
that
Dr.
Shannon
had
only
a
few
minutes
to
spare.
He didn't spend timeon
subjects
that didn't interest
him.
Conscious
that the meter
was
running,
Thorp handed
Shannon
his
paper and
quickly
ticked
off its
main
points.
Shannon
asked
as
tute
questions
and
was
satisfied
withThorp's
answers.
Shannon
told
Thorp that he
appeared
to
have
made
the big
theoretical
break
throughon the
subject.
Shannon's
main
objection
was
the title.
Thorp had titled the paper
"A
Winning
Strategy
for
Blackjack."
Shannon
thought that
was
too
much
of a hard
sell
for the
National
Academy.
The title should be more
sedate.
43


## Page 49

FORTUNE
S
FORMULA
Like
what?
Thorp
asked.
Shannon thought a moment and
said:
"A
Favorable
Strategy
for
Twenty-one."
Shannon proposeda
few
editorialcuts. Fietold Thorp to typeup
a
revision
and send it to
him.
He
would
forward
it to the
academy.
"Arcyou working on anything else in the gambling
area?"
Shan
non
asked.
Thorp
hesitated,
then told Shannon about the roulette idea.
Shannon was riveted. He was
possibly
more interested in the
roulette scheme than the
blackjack
system because there was a
gadget
to
build.
They
spoke
for
several
hours.
By
the time they ad
journed.
Thorp had
inadvertently
set one of the
century's
great
minds on yet
another
tangent. It was agreed that Shannon and
Thorp
would collaborate on building a roulette prediction machine.
Shannon said that the best place to work would be his home.
Toy
Room
"We
had
a
very
informal
house,"
Betty
Shannon
once ex
plained.
"If there
was
somethingthat interested us,we did it."
The
Shannons'
home
was
a big
three-story
house
in
Winchester,
Massachusetts.
It sat on a
large
lot
sloping
down to the shore of one
of the
Mystic
Lakes.
The Shannons had three children, Robert, An
drew,
and
Margarita.
Their
amusement
was
the pretext for
some
of
their father's
gadget-building.
Shannon
constructed a
"ski
lift" to
help
the
family
zip
between
house
and
lake.
Fie
rigged
a
tightrope
a
couple
of feet
above
the
ground;
Shannon
and the children used it
44


## Page 50

Entropy
for
acrobatic
feats.
On
placid
summer
days
Shannon
could
occasion
ally
be
seen
strolling
across
the
green-black
water
of the
lake.
He
achieved
this
by
wearing
outsizcd
"shoes"
made
outof
plastic
foam.
The
garage
was
a
clutter
of
dusty
unicycles
and
penny
farthings.
Inside,
Shannon's
"Toy
Room"
was
a
curiosity
cabinet
of
weird
ma
chines,
globes,
skeletons,
musical
instruments,
juggling
equipment,
looms,
chess
sets,
and
memorabilia.
The
Shannons
had
five
pianos
and
thirty-some
instruments
ranging
from
piccolos
to
sousaphones.
There
was
a
flamethrowing
trumpet
anda
rocket-powered
Frisbee.
Claude
spent
much
time
inventing
new
gismos
in
his
basement
workshop.
"What
it
was was
a
collection
of
rooms,"
Thorp
recalled.
"Some
of the
rooms
had open
shelving.
We
estimated
he had about
SlOO.OOO
worth of
surplus
equipment.
At
surplus
rates,
that's
a
lot of
stuff.
There'd
be
whole
sections
of
switches—toggles,
mer
cury
switches,
and so on;
capacitors,
resistors,
little motors. He liked
both
electrical
and
mechanical
things.
Something
that
was
electro
mechanical was ideallysuited for him."
One of
Betty's
first
gifts
to
Shannon
after their
marriage
was
"the
biggest
Erector
set
you
could
buy
in
this
country.
It
was
fifty-
bucks
and
everyone
thought
I
was
insane!"
Betty
said.
Claude
in
sisted that the set
was
"extremely
useful"
for trying out
scientific
ideas.
Today's
distinction
between
robotics
and
artificial
intelligence
was
moot in the
early
1960s.
There
were
no
inexpensive
program
mable
computers
and
scarcely
any
video
displays.
The
first
experi
ments
in
AI
were
hard-wired
machines
that
moved.
Shannon
was
responsible for a number of them. One was "Theseus," a robotic
mouse
capable
of
threading
a
maze.
As
it
dated
to the
Stone
Age
of
electronic
miniaturization,
Theseus
was
simply
a
metal
toy on
wheels
guided
magnetically
by
a
special-purpose
computerbuilt into
the
base
of the
maze.
When the
mouse's
copper
whiskers
touched
an aluminum
wall
of the
maze,
the mouse
changed
direction.
One of
Shannon's
chess-playing
machines
was
a
three-fingered
robot arm that
moved
pieces
on a real board. The machine made
sarcastic
comments when it took a
piece.
Shannon built a computer
that
calculated
not in
his
own
scheme
of
binary,
but in
Roman
nu
merals.
45


## Page 51

FORTUNES
FORMULA
Shannon's "Ultimate
Machine"
was
the size and shape of a cigar
box.
On the
front
panel
was
a
toggle
switch.
The
unsuspecting
visi
tor
was
invited
to
flip
the
switch
on.
When
that
happened,
the top
slowly
opened.
A
robot
hand
emerged,
reached
down,
and
flipped
the switch off. The hand retreated, and the lid snapped shut.
The
Charles
Addams-esque
theme of
disembodied
limbs
in
boxes was a Shannon motif. In the kitchen was a mechanical
finger.
By
pulling
a
cable
in
the
basement,
Claude
could
cause
it to
curl
in
summons
to
Betty'.
Another
device
was
a
simple
flexible
metal
arm that
tossed
a
coin.
It
could
be set to
flip
the
coin
through
any
desired
number
of
rotations.
This
demonstrated
a favorite
theme
of
Shannon's,
the rel
ativity
of
random.
In
American
culture
the
coin
toss
is
the
paradigm
of
a random event. A coin toss decides who kicks
off
the
Super
Bowl.
Looked
at another
way.
a coin toss is not random at
all.
It is
physics.
An
event
is
random
only
when
no one
cares
to
predict
it—
asThorp
and
Shannon
intended
to
demonstrate
with
their
roulette
machine.
Roulette
Thorp
worked
with
Shannon
as time permitted from
early
i960 to
June
1961.
Shannon's
free-spending
ways
came
in
handy.
They
needed
a
professional
roulette
wheel
to
study.
Shannon
ordered a reconditioned
wheel
from
Reno.
With a set
of
ivory
balls,
it
cost
Si.SOO.
46


## Page 52

Entropy
Theyset the
roulette
wheel
on a
dusty
old
slate
billiard
table
and
filmed
it
using
a
strobe
light.
A
special
clock
with
a
high-speed
hand
that
made
one
revolution
every
second
allowed
them
to time the
motion
more
accurately
than Thorp
had.
A
roulette
wheel's
innerpart (the
rotor)
rotates
within
a station
ary outer part (the stator). The
croupier
spins
the rotor in one di
rection
and
tosses
the
ball
into
the stator in the
opposite
direction.
Initially
the
ball
is
moving
so
fast
that
centrifugal
force
presses
it
snug against the near-vertical rim
of
the stator. As
momentum
de
creases,
the
ball
drops
onto the
sloped
part of the
stator.
Like
a
satellite
in
a
decaying
orbit,
it
falls
inward
in
a
spiral
trajectory.
The
stator
contains
"vanes"
or
"deflectors."
These
arc
(typically)
eight
diamond-shaped
metal
pieces
arranged
in a neat
pattern.
A
spiraling ball that hits a deflector
will
often carom off in a different
direction.
About
half
the
time,
though,
the
ball
slips
between
the
deflectors
or
skips
over
one
without
much
changing
its
trajectory.
The
ball
then
spirals
down
the
inner
partof thestator
and
skips
over
to the
rotor.
Since
the
rotor
is
spinning
ina
direction
opposite
to
the
movement
of the
ball,
the
friction
increases.
The
ball
slips
farther
inward,
finally
encountering
the
pockets.
There
are
thirty-eight
numbered
pockets
in
the
American
game.
A
divider
called
a
"fret"
separates
each
pocket
from
its
neighbors.
The
ball
usually
hits
a
few
frets
before
settling
intoa
pocket.
As
in a
head-on
freeway
collision,
the
relative
speed
between
ball
and
frets
is
high.
This part of the
ball's
trajectory
ishardestto
predict.
Theydidn't
need
an
exact
prediction.
Narrowing
down
the
ball's
destination
to a
half
of
the
wheel
would
provide
a
whopping
ad
vantage.
During one of these
sessions.
Thorp
discovered
that he
was
able
to guess
approximately
where the ball would land. It was like
ESP.
He and
Shannon
discovered
the
reason.
The
wheel
was
slightly
tilted.
This
made
the
ball
favor
the
downhill
side
of
the
wheel.
Picture a roulette
wheel
mounted
vertically
on the
wall,
like a
clock.
The
ball would
have
to come to rest in the
lowermost,
six
o'clock
position.
You
would
need to
predict
only
which
pocket
of
47


## Page 53

FORTUNE
S
FORMULA
the rotor
would
end up in the
six
o'clock
position.
It is
easier
to pre
dict one
moving
object
than
two,
and
the
motion
of the
spinning
rotoris
much
simpler
thanthatof the
skittering
ball.
The effect
was
of course much subtler with a
slightly
tilted
wheel.
Shannon
and
Thorp put
roulette
chips
under
the
wheel
to
experiment
with
different
degrees
of
tilt.
They
concluded
thata tilt
amounting
to halfa
chip's
thickness
would
give
them
a
substantial
advantage.
They
joked
about
slipping
a
chip
under
the
wheel
in the
casinos.
Shannon
proposed
slipping
a
sliver
of
ice
underthe
casino's
wheel.
It
would
destroy
the
evidence
as
it
melted.
The
device
they built
was
the
size
of a
cigarette
pack.
It con
tained
twelve
transistors
and
slipped
into a
pocket.
The user
needed
to
measure
the
initial
position
and
velocity
of the
two
moving
ob
jects,
the
ball
and
the
rotor.
To
do
that,
the
user
mentally
picked
a
reference
point on the
stator.
When
a point on the rotor
passed
this
reference
point,
the user
clicked
a
toe-operated
switch
con
cealed
in his
shoe.
He
clicked
again
when
the rotor point
passed
the
reference
point
again,
having
made
a
full
revolution.
A
third
click
signaled
when
the
ball
passed
the
reference
point,
and
a
fourth
when
it
had
made
a full
revolution.
From this data the
device
predicted
the segmentof the
wheel
in
which
the ball
was
most
likely
to
land.
The
device's
predictions
were
accurate
only
to within about ten
pockets.
There
was
not
much
pointin
informing
the
user
ofthe
exact
"most
likely
number."
Imag
ine the roulette
wheel
as a
pizza
divided
into eight equal
pieces.
Shannon
called
the
pieces
octants.
The
device
assigned
a distinct mu
sical
tone to each octant and communicated its prediction via a con
cealed
earphone.
Thorp
mentally
ticked
off the notes
as
do
re
mi
fa
so
la
ti
do.
The
computer
played
notes
while
it
was
computing,
then
stopped.
The lastnote told
what
octant to bet on.
Each octant consisted of
five
numbers that are close together on
the rotor
(some
octants
overlapped).
One of the
octants
was
OO,
I,
13,
36,
24.
An octant's
numbers
are not
close
on the betting table
layout.
The bettor
would
have
to
scramble
to
place
bets
on
five
assorted
numbers.
It was
not
crucial
that
he
bet
all
the
numbers
as
longas he
only
placed
betson the right
numbers.
48


## Page 54

Entropy
Shannon
and
Thorp
estimated
that
with
the
octant
system
and
a
modest
degree
of
tilt,
they
could
achieve
a 44
percent
edge
on the
house.
Both
men
realized
how
fragile
their
scheme
was.
If
ever
the
casinos
got
word
ofthe
operation,
they
could
simply
refuse
to
accept
bets
after
the
ball
had
been
thrown.
The
scheme
thus
depended
on
keeping
it
secret.
Shannon
told
Thorp
thatan
analysis
had
shown
that
any
two
people
in the
United
States
were
likely
to be
connected
bya
chain
of about three
mutual
friends.
(He
must
have
been
referring
to the
1950s
work
of MIT
political
scientist
Ithicl dc Sola Pool
rather
than the
now-bctter-
known
1967
study
of
Harvard
psychologist
Stanley
Milgram
that
found
"six
degrees
of
separation.")
Shannon
was
concerned
that
word
might
have
already
gotten
out,
maybe
from
the
original
UCLA
discussion.
A few nodes in the social
network
could
link an
M
IT
scientist to a Las
Vegas
casino
boss.
Gambler's
Ruin
Shannon
had
another
worry
It
is
easy
to
lose
money,
evenwith a
mathematical
advantage.
Professional
gamblers,
who
have
to
have
an
advantage,
speak
of
"money
management."
This
refers
to the
tricky
and all-important
issue
of
how
to
achieve
the
greatest
profit
from
a
favorable
betting
opportunity.
You
can be the
world's
greatest
poker
player,
backgam
mon
player,
or
handicapper,
but if
you
can't
manage
your
money
you'll
end up
broke.
The sad
fact
is,
almost
everyone
who
gambles
goes broke in the long run.
49


## Page 55

FORTUNES
FORMULA
Make
a chart of a
gambler's
wealth.
The
gambler
starts
with
X
dollars.
Each
time
the
gambler
wins
or
loses
a bet, the
wealth
changes.
If
the
wagers
are
"fair"—that
is,
if
the
gambler
has
no
advantage
and
no
one
is
skimming
a
profit
off
the
bets—then
the
long-term
trend
of
wealth will be a horizontal line. In
mathematical
terms, the
"expectation"
is
zero.
That
means
that
inthe
long
run,
a
gambler
is
justas
likely
to
gain
as to
lose.
Expectation
is
a
statistical
fiction,
like
having
2.5
children.
A
gambler's
actual
wealth
varies
wildly.
The
diagram's
jagged
line
shows
the
fate
ofa
typical
gambler's
bankroll.
It
is
based
on a
simple
simu
lation
where
the
gambler
bets the
same
dollar
amount
each
time.
The
jagged
line
wavers
without
rhyme
or
reason.
Mathematicians
call
this
a
"random
walk."
Gambler's
Ruin
The
only
trend
you
might
notice
is
that the
swings,
both
up
and
down,
tend to get
wider
as
time
goes
on. This is a
mathematically
50


## Page 56

Entropy
demonstrable
fact
and
would
be
more
apparent
were
the
chart
con
tinued
indefinitely
to
the
right.
The
gambler's
wealth
tends
to
stray
ever
farther
from
the
original
stake.
There
are
long
runs
of
good
luck
in
which
the
gambler
is
ahead,
and
long
runs
of
bad
luck
in
which
he
is
behind.
If
someone
could
gamble
forever,
the
line
rep
resenting
wealth
would
wander
across
the
"original
stake"
line
an
infinite
number
of
times.
But
look:
Relatively
early
in this
chart,
the
wealth
hits zero
(the
line
marked
"Bankrupt").
Had
this
happened
in a
casino,
the
gambler
would
be
tapped
out.
He'd
have
to quit
and
go
home
a
loser.
That
means
that the rightpart of the chart is
irrelevant.
Assum
ing
the
original
stake
is
everything
the
gambler
has
or
can
get
to
gamble
with,
he's
out of the
game
permanently.
In
casino
games,
the
house
normally
has
an
edge.
This
means
that the
player
tends
to go
broke
faster.
It
is
possible
to go
broke
even
in
those
unusual
cases
where
the
player
has
a
small
advantage.
When
that
happens,
the
gambler's
loss
is
someone
else's
gain
(a
casino's,
a
bookie's,
a
pari-mutuel
track's).
That
"someone
else"
usu
ally
has
more
money.
That
means
that
the
gambler
is
likely
to
go
bust
long
before
he
has
such
a
winning
streak
asto
"break
the
bank."
The
net
effect
of
gambling
is
to
extract
the
stake
from
the
gambler's
pocket
and
give
it to
the
house.
How
often
have
you
heard
of a
friend
who
went
to the
casinos,
won
a
nice
little
jackpot,
and
poured
it
all
back?
Mathematicians
give
this
phenomenon
the
faintly
Victorian
name of "gambler's ruin." Gamblers have dozens of names for it.
among
them
"having
an
accident"
and
"getting
grounded."
Over the
centuries,
gamblers
have
devised
all
sorts of
money
management
systems to
minimize
the chance
of
ruin.
The
simplest
and
most
foolproof
system
is
to not
gamble
(with
someor
all
of your
money).
If
you're
going
to
Las
Vegas
withSi.ooo
and are
determined
to
come
back
with
at
least
S500.
then put the
S500 in the hotel safeand don't
gamble
with it.
This isnot the kindof
advice
that most
gamblers
want to
hear.
It
does not
fundamentally
address
the ruin problem at that.
You
still
51


## Page 57

FORTUNES
FORMULA
need
a
money
management
system
for
the
amount
you
are
gambling
with. It is
easy
to lose
all
of that.
The
best-known
betting
system
is
"martingale"
or
"doubling
up."
This
is
the
system
where
a
bettor
keeps
doubling
her
bet
until
she
wins.
You
might
begin
by
placing
a
dollar
on
an
even-money
bet
like
"red"
in
roulette.
If
you
win,
great.
You've
made
a
dollar
profit.
If
you
lose,
you
bet
S2
on
red
the
next
time.
Should
you
win
this
time,
you
get
twice
that
back,
or
S4.
Notice
that$4
is
a
dollar
more
than
the
S2
plus
Si
total that
you
have
wagered.
Should
you
lose
again,
you
place
a
new
bet
for
$4.
Win
this
time,
and
you
get
$8,
for
a
Si
profit
(you've
then
bet
S7
total).
Lose
again,
and
you
bet
S8
...
then
S16
...
S32
...
S64
...
An
unlucky
streak
has
to end
sometime.
When it does, you are guaranteed to be a dollar
ahead. Repeat as desired.
The
eighteenth-century
journalist,
gambler,
and
scoundrel
Ca
sanova
used
martingale
in the
Venetian
casinos.
Fie
was
playing
a
card
game
called
Faro
that
offered
even-money
bets
with
little
or no
house
advantage.
Casanova
was
mostly
betting
the
money
of
his
mistress,
the
wealthy
young
nun
he
calls
M—
M—.
"I
still
played
on
the
martingale,"
Casanova
wrote,
"but
with
such
bad
luck
that I
was
soon left withouta
sequin.
As
I
shared
mypropertywith
M— M—
I
was
obliged
to
tell
her
of
my
losses,
and
it
was
at
her
request
that I
sold
all
her
diamonds,
losing
what
I got for
them;
she had now
only
five
hundred
sequins
by
her."
This
dashed
M—
M—'s
hope of es
caping
the
convent
to
marry
Casanova—a
long
shot
in
any
case,
as
the
rest
of
the
memoir
makes
clear.
Far
from
preventing
gambler's
ruin,
martingale
accelerates
it. The
amount a losing
player
must bet is soon
S128
. . .
S256
. . .
S512
. . .
Either
the
player
runs
outof
money
(or
nerve),
or the
casino
refuses
the bet as too
large.
That
leaves
the
martingale
player
with no
way
of
recouping the string of
losses.
In the
days
of the
Wild
West,
faro
dealers
traveled
from
saloon
to
saloon
setting up
portable
betting
layouts.
Most
of those
faro
deal-
52


## Page 58

Entropy
ers
were
cheats,
it
appears.
The
game
survived
into
the
early
days
of
legalized
gambling
in
Nevada.
Faro
still
lured
players
who
thought
themselves
smart
for
playing
a
game
with
no
house
advantage.
The
movie producer Carl Laemmleonce staked Nick the Greek to three
months
of
playing
faro
in
Reno.
Nick
lost
everything.
So
did
an
anonymous
California
woman
in
a
tale
told
by
Reno
casino
propri
etor
Harold
S.
Smith,
Sr.
(whom
we
are
about
to
meet).
The
Cali
fornia woman
was
so addicted to faro that she
was
seen in Reno
every
weekend.
It
was
a
marvel
how
she
could
play
for
twelve
hours
straight.
The
woman
began
dispensing
with
her
trips
home
to
California.
Her
real
life
was
at the
faro
tables.
Afterher
husband
divorced
her,
the
woman
moved
to
Reno
full-time.
She
burned
her
way
through
a
S50.000
divorce
settlement.
Then
she
turned
prostitute
on
Doug
las
Alley
to
feed
her
gambling
habit.
As
Smith
told
it,
she
wasn't
any
bargain
beauty
and
the
Line
was
open
in
Reno
then
with
attractive
young
women
selling
for
S3.
Our
woman
had
to
offer
cut
rates
and
take
what
she
could
get.
She
sold
her
self
for
50
cents
an
act.
Fifty
cents—the
minimum
bet on the
Faro
table,
which—if
it
won—would
pay
exactly
fifty
cents.
Randomness,
Disorder,
Uncertainty
In
a
1939
letter
to
Vannevar
Bush,
Shannon
wrote,
"Off
and
on, I
have
been
working
on an
analysis
of
some
of the
fundamental
53


## Page 59

fortune's
formula
properties
of
general
systems
for
the
transmission
of
intelligence,
including
telephony,
radio,
television,
telegraphy,
etc."
This
letter
describes
the
beginning
of
information
theory.
As
Shannon
would
ultimately
realize,
his
theory
of
communication
has
surprising
rele
vance
to the
problem
of
gambler's
ruin.
Before
Shannon,
most
engineers
did not
see
much
of a
connec
tion between the various communications media. What applied to
television
did not
apply
to
telegraphs.
Communications
engineers
had learned some of the
technical
limits of each medium through
trial
and
error,
in
about
the
way
the
cathedral
builders
ofthe
Middle
Ages
learned
something
of
structural
engineering.
Through
trial
and
error,
they
learned
what
didn't
work.
Shannon sensed that the
field
was due for a new synthesis. He
apparently
came
to
this
subject
without
any
coaching
from
Bush,
and before he worked for
Bell
Labs,
where it would have obvious
economic
value
to
AT&T.
Your
home
may
have
a
fiber-optic
cable
leading
into it,
carrying
TV
channels,
music,
web
pages,
voice
conversations,
and
all
the
other
content
we
loosely
call
information.
That
cable
is
an
example
of a
"communications
channel."
It is a pipeline for
messages.
In
some
ways,
it's
like
the
water
pipe
leading
into
your
home.
Pipe
or
cable,
each
can
carry
so
much
and
no
more.
In the
case
of a
water
pipe,
capacity
is
simply
a
matter
of
the
width
of
the
pipe's
bore.
With a
communications
channel,
the
capacity
is
called
bandwidth.
Flow
of
water
through
pipes
is
limited,
not
only
by
capacity
but
also
by
friction.
The
contact
between
the
water
and
the
inner
wall
of
the
pipe
causes
drag
and
turbulence,
diminishing
the
flow.
Com
munications
channels
are
subject
to
noise
that
garbles
messages.
One of the
rules
of thumbthat
engineers
had
evolved
was
that
noise
diminishes
the flow
of
information.
When
there's a lot
of
noise, it
may
not be
possible
to
transmit
at
all.
There isone
extremely
important
way
in
which
a
fiber-optic
ca
ble
(or
any
communications
channel)
is
different
from
a
water
pipe.
Water cannot be
compressed,
at
least
not
much
at the
pressures
used
in
household
plumbing.
A
gallon
of water
always
occupies
a
gallon's
worth
of
pipe.
You
can't
squish
it
into
a
pint
in
order
to
54


## Page 60

Entropy
send
more
water
through
the
same
pipe.
Messages
are
different.
It
is
often
easy
to
abbreviate
or
compress
a
message
with
no
loss
of
meaning.
The
first
telegraph
wires
were
precious
commodities.
Operators
economized
their
nineteenth-century
bandwidth
by
stripping
out
unnecessary
words,
letters,
and
punctuation
marks.
Today's
mobile
phone
users
economize
with
text
messages
or
slangy
codes.
As
long
as
the
receiver
can
figure
out
what
was
meant,
that's
good
enough.
You
might
compare
messages
to
orange
juice.
Brazilian
orange
producers
boil
their
juice
into
a
syrupy
concentrate.
They
send
the
concentrate
to the
United
States,
saving
on
shipping
costs.
At the
end
of
the
process,
American
consumers
add
water,
getting
ap
proximately
(?)
what
the
producers
started
with.
Sending
messages
efficiently
also
involves
a
process
of
concentrating
and
reconstitut
ing.
Of
course,
with
messages
as
well
as
orange
juice,
there
is the
question
of
whether
some
of
the
subtler
nuances have been lost.
A
particularly
powerful
way
to
compress
messages
is
to
encode
them.
Mobile
phone
and
Internet
connections
do
this
automatically,
without
us
having
to
think
about
it.
A
good
encoding
scheme
can
compress a
message
a lot more than a few abbreviations can.
The
code
that
Morse
devised
for
his
telegraph
was
relatively
good
because
the
most
common
letter,
E,
is
represented
with
the
shortest
code,
a
single
dot.
Uncommon
letters
like
Z
have
longer
codes
with
multiple
dots
and
dashes.
This
makes
most
messages
more
concise
than
they
were
in
some
of the
early
telegraphic
codes.
This
principle,
and
many
more
subtle
ones,
figures
in
today's
codes
for
compressing
digital
pictures,
audio,
and
video.
The
success
of
these
compression
schemes
implies
that
messages
are like
sponges.
They are
mostly
"air"
with little
"substance."
As
long
as
you
preserve
the
substance,
you
can
squeeze
out the
air.
The
question
that
all
of
Shannon's
predecessors
tried to
tackle
was:
What
is
the
"substance"
of a
message,
the
essential
part that
can't
be
dispensed
with?
To
most
the
answer
was
meaning.
You
can
squeeze
anything
out of a
message
except
meaning.
Without
mean
ing,
there
is no
communication.
Shannon's
most
radical
insight
was
that
meaning
is
irrelevant.
To
55


## Page 61

FORTUNE
S
FORMULA
paraphrase
Laplace,
meaning
was
a
hypothesis
Shannon
had
no
need
of.
Shannon's
concept
of
information
is
instead
tied
to
chance.
This
is
not
just
because
noise
randomly
scrambles
messages.
Information
exists
only
when
the
sender
is
saying
something
that
the
recipient
doesn't
already
know
and
can't
predict.
Because
true
information
is
unpredictable,
it
is
essentially
a
series
of
random
events
like
spins
of
a
roulette
wheel
or
rolls
of
dice.
If
meaning
is
excluded
from
Shannon's
theory,
what
is
the
in
compressible
substance
that
exists
in
every
message?
Shannon
con
cluded
that
this substance can be described in statistical terms. It
has
only
to
do
with
how
unpredictable
the
stream
of
symbols
compos
ing the
message
is.
A
while
back,
a
phone
company
ran
ads
showing
humorous
mis
understandings
resulting
from
mobile
phone
noise.
A
rancher
calls
to order "two hundred
oxen."
Because
of the poor
voice
quality,
he
gets
two
hundred
dachshunds—which
are
no
good
at
pulling
plows
at
all.
A wife
calls
her
husband
at work and
asks
him to bring home
shampoo.
Instead
he
brings
home
Shamu,
the
killer
whale.
The
humor
of
these
spots
derived
from
a
gut-level
understand
ing
of
Shannon's
ideas
that
we
all
share
whether
we
know
it or
not.
Try
to
analyze
what
happened
in
the
Shamu
commercial:
(i)
The
wife
said
something
like,
"Pick
up
shampoo!"
(2)
The
husband
heard
"Pick
up
Shamu!"
(3)
The
husband
wound
up the
conversa
tion,
said
goodbye,
and
on
the
way
home
picked
up
the
killer
whale.
It is
only
the
third
action
that
is
ridiculous.
It
is
ridiculous
be
cause
"Pick
up
Shamu"
is an
extremely
low-probability
message.
In
real
conversations,
we are
always
trying
to
outguess
each
other. We
have
a
continuously
updated
sense
of
where
the
conversation
is go
ing,
of
what
is
likely
to
be
said
next,
and
what
would
be
a
complete
non
sequitur.
The
closer
two
people
are
(personally
and
culturally),
the
easier
this
game
of
anticipation
is.
A
long-married
couple
can
finish each other's sentences. Teen best friends can be in hysterics
over a
three-character
text message.
It
would
be
unwise
to
rely
on
verbal
shorthand
when
speaking
to
a
complete
stranger
or
someone
who
doesn't
share
your
cultural
ref-
56


## Page 62

Entropy
ercnce
points.
Nor
would
the
laconic
approach
work,
even
with
a
spouse,
when
communicating
a
message
that
can't
be
anticipated.
Assuming
you
wanted
your
spouse
to
bring
home
Shamu,
you
wouldn't
just
say.
"Pick
up
Shamu!"
You
would
need
a
good
explana
tion.
The
more
improbable
the
message,
the
less
"compressible"
it
is,
and
the
more
bandwidth
it
requires.
This
is
Shannon's
point:
the
essence
ofa
message
is
its
improbability.
Shannon
was
not
the
first
to
define
information
approximately
the
way
he
did.
His
two
most
important
predecessors
were
both
Bell
Labs
scientists
working
in
the
1920s:
Harry
Nyquist
and
Ralph
Hartley.
Shannon
read
Hartley's
paper
in
college
and
credited
it
as
"an important
influence
on
my
life."
As he
developed
these
ideas,
Shannon needed a name for the in
compressible
stuff
of
messages.
Nyquist
had
used
intelligence,
and
Hartley
had
used
information.
In
his
earliest
writings,
Shannon
fa
vored
Nyquist's
term.
The
military
connotation
of
"intelligence"
was
fitting
for
the
cryptographic
work.
"Intelligence"
also
implies
meaning,
however,
which
Shannon's
theory
is
pointedly
not
about.
John
von
Neumann
of
Princeton's
Institute
for
Advanced
Study
advised
Shannon
to
use
the
word
entropy.
Entropy
is
a
physics
term
loosely
described
as a
measure
of
randomness,
disorder,
or uncer
tainty.
The
concept
of
entropy
grew
outof
the
study
of
steam
en
gines.
It
was
learned
that it is
impossible
to
convert
all
the
random
energy
of
heat
into
useful
work.
A
steam
engine
requires
a
tempera
ture
difference
to
run
(hot
steam
pushing
a
piston
against
cooler
air).
With time, temperature
differences
tend to evenout, and the steam
engine grinds to a halt.
Physicists
describe this as an increase in en
tropy.
The
famous
second
law
of
thermodynamics
says
that the
entropy
of the
universe
is
always
increasing.
Things
run
down,
fall
apart, get used up.
Use
"entropy"
and you can never lose a debate, von
Neumann
told
Shannon—because
no one
really
knows
what
"entropy"
means.
Von
Neumann's
suggestion
was
not
entirely
flippant.
The
equation
57


## Page 63

fortune's
formula
for
entropy
in
physics
takes
the
same
form
as
the
equation
for
infor
mation
in
Shannon's
theory.
(Both
are
logarithms
of a
probability
measure.)
Shannon
accepted
von
Neumann's
suggestion.
He
used
both
the
word
"entropy"
and
its
usual
algebraic
symbol,
H.
Shannon
later
christened
his
Massachusetts
home
"Entropy
House"—a
name
whose
appropriateness
was
apparent
to
all
who
set
eyes
on
its
interior.
"I didn't
like
the term
'information
theory,'
" Robert
Fano
said.
"Claude didn't like it either." But the familiar word "information"
proved
too
appealing.
It
was
this
term
that
has
stuck,
both
for
Shan
non's
theory
and
for
its
measure
of
message
content.
The
Bandwagon
Shannon
went
far
beyond
the work
of
his precursors. Fie
came
up
with
results
that
surprised
everyone.
They
seemed
almost
magical
then. They still
do.
One of these
findings
is that it is
possible,
through
the
encoding
of
messages,
to
use
virtually
the
entire
capacity
ofa
communication
channel.
This
was
surprising
because
no
one
had
come
anywhere
close
to
that
in
practice.
No
conventional
code
(Morse
code,
ASCII,
"plain
English")
is
anywhere
near
as
efficient
as
the
theory
said
it
could
be.
It's
as if
you
were
packing
bowling
balls
into an
orange
crate.
You're
going
to
find
that
there's
a
lot
of
unused
space
no
matter
how
you
arrange
the
bowling
balls,
right?
Imagine
packing
bowling
balls
so
tightly
that
there's
no
empty
space
at
all—the
crate
is
filled
58


## Page 64

Entropy
ioo
percent
with
bowling
balls.
You
can't
do
this
with
bowling
balls
and
crates,
but
Shannon
said
you
can
do
it
with
messages
and
com
munications
channels.
Another
unexpected
finding
involves
noise.
Prior
to
Shannon,
the
understanding
was
that
noise
may
be
minimized
by
using
up
more
bandwidth.
To
give
a
simple
example,
you
might
take
the
pre
caution
of
sending
the
same
message
three
times
(Pick
up
shampoo-
Pick
up
shampoo—Pick
up
shampoo).
Maybe
the
other
person
receives
Pick
up
shampoo—Pick
up
Shamu—Pick
up
shampoo.
By
comparing
the
three
versions,
the
recipient
can
identify
and
correct
most
noise
errors.
The
drawback
is that
this
eatsup
three
times
the
bandwidth.
Shannon
proved
that
you
can
have
your
cake
and
eat it
too.
It
is
possible
to
encode
a
message
so
that
the
chance
of
noise
errors
is
as
small
as
desired—no
matter
how
noisy
the
channel—and
do
this
without
using
any
additional
bandwidth.
This
defied
the
common
sense
of
generations
of
engineers.
Robert
Fano
remarked.
To
make
the
chance
of
error
as
small
as
you
wish?
Nobody
had
ever
thought
of
that.
How
hegotthat
insight,
how
he
even
came
to
believe
such a
thing,
I don't
know.
But
almost
all
modern
communication engineering is based on that work.
Initially
it
was
hard
to
imagine
how
Shannon's
results
would
be
used.
No
one
in
the
1940s
pictured
a
day
when
people
would
navi
gate
supermarket
aisles
with
a
mobile
phone
pressed
to the
side
of
their
face.
Bell
Labs'
John
Pierce
had
his
doubts
about
the
theory's
practical
merit.
Just
use
more
bandwidth,
more
power,
Pierce
sug
gested.
Laying
cable
was
cheap
compared
to
the
computing
power
needed
to use
digital
encoding.
Sputnik
and
the
U.S.
space
program
changed
that
mind-set.
It
cost
millions
to put a
batter)'
in
space.
Satellite
communications
had
to
make
the
best
of
anemic
power
and
bandwidth.
Once
developed
for
NASA,
digital
codes
and
integrated
circuits
became
cheap
enough
for
consumer
applications.
We
would
be
living
in a
very
different
world
today
without
Shannon's
work.
All
ofour
digital
gear
is
subject
to the
noise
of
cur-
59


## Page 65

fortune's
formula
rent
surges,
static,
and
cosmic
rays.
Every
time
a
computer
starts
up,
it
reads
megabytes
of
information
from
disk.
Were
even
a
few
bits
garbled,
programs
would
be
corrupted
and
would
likely
crash.
Shan
non's
theory
showed
that
there
is
a
way
to
make
the
chance
of
mis
read
data
negligible.
The
ambivalent
blessing
of
Internet
file
sharing
also
derives
from
Shannon.
Were
it not for
Shannon-inspired
error-
correcting
codes,
music
and
movie
files
would
degrade
every
time
they
were
transmitted
over
the
Internet
or
stored
on
a
hard
disk.
As
one
journalist
put
it
recently,
"No
Shannon,
no
Napster."
By
the
1950s,
the
general
press
started
to
pick
up
on
the
importance
of
Shannon's
work.
Fortune
magazine
declared
information
theory
to
be
one
of
humanity's
"proudest
and
rarest
creations,
a
great
sci
entific
theory
which
could
profoundly
and
rapidly
alter
man's
view
of
the
world."
The
very
name
"information
theory"
sounded
expansive
and
open-ended.
In
the
1950s
and
1960s,
it
was
often
used
to
embrace
computer
science,
artificial
intelligence,
and
robotics
(fields
that
fascinated
Shannon but
which
he
considered
distinct from informa
tion
theory).
Thinkers
intuited
a
cultural
revolution
with
comput
ers, networks, and mass media at its base.
"The word communication will be used here in a very broad
sense
to
include
all
ofthe
procedures
by
which
one
mind
may
affect
another,"
begins
the
introduction
to a
1949
book,
The
Mathematical
Theory
of
Communication,
reprinting
Shannon's
paper.
"This,
of
course,
involves
not
only
written
and
oral
speech,
but
also
music,
the
picto
rial arts, the theater, the
ballet,
and in fact all human
behavior."
These
words
were
written
by
Shannon's
former
employer
Warren
Weaver.
Weaver's
essay
presented
information
theory
as
a
humanis
tic
discipline—perhaps
mislcadingly
so.
Strongly
influenced
by
Shannon,
media
theorist
Marshall
Mc-
Luhan
coined
the term
"information
age"
in
Understanding
Media
(1964).
Oracular
as
some
of
his
pronouncements
were,
McLuhan
spoke
loud
and
clear
with
that
concise
coinage.
It
captured
the
way
the
electronic
media
(still
analog
in
the
1960s)
were
changing
the
60


## Page 66

Entropy
world.
It
implied,
more
presciently
than
McLuhan
could
have
known,
that
Claude
Shannon
was
a
prime
mover
inthat
revolution.
There
were
earnest
attempts
to
apply
information
theory
to
se
mantics,
linguistics,
psychology,
economics,
management,
quantum
physics,
literary
criticism,
garden
design,
music,
the
visual
arts,
and
even
religion.
(In
1949
Shannon
was
drawn
into
a
correspondence
with
science
fiction
writer
L.
Ron
Hubbard,
apparently
by
way
of
John
Pierce.
Hubbard
had
just
devised
"Dianetics,"
and
Shannon
referred
him
to
Warren
McCuIloch,
a
scientist
working
on
neural
networks.
To
this
day
Hubbard's
Scientology
faith
cites
Shannon
and
information
theoretic
jargon
in
its
literature
and
web
sites.
Hubbard
was
known
for
repeating
George
Orwell's
dictum
that the
way
to get
rich
is
tostarta
religion.)
Shannon
himself
dabbled
with
an
information-theoretic
analysis
of
James
Joyce's
Finnegans
Wake.
Betty
Shannon
created
some
of the
first
"computer-generated"
music
with
Pierce.
Bell
Labs
was
an in
terdisciplinary
place.
Several
of
its
scientists,
notably
Billy
Kluver,
collaborated
with
the
New
York
avant-garde:
John
Cage,
Robert
Rauschenberg,
Nam
June
Paik,
Andy
Warhol,
David
Tudor,
and
others,
some
of
whom
lived
and
worked
steps
away
from
Bell
Labs'
Manhattan
building
on
West
Street.
Many
of
these
artists
were
ac
quainted
with
at
least
the
name
of
Claude
Shannon
and
the
concep
tual
gist
of
his
theory.
To
people
like
Cage
and
Rauschenberg,
who
were
exploring
how
minimal
a
work
of
music
or art
may
be,
infor
mation
theory
appeared
to
have
something
to
say—even
if no one
was ever
entirely
sure what.
Shannon
came
to
feel
that
information
theory
had
been
over
sold.
In a
1956
editorial
he
gently
derided
the
information
theory
"bandwagon."
People
who
did not
understand
the
theory
deeply
were
seizing
on it asa trendy
metaphor
and
overstating
its
relevance
to
fields
remote
from
its
origin.
Other
theorists
such
as Norbert
Wiener
and
Peter
Elias
took
up
this
theme.
It
was
time,
Elias
acidly
wrote, to stop publishing papers with titles like
"Information
The
ory,
Photosynthesis,
and
Religion."
To Shannon, Wiener,and
Elias,
the question of information the
ory's
relevance
was
more
narrowly
defined
than it
was
for
Marshall
61


## Page 67

fortune's
formula
McLuhan.
Does
information
theory
have
deep
relevance
to
any
field
outside of
communications?
The
answer,
it
appeared,
is
yes.
That is
what
a
physicist
named
John
Kelly
described,
in
a
paper
he
titled
"Information Theory and
Gambling."
*
John
Kelly,
Jr.
In 1894
THE
CITY
FATHERS
ofCorsicana,
Texas,
were
drilling
a
new
well.
They
struck
oil
instead
of
water.
Corsicana
became
oneof
the
original
petroleum
boomtowns.
For
a
time
the
town
was
wealthy
enough
to
boast
an
opera
house
where
Caruso
sang.
Then
the
De
pression
came
and
changed
everything.
Oil
prices
plummeted
to
as
low
as ten
cents
a
barrel.
The
region's
economy
fell
into
chaos.
The
town's
most
enduring
industry
was
and
is
a
mail-order
fruitcake.
John
Larry
Kelly,
Jr.,
was
born in
Corsicana
on
December
26,
1923.
His
mother,
Lillian,
worked
for the state
teachers'
retirement
program.
Of
Kelly's
namesake
father,
I
could
discover
little
except
that he
was
a
CPA.
Kelly
rarely
if ever
spoke
of his father to
friends.
Possibly
he
never
knew
him.
The
1930
census
reports
that
six-year-
old John
lived
with his
mother,
Lillian,
his
maternal
grandmother,
and an
aunt
in a
$30-a-month
apartment.
Kelly
came
of
age
during
World
War
II andspent
four
years
asa
flier for the
Naval
Air
Force.
He then did
undergraduate
and grad
uate work at the
University
of
Texas
at Austin,
segueing
into an
unglamorous
end
of
physics.
The
subject
of
his
master's
thesis,
"Variation
of
Elastic
Wave
Velocity
with Water
Content
in Sedi
mentary
Rocks,"
hints
at an
application
to the
oil
industry.
Kelly's
62


## Page 68

Entropy
1953
PhD.
topic
was
an
"Investigation
of
Second
Order
Elastic
Properties
of
Various
Materials."
The
work
was
important
enough
to get
Kelly
a job offer from
Bell
Labs.
In no small part due to Shannon,
Bell
Labs was one of the
world's
most
prestigious
research
centers.
American
Telephone
and
Telegraph's
benign
monopoly
gave
it
the
luxury
of
supporting
basic
research
on a grand
scale.
It was said that
Bell
Labs
was like a uni
versity except that its researchersdidn't have to teach, and there was
always
enough
money
for
experiments.
Kelly
was
barely
thirty
when
he
arrived
at
Bell
Labs'
Murray
Hill
site.
He
was
strikingly
handsome,
although
he
struck
some
as
slightly
unhealthy-looking.
Bags
under
his
eyes
made
him
look
older,
mysterious,
and
dissipated.
Kelly
was
a
chain-smoker
and
lib
eral
drinker—"a
lotof
fun,
the
life
of
the
party."
He
was
gregarious,
loud, and
funny,
quick to loosenhis tic and
kick
his shoesoff.
His
Texas
drawl set him apart at
Bell
Labs.
So did his interest in
guns.
Kelly
collected
guns
and
belonged
to a
gun
club.
Among
his
prize
possessions
was
a
Magnum
pistol.
Another
passion
was
pro
and
college
football.
Kelly
built
resistor
circuits
on
breadboards
to model and predict the results of football matches. A team's win-
loss
record
would
be
represented
with
a
resistor
ofa
particular
ohm
rating.
Kelly
was
married
to
Mildred
Parham.
As
a
couple,
they
were
ruthless
tournament
bridge
players.
The
Kcllys
raised
three
chil
dren—Patricia,
Karen,
and
David—in
a
suburban
house
at
17
Holly
Glen
Lane
South,
Berkeley
Heights,
New
Jersey.
One
of
Kelly's
best friends at
Bell
Labs was a fellow Texan, Ben
Logan.
Each
morning,
Kelly
and
Logan
would
make
coffee,
then
go
into
Logan's
office.
Kelly
would
immediately
put
his
feet
up on the
chalk
rim
of the
blackboard
and
light
up
a
cigarette.
With
a
wave
of
his
hand,
he
would
flick
the
ashes
in
the
general
direction
of the
trash can on the
other
side
of
the room.
The
ashes, insensible to
Kelly's
cue,
fell
straight
down.
When
one
cigarette
burned
down,
it
was
time
to
light
the
next.
Kelly
ceremoniously
stamped
each
butt
out
on Logan's floor.
Faced
with
a
difficult
problem,
Kelly
would
sit
back,
put
his
feet
63


## Page 69

FORTUNE'S
FORMULA
up
somewhere,
take
another
drag,
and
say
something
showing
the
most
amazing
insight.
Manfred
Schroeder
and
Billy
Kluver
rated
Kelly
the
smartest
person
at
Bell
Labs
next
to
Shannon
himself.
Kelly
and
Shannon
did
not
become
well
acquainted
until
just
be
fore Shannon left
Bell
Labs.
I came across one anecdote involving
them
both.
Robert
Fano
remembered
the two men visiting
MIT
circa
1956.
One
evening
after
dinner
they
walked
past
the
school's
Kresge
Auditorium.
Designed
by
Eero
Saarinen,
it
is
a
low,
dome-
shaped
building
whose
roof
is
thinner
in
proportion
to
its
area
than
an
eggshell.
Students
found
it
an
irresistible
climbing
challenge.
Upon
hearing
this,
Shannon
and
Kelly
kicked
off
their
shoes
and
began
scaling
the
dome.
Campus
police
showed
up
to
stop
them.
Fano
was
barely
able
to
talk
them
outof
arresting
the
"distinguished
visitors
from
Bell
Telephone
Laboratories."
Kelly's
career
covered
a
variety
of
fields.
He
started
out
studying
ways
to
compress
television
data.
This
brought
him
into
Shannon's
new
discipline
of
information
theory,
which
Kelly
probably
ab
sorbed
through
his
own
reading.
Kelly
was
drawn
into
a
line
of
research
that
had
proven
to
be a
black
hole of
time,
money,
and
talent.
It
was
voice
synthesis-
teaching
machines
to
talk.
Bell
Labs'
people
had
been
interested
in that idea since the
1930s.
It
was
like
alchemy.
The people in the
field
perpetually
felt
themselves
to be on the
verge
of a
great
and
profitable
breakthrough
that
required
just
a
few
more
years
and
a
few more
dollars.
The
breakthrough
was
never to come,at least not
in
Kelly's
short
life.
The
original
goal
was
not
talking
computers
but
conserving
bandwidth. In the
1930s,
Bell
Labs'
Homer
Dudley
determined that
phone
conversations
could
be
compressed
by
transmitting
phonetic
scripts
rather than
voices.
In
Dudley's
scheme,
the
system
would
break
speakers'
words
into
a
series
of
phonetic
sounds
and
transmit
a code for those sounds. At the
other
end
of
the line, the phone
would reconstitute the words
phonetically,
with some approxima
tion of the
original
voice
and
intonation.
This
system
was
called
a
64


## Page 70

Entropy
"vocoder"
(for
voice
coder).
Dudley
exhibited
such
a
device
in a
grand
art
dcco
pavilion
at
the
1939
World's
Fair.
Dudley's
vocoder
could
send
twenty
conversations
on
a
line
that
previously
carried
one.
The
downside
was
that
the
reconstituted
voices
were
barely
intelligible.
Bell
Labs
was
slow
to
abandon
the
vocoder
concept.
As
late
as
1961,
Betty
Shannon's
former
boss,
John
Pierce,
half
seriously
pro
posed
to
extend
the
vocoder
concept
to
television
or
videophones.
"Imagine
that
we
had
at
the
receiver
a
sort
of
rubber)'
model
of
the
human
face,"
Pierce
wrote.
The
basic
idea
was
that
every
American
home
would
have
an
electronic
puppet
head.
When
a
call
came
in,
the
puppet
head
would
morph
to the
appearance
of a
distant
speaker,
and
you'd
converse
with
it, as the
puppet
head
mimicked
every
word
and
facial
expression
of
the
calling
party.
Kelly
worked
on a
more
sophisticated
idea,
rule-based
speech
synthesis.
Given
the
phonetic
pronunciation
of a
dictionary,
a
hu
man can
pronounce
almost
any
word.
Kelly
was
attempting
to pro
gram a computer to perform the same feat. He would feed a
computer
phonetic
spellings
on
punch
cards.
The
computer
would
use
that,
and a set of
rules,
to
enunciate
the
words.
Kelly
and
others
discovered,
however,
that
spoken
language
is
a
slipper)',
intercon
nected
thing.
The
way
a
letter
or
syllabic
sounds
depends
on
con
text. Kelly tried to devise rules to account for this, and an efficient
way
of
encoding
not
only
word
sounds
but
also
intonation.
At the same world's fair where AT&T
debuted
the vocoder,
NBC's
General
Sarnoff
made
the
famously
misguided
prediction
that
"tele
vision
drama of
high
caliber
and
produced
by
first-rate
artists
will
materially raise the level of dramatic taste of the nation." Moe
Annenberg's
son,
Walter,
bet
his
fortune
on the
new
medium
by
founding
TV
Guide.
For
every
Paddy
Chayevsky,
however,
there
were
a
thousand
hucksters
dreaming
up
new
and
improved
ways
for
TV
to
prostitute
itself.
The
latest
outrage
of the
postwar
era
was
"give
away
shows."
A
show's
host would phone a random
American.
The
luck)'
citizen
would
have
to
answer
the
phone
with a
prescribed
65


## Page 71

fortune's
formula
catchphrasc
that
had
been
given
out
on
the
broadcast—or
else
an
swer
a
question
whose
answer
had
been
supplied
on the
show—in
order
to win a prize.
The
shows
were
a
way
of
bribing
people
to
stay
glued
to theTV
screen or radio dial. In 1949 the Federal
Communications
Commis
sion,
in
one
of
its
periodic
turns
as
guardian
of
public
taste,
banned
giveaway
shows.
It
did
this
on
the
dubious
theory
that
they
consti
tuted
illegal
gambling.
The
FCC
vowed
not
to
renew
the
license
of
any
station
broadcasting
giveaway
shows.
Such
programs
disap
peared
from
the
air.
The
three
major
broadcast
networks
took
the
case
to the
Supreme
Court.
In
1954
the
Court
sided
with
the
networks.
Give
away
shows
were
legal.
This
ruling
opened
the
floodgates.
On
June
7,
1955,
CBS
Televi
sion
responded
by
airing
a
new
quiz
show,
The
$64,000
Question.
It
was
loosely
based
on oneofthe
old
radio
giveaway
shows.
Take
It
or
Leave
It.
The
show's
producers
took
the
Supreme
Court
decision
as
license
to
award
vastly
bigger
prizes
than
had
ever
been
offered
on a
game
show.
The top
prize
on the old
radio
show
had been
S64.
A contestant who
answered
the
first
question
correctly
on the
TV
show won Si.
Prizes
doubled with each
succeeding
question-
jumping
from
S512
to
Si.ooo
to
keep
the
amounts
round—and
con
tinuing
to
double,
all
the
way
up
to a
top
prize
of
$64,000.
The
twist
was
that the contestants had to risklosingeverythingthey had
won in order to have a crack at the next question. It was double or
nothing.
The
most
successful
contestants
sat
in
the
"Rcvlon
Isolation
Booth"
to
keep
them
from
hearing
shouted
help
from
the
studio
au
dience.
The
producers
turned
off
the
air-conditioning
in
the
booth
so that
close-ups
would
show
beads
of
sweat
on the
contestants'
foreheads.
The
quiz
show
was
as big a
sensation
as the
Kefauver
hearings
had
been.
It
captured
as
much
as
85
percent
of the
viewing
audience and led to dozens of copycat shows.
The
show's
contestants
became
celebrities.
There
was
Redmond
O'Hanlon, the Staten
Island
cop who
was
an expert on
Shakespeare
...
Joyce
Brothers,
the
psychologist
who
knew
about
prizefighters
...
66


## Page 72

Entropy
Gino
Prato,
the
Bronx
cobbler
who
knew
opera
. . .
Some
viewers
placed
bets on
which
contestants
would
win.
The
$64,000
Question
was produced in New
York
and aired live on the East Coast. It was
delayed
three
hours
on the
West
Coast.
One
West
Coast
gambler
learned
the
winners
by
phone.
Fie
placed
his
bets
before
the
West
Coast airing, already knowing the winners.
According
to the
mimeographed
notes for a lecture that Shan
non
gave
at
MIT
in
1956,
it
was
"news
reports" of this con that
inspired
John
Kelly
to
devise
his
mathematical
gambling
system.
I
have
looked
through
back
issues
of
newspapers
and
magazines
try
ing
to
find
stories
about
betting
on
The
S64,ooo
Question
or the un
named
West
Coast
bettor,
without
luck.
The
only
thing
I
came
up
with
was
that
similar
scams
have
been
reported
for
the
recent
reality
shows
Survivor,
The
Bachelor,
and
The
Apprentice.
All
were
taped
in re
mote
locales
or on
closed
sets,
and
contestants
and
crew
pledged
to keep the winner secret until the
airdate.
An Internet
casino,
Antigua-based
BetWWTS.com,
was
taking
betson the
shows'
win
ners.
In
each
case,
the
casino
suspended
betting
after a
number
of
large
bets
were
placed
on
one
contestant,
suggesting
that
someone
had
inside
information.
In any
case,
Kelly
wasable to connect the
$64,000
Question
con to a
theoretical
question
about
information
theory.
Shannon's
theory,
born
of
cryptography,
pertains
exclusively
to
coded
messages.
Some
wondered
whether
the
theory
could
apply
in
situations
where
no
coding
was
involved.
Kelly
found
one.
Though
he
worked
in a dif
ferent department and did not then knowShannon
well,
he decided
he
should
tell
him.
Shannon
urged
Kelly
to
publish
his
idea.
Unlike
Shannon,
Kelly
was
prompt
at doing so.
67


## Page 73

FORTUNE
s
formula
Private
Wire
Kelly
described
his
idea
this
way:
A
"gambler
with a private
wire"
gets
advance
word
of
the
outcome
of
baseball
games
or
horse
races.
These
tips
may
not be
lOO
percent
reliable.
Theyare
accurate
enough
to
give
the
bettor
an
edge.
The
bettor
is
able
to
place
bets
at
"fair"
odds that
have
not been
adjusted
for the secret
tips.
Kelly
asked
how
the
bettor
should
use
this
information.
This is not the
no-brainer
you
might
think.
Take
an
extreme
case.
A
greedy
bettor
might
be
tempted
to bet
his
entire
bankroll
on
a horseon the
basis
of the
inside
tips.
The more he
wagers,
the more
he
can
win.
The
trouble
with
this
policy
is that the
tips
are not
necessarily
sure
things.
Sooner
or
later,
a
favored
horse
will
lose.
The
gambler
who
always
stakes
his
entire
bankroll
will
lose
everything
the
first
time
that
a tip is wrong.
The
opposite
policy
is
bad,
too.
A
timid
bettor
might
make
the
minimum bet on eachtip.That
way
he can't losetoo muchon a bum
tip.
But
minimum
wagers
mean
minimum
winnings.
The
timid
bet
tor
squanders
the
advantage
his
inside
information
provides.
What
should
the
bettor
do?
How
can he
make
the
most
of
his
tips without
going
broke?
Those
lucky
souls
who
strike
it
rich
at
the
track
do
so
by
parlaying.
They
win,
then
put
some
or
all
of
their
winnings
on
another
win
ning
horse,
and
then
on
another,
and
so
on,
increasing
their
wealth
exponentially
at
each
step.
Kelly
concluded
thata
gambler
should
be
68


## Page 74

Entropy
interested
in
"compound
return,"
much
as
an
investor
in
stocks
or
bonds
is.
The
gambler
should
measure
success
not in
dollars
but
in
percentage
gain
per
race.
The
best
strategy
is
one
that
offers
the
highest
compound
return
consistent
with
no
risk
of
going
broke.
Kelly
then
showed
that the
same
math
Shannon
used
in
his
the
ory of
noisy
communications
channels
applies
to this
grecdy-
though-prudent
bettor.
Just
as it is
possible
to
send
messages
at a
channel's
bandwidth
with
virtually
no
chance
of error, it is
possible
for
a bettor to
compound
wealth
at a
certain
maximum
rate,
with
virtually
no
risk
of
ruin.
The
have-your-cake-and-eat-it-too
feature
of Shannon's theory also
applies
to
gambling.
Kelly
analyzed
pari-mutuel
betting.
At
U.S.
and
many
Asian
race
tracks, the
bettors
themselves set the odds.
The
track adds up every
"win"
wager
on a
given
race,
deducts
a
track
take
for
expenses
and
taxes,
and
distributes
the
remaining
money
to the
people
who bet
on the winning horse.
The
payoffs
therefore
depend
on
how
much
money
was
wagered
on the
winning
horse.
This
is
easiest
to
explain
in the
case
of a
track
with no take. Suppose
one-sLxth
of the money is bet on Smarty
Jones,
and SmartyJones
wins.
Everyone
who bet on Smarty
Jones
to
win
will
then get
back
six
times
their
wager.
This is
conventionally
expressed
as
odds:
"Smarty
Jones
is
paying
5 to
1."
That
means
that
someone
who
betsSio
wins
a
profit
of
S50
plus
the returnof the Sio
wager
(for a total of S60).
Kelly
described
a
simple
way
for
a
gambler
with
inside
tips
to
bet. It is
practical
only
at a
track
with
no
take
(there aren't
any!)
or
in a case where the inside tips are highly
reliable.
The strategy is to
bet
your
entire
bankroll
each
race,
apportioning
it
among
the
horses
according
to
your
informed
estimate
of
each
horse's
chance
of
winning.
With
this
system,
you
bet on
every
horse
running.
One
horse
has
to win. You
are
certain
to win
one
bet
each race. You
can
never
end
up completely broke.
69


## Page 75

FORTUNE
S
FORMULA
Strangely
enough,
this
is
also
the
fastest
way
to
increase
your
bankroll.
Most
people
find
this
hard
to
believe.
You
don't
get
rich
in
roulette by betting on every
number.
That's
because
the
payoffs
in roulette
favor
the
house.
The situa
tion is different at our
imaginary
track
with no
take—and
with
inside
tips.
Look
at the tote
board.
The
posted
odds
reflect
the
aggregate
beliefs
of
all
the poor slobs with no inside information.
Should
you
bet
your
bankroll
according
to
posted
odds,
you
would
invariably
win
back
your
bankroll
every
race
(again,
assuming
no
track
take).
If
the
odds
on
Scabiscuit
are
2 to
I—meaning
that
the
public
believes
he
has
a
i-in-3
chance
of
winning—you
would
put'/,
of
your
bankroll
on
Scabiscuit.
And
if
Seabiscuit
won,
you
would
get
back
three
times
your
wager,
or
100
percent
of
your
original
bankroll.
The
same
goes
for
any
other
horse,
favorite
or
long
shot.
Kelly's
gambler
ignores
the
posted
odds.
The
private
wire
gives
him a more accurate picture of the
real
chances
of the
horses
win
ning.
He
apportions
his
money
according
to
his
superior
estimates
of the probabilities.
Take
the
most
clear-cut
case.
The
private
wire
says
that
Man
o'
War is a sure thing. It is
known
from
experience
that the
wire's
in
formation
is
always
right.
You
can be certain that
Man
o' War
has
a
lOO
percent
chance
of
winning
and the other
horses
have
zero
chance.
Then
that
is
how
you
should
apportion
your
money.
Bet
lOO
percent
on Man o' War and zero on the
other
horses.
When
Man
o' War
wins,
you
will
collect
a profit
according
to the tote-
board
odds.
This
is
obviously
the
best
way
of
profiting
from
a
100 percent sure inside tip.
Kelly's
(and
Shannon's)
system
more often deals with uncer
tainty.
In the
real
world,
nothing
is
a
sure
thing.
It
might
be
that the
wire
service
is
sometimes
wrong
or
intentionally
deceptive—or
there's
noise
on the
line
and
you
can't
be
sure
you
heard
the tip
right.
It
might
be that the
wire
service
gives
only
probabilities,
like
a
rain
forecast,
or it
supplies
inside
information
whose
significance
you
must
interpret
for
yourself
("Phar
Lap
didn't
eat
his
breakfast").
Shannon's
theorem
of
the
noisy
channel
describes
a
quantity
70


## Page 76

Entropy
aptly
called
equivocation.
It isa
measure
of
ambiguity.
In the
case
of an
unreliable
source
(assuming
you
choose
to
consider
that
source
as
part of the
communications
channel),
equivocation
can be due to
words that sound alike, typos, intentionally
vague
statements, mis
takes,
evasions,
or
lies.
Equivocation
describes
the chance that a re
ceived
message
is
wrong.
Shannon
showed
that
you
must deduct
equivocation
from
the
channel
capacity
to get the
information
rate.
Kelly's
gambler must also take
equivocation
into account. He
places
bets
according
to
his
best
informed
estimates
of the
probabil
ities.
When
you
believe
that War
Admiral
has a 24 percent
chance
of
winning,
you
should
put 24
percent
of
your
capital
on War
Admi
ral.
This
approach
has
come
to be
called
"bettingyour
beliefs."
In the long run, "bet your
beliefs"
will
earn you the
maximum
possible
compound
return—provided
that your
assessment
of the
odds is more accurate than the public's.
You
may
still be
wondering,
why
not just bet on the
horse
most
likely
to
win?
The
quick
answer
is that the
horse
most
likely
to win
might
not
win.
Say
you
have
a
very
accurate
wire
service
and
believe
that Northern Dancer has a 99 percent
chance
of
winning.
You
bet
99 percent of your money on Northern
Dancer.
But you keep the
other I percent in your
pocket.
There
is a 1 percent chance that Northern Dancer
won't
win.
Should that
happen,
you'll
be left with only the pittance in your
pocket.
You
would
have
done better to
hedge
your bets by
wagering
that pittance on
all
the other
horses.
You
would
be sure to win
something,
and
possibly
a
lot.
The betson the
horses
you
think
will
lose are a valuable "insurance
policy."
When rare disaster strikes,
you'll be glad you had the insurance.
There is a
poetic
elegance
to "bet
your
beliefs."
You
play
the
happy
fool.
You
ignore the odds on the tote board and bet on every
horse
according
to your
own
private
beliefs.
Nothing
could
be more
simple (-minded). Nothing
achieves
a better return on investment.
Those of
less
poetic
mind
will
note that "bet your
beliefs"
is of
71


## Page 77

FORTUNES
FORMULA
little
use
at a
real
track.
U.S.
racetracks
skim
anywhere
from
14 to
19
percent
of the
amount
wagered.
It's
25
percent
in
Japan.
That
means
that
anyone
who
betsan
entire
bankroll
on
every
race
is
giv
ing 14 to 25 percent of that bankroll to the track each time out. It
would
take a
phenomenally
accurate
stream
of
inside
tips to over
come
that.
Kelly
describes an alternate and more useful version of the same
basic
system.
I
will
give
a
slightly
different
formula
from the one in
Kelly's
1956
article.
It is easier to remember and can be used in
many
types
of
gambling
situations.
It is what
gamblers
now
call
the
"Kelly
formula."
The
Kelly
formula
says
that
you
should
wager
this
fraction
of
your bankroll on a
favorable
bet:
edge/odds
The
edge
is
how
much
you
expect
to
win,
on the
average,
assum
ing
you
could
make
this
wager
over
and
over
with
the
same
proba
bilities.
It is a
fraction
because
the profit is
always
in proportion to
how much you
wager.
Odds
means
the
public
or
tote-board
odds.
It
measures
the profit
if
you
win.
The
odds
will
be
something
like
8 to
1,
meaning
that
a
winning
wager
receives
8 times the amount
wagered
plus return of
the
wager
itself.
In the
Kelly
formula,
odds
is not
necessarily
a
good
measure
of
probability.
Odds are set by
market
forces,
by
everyone
else's
beliefs
about the
chance
of
winning.
These
beliefs
may
be
wrong.
In
fact,
they
have
to be
wrong
for
the
Kelly
gambler
to
have
an
edge.
The
oddsdo not
factor
in the
Kelly
gambler's
inside
tips.
Example: The
tote-board
odds for
Secretariat
are 5 to I.
Odds
are a
fraction—5
to 1
means
V,
or
5.
The 5is
all
you
need.
The
wire
service's
tips
convince
you
that
Secretariat
actually
has
a
i-in-3
chance
of
winning.
Then
by
betting
Sioo on
Secretariat
you
stand a
'/(
chance
of
ending
up
with
S600.
On the
average,
that is
worth S200, a net profit of Sioo. The edge is the
Sioo
profit di
vided by the Sioo
wager,
or
simply
I.
72


## Page 78

Entropy
The
Kelly
formula,
edge/odds,
is
'A.
This means that youshould bet
one-fifth of your bankrollon
Secretariat.
A couple of
observations
will
help to
make
sense of this.
First:
Edge
is
zero
or
negative
when
you
have
no
private
wire.
When
you
don't
have
any
"inside
information,"
you
know
nothing that
anyone
else
doesn't.
Your
edge
will
be zero (or
really,
negative
with the track
take).
When
edge
is
zero,
the
Kelly
wager,
edge/odds,
is
zero.
Don't bet.
Edge
equals
odds
in
a
fixed
horse
race.
The most
informative
thing
you
can learn from a privatewire is that the race has been
fixed
and that
such and such a horse is certain to win. How much you can make on
a
fixed
race depends on the odds. It's better for the sure-to-win
horse to
have
long odds. At odds of 30 to
1,
a
Sioo
wager
will
get
you $3,000 profit. When a horse
has
to
win,
your edge and the pub
lic odds are the
same
thing (30 in this
case).
The
Kelly
formula
is
30/30 or 100 percent.
You
stake everything you'vegot.
You
do unless you suspect that people who fixhorse racesarc not
always
trustworthy.
"Equivocation"
will
reduce
your
estimated
edge
and should reduceyour
wager.
One of
Kelly's
equations is as
beautifully
daring as £ =
mc1.
Kelly
showed
that
G = R
max
The G is the
growth
rate of the
gambler's
money.
It's a
way
of
stating the
compound
return rateon the bettor's
"investment."
The
subscript
max
means
that
we're
talking
about the
maximum
possible
rate
of
return.
Kelly
equates this optimal return to
R,
the information transmis
sion rate in Shannon's
theory.
The maximum rate
of
return is equal
to
the
flow
of
"inside
information."
To many of
Einstein's
contemporaries,
£ =
mc1
made no sense.
Matter and energy were
totally
different
concepts.
Kelly's
equation
provokes
similar
mystification.
Money
equals
information?
Howdo
you equate bits and bytes to
dollars,
yen,
and
euros?
73


## Page 79

FORTUNE
S
FORMULA
Well, first
of
all,
currency
units
don't
matter. G
describes
a rate
'
max
of
return,
as
ina
percentage
gain
per
year,
or
so
many
basis
points
(a
basis
point is a hundredth of a
percentage
point of
annual
return).
A 7
percent
return
is a 7
percent
return in any currency.
The R is the
information
rate in bits per time unit. The time
units
have
to be the
same
on both
sides
of the
equation.
When
you
measure return in percent per
year,
you need to measure informa
tion rate in bits per
year,
too.
Today,
a
racetrack
tip is
likely
to
come
by
mobile
phoneor Inter
net. These
relatively
high-bandwidth
channels
may
use
thousands
or
millions
of bits just to
say
"Seabiscuit
is a sure
thing."
The tipster
may
fill
more bandwidth with small talk.
Obviously,
small
talk
does
not add to the
gambler's
potential
gain.
Nor
does
having
a
voice
channel
add
anything,
when
the
same
information
could
be
conveyed
in
fewer
bits
as
a
text
message
or
something
even
more
concise.
Kelly's
equation
sets
only
an upper
limit on the profit
you
can
obtain
from
a
given
bandwidth.
This
maximum
will
occur
only
when
the
winning
horse
is
signaled
in the
fewest
bits
possible.
Think of
something
more
along
the
lines
of the
original
wire
services,
with a
messenger
flashing
the winner with a
flash
or
no-flash
code.
The most
concise
way
of
identifying
one
winning
horse
out of
eight equally likelycontenders is to use a
three-bit
code.
There
are
eight
3-digit
binary
numbers
(000, 001, 010, Oil,
lOO,
101,
no,
in).
Assign
a
number
to
each
of the
horses.
Then
you
need
3bitsto
identify
the
winning
horse.
Were
this 3-bit tip a sure
thing,
the bettor
could
wager
hisentire
bankroll
on the
named
horse.
At a
take-free
track
where
all
eight
horses are judged
equally
likely
to
win,
every
dollar bet on the win
ning
horse
would
return
S8.
Kelly's
bettor can
increase
his
wealth
by
a factor of 8 every time he
receives
3 bits of information. Notice that
8 =
23.
The 3 is an
exponent,
and it
determines
how
fast
the
gam
bler's
wealth
compounds.
This
exponent
is
equal
to the number of
bits worth of inside tips
received.
In the more
realistic
case
where
the
inside
tips are not
always
right, an equivocation term must be deducted, and the true in-
74


## Page 80

Entropy
formation rate is less than 3 bits per
race.
With lcss-than-totally-
rcliable
tips, the optimal
gambler's
wealth
grows
more
slowly.
£ =
mc1
implies that the merest speck
of
matter contains enough
energy to power a
city,
or incinerate it. G = R
claims
that a
few
bits cangeneratea return
beyond
the
dreams
of any
portfolio
man
ager or loan shark. A
single
bit (per
year,
or per any time unit you
choose)—such
as one
giving
certain word of the outcome of a
fixed
prizefight at even
odds—would
allow a
bettor
to double his
money.
That
is a
lOO
percent return for I bit.
To
translate
G
- R
into
the language
of
Wall
Street:
A
bit
is
max
O o
worth
10,000
basis points.
Minus
Sign
In
ITS
broadest
mathematical
form,
Kelly's
betting
sys
tem is called the
"Kelly
criterion." It may be used to achieve the
maximum
return from any type of
favorable
wager.
In
practice,
the
biggest
problem is
finding
those rare situations in
which
the gam
bler has an
advantage.
Kelly
was
aware
that there is one type of fa
vorable bet
available
to
everyone:
the stock market. People who are
willing to "gamble on stocks make a higher return, on the
average,
than people choosing safer investments like bonds and savings ac
counts. Elwyn
Bcrlckamp,
who worked for
Kelly
at
Bell
Labs, re
members
Kelly
saying
that
gambling
and investmentdiffer only by a
minus
sign.
Favorable
bets are
called
"investments."
Unfavorable
bets constitute
"gambling."
Kelly
hints at an application to investing in his
1956
paper.
75


## Page 81

FORTUNE
S
FORMULA
Although the model adopted here is drawn from the real-life sit
uation of
gambling
it is
possible
that it
could
apply
to certain
other
economic situations. The essential requirements for the
validity
of the theory are the
possibility
of
reinvestment
of
profits
and the
ability
to
control
or
vary
the
amount
of
money
invested or bet in different
categories.
The
"channel"
of the the
ory might correspond to a real communications channel or sim
ply to the totality of inside information
available
to the investor.
"Totality
of
inside
information
available
to the
investor"
may
suggest
insider
trading.
Shannon
was
once
asked
what kind of
"information"
applied
to the stock
market.
His
slightly
alarming
answer
was
"inside
information."
The
informational
advantage
need not be an
illegal
one. An in
vestor who uses research or computer models to estimate the values
of
securities
more
accurately
than the rest of the market mayuse the
Kelly
system.
Yet
it
may
be worth
acknowledging
that a certain eth
ical
ambiguity
has
always
been attached to
Kelly's
system.
In de
scribing
his
system,
Kelly
resorted
to
louche
examples
(rigged
horse
races,
a con game
involving
quiz
shows
...).
The subtext is that peo
ple do not
knowingly
offer the
favorable
opportunities
that the
Kelly
system
exploits.
The
system's
user must
keep
quiet about what he or
she is doing. Just as a steam engine cannot
move
when all tempera
ture
differences
are
eliminated,
the
Kelly
gambler must stop when
his
private
information
becomes
public
knowledge.
The storyof the
Kelly
system
isa storyof
secrets—or
if you pre
fer,
a story of
entropy.
Some
AT&T
executives
detected
an
unwholesome
moral
tone
in
Kelly's
article. He had submitted it to the
Bell
System
Technical
Journal.
The
executives
worried
about the
title,
"Information
Theory and
Gambling."
They
feared
the
press
might
get hold of the articleand
conclude that
Bell
Labs
was
doing work to benefit
illegal
bookies.
That
was
still a
touchy
subject
with
AT&T.
Bookies
were still big
customers.
76


## Page 82

Entropy
Kelly
played
good
employee.
Fie
changed
the titleof
his
paper
to
the understated
"A
New Interpretation of Information
Rate."
Shan
non
rcferecd
the
paper,
and it
appeared
under that title in the
July
1956
issue.
Kelly
didn't mention TV quiz
shows
in his article. He had no
way
of
knowing
that
many
of the
contestants
were
being
fed
ad
vance
knowledge
of
questions
or
answers.
(The quiz
show
scandal
broke in
1958.)
Kelly's
chosen
metaphor,
of a
racetrack
wire
service,
was
topical
enough
in the
post-Kefauvcr
era.
It too
had
a
signifi
cance
Kelly
probablydidn't
appreciate.
J.
Edgar
Hoover
had
long
denied
the
existence
of a
nationwide
organized
crime
syndicate.
This
stance
changed
only
modestly
with
the
Kefauver
hearings.
Hoover
biographers
have
theorized
that the
FBI
head
felt
the
Combination
was
too
well
connected
to
eliminate
and he preferred not to pick a
fight
he couldn't
win;
that the viru
lently
anti-Communist
Hoover
harbored
sympathy
for
self-made
mob
figures,
whom
he
saw
as
examples
of the
American
capitalist
system;
that
Meyer
Lansky
or
Frank
Costcllo
had
a
photograph
of
Hoover
in a
sexual
situation
with
a
male
friend
and
were
blackmail
ing him.
The
best-supported
explanation
(it need not
exclude
the other
theories)
is
this:
Hoover
and
his
partner
Clyde
Tolson
would
regu
larly
leave
the
office
when
the
horses
were
running.
They
would
take a
bulletproof
car to
Pimlico,
Bowie,
Charleston, or
other
area
racetracks.
News
photographers
snapped
Hoover
at the
$2
betting
windows,
and
Hoover
had
a
form
letter
he
sent
irate
citizens
who
complained
about his
wagering.
The letter said he had
made
a
few
minimal
bets
in
order
not
to
offend
business
associates.
In a 1979 book.
The
Bureau:
My
Thirty
Tears
in
Hoover's
FBI,
the
agency's
William
C.
Sullivan
reported
that
Hoover
"had
agents
. . .
place his real bets at the
hundred-dollar
window,
and
when
he won
Hoover
was
a
pleasure
to workwith for
days."
According
to FBI
sources
and
staffers
of
gossip
columnist
Wal
ter
Winchell,
Hoover
was
getting inside tips from Frank
Costello.
When
the
mob
fixed
a
race—and
this
apparently
meant
with
close
to 100 percent
certainty—Costello
passed
the name of the winning
77


## Page 83

fortune's
formula
horse to
Floover
by
way
of
Winchcll,
a
mutual
friend.
These tips let
Hoover
make
a
small
fortune—and
presumably
left him
disinclined
to pursue Costcllo and his
business
partners.
After Floover's 1972 death, Costello told a Justice
Department
chief:
"You'll
never know how manyraces I had to
fix
for those lousy
bets
of
his."
78


## Page 85

*
Pearl
Necklace
In
January
1961
the
American
Mathematical
Society
held its
winter
meeting
in
Washington.
Ed
Thorp
was
there to
present
a
version
of the
paper
Shannon
submitted
to the
National
Academy.
Since
this paper
was
not for the
National
Academy,
Thorp titled it
"Fortune's
Formula:
A
Winning
Strategy
for
Blackjack."
That title
caught
the
eye
of
an
AP
reporter
in
Washington.
Thorp did an
impromptu
interview
and
photo
session.
The
morn
ing
of
January
21,
a
feature
appeared
on the
front
page
of
The
Boston
Globe
and in
papers
nationwide.
Gamblers
from
all
over
the
country
began
calling
Thorp's
hotel
to
ask
for
copies
of
his
paper.
Some
of the
callers
wanted
to
buy
Thorp's
blackjack
system
or take private
lessons.
Others wanted to
finance
Thorp in the
casinos
for a shareof the
profit.
The
messages
continued after he returned home. Vivian filled
every
page
of a
legal
pad
with
messages.
Then
she
said
enough
and
refused to take any
more.
The
Pavlovian
connection between the
telephone
ringing
and
family
discord
affected
the Thorps' baby
daughter.
She
burst
into
tears
whenever
the
phone
rang.
At MIT Thorp shareda groupof six
secretaries
with his depart
ment. Thorp got more
mail
from
the
blackjack
paper than
all
the
other
mathematics
instructors
had
gotten
for
every
paper
they
ever
published
put
together.
The
university
told Thorp they
could
not
permit the
secretaries
to
deal
with
any
more
gambling
correspon
dence. In all,
Thorp
received
thousands of letters.
81


## Page 86

FORTUNES
FORMULA
Thorp
discussed
the
situation
with
Shannon.
Thorp
wanted
to
accept
oneof the
offers.
It
would
be
fun
to try the
blackjack
system
out in a
real
casino.
Shannon
suggested
that Thorp
use
Kelly's
for
mulato decide how
much
to bet.Thorp read
Kelly's
1956
article and
instantly
appreciated
its
relevance.
It
told
exactly
how
much
to
bet,
depending
on
how
favorable
the
deck
was.
Despite
the
Kelly
for
mula's
theoretical
protection
against
ruin,
both
Shannon
and Thorp
realized
that there are
many
variables
in
casino
play.
They
agreed
that Thorp
needed
to
make
sure
his
financial
backer
could
afford
to
lose
the
money
he put
up.
Some
of the
offers
had
the
reck
of
des
peration.
Thorp
decided
that
the
best
offer
was
the
biggest
one.
A
syndi
cate
of
two
wealthy
New
Yorkers
was
offering
$100,000 to
take
on
the
Nevada
casinos.
Thorp
dialed
the number on the letter and
asked
to speakto
Emmanuel
Kimmel.
One
Sunday
in
February
1961,
a
midnight
blue
Cadillac
pulled
up to
the
Thorps'
Cambridge
apartment.
Driving
the
car
was
a
dazzling
young
blonde
woman
in a
mink
coat.
Next
to her
was
another
blonde,also in a mink coat. Not until the womengot out of the car
was it evident that there had been someone sitting between them.
The someonewas
"Manny"
Kimmel.
Kimmel
was
an
elderly,
gnomelikc
man
standing
about
five
feet
five.
He wore a long
cashmere
coat and had a
ruddy
face
topped
with
a
shock
of
white
hair. He
introduced
the
two
blondes
as his
nieces.
Fiedid not seem to be
joking.
The minks and
cashmere
were
justified
by the bitter
weather.
Kimmel
complained
that the
snow
in
New
York
had just cost him
$1.5
million.
Asked
how,
he
explained
that he owned sixty-four
parking
lots.
They had been
snowed
out for two
days.
I hope
you've
been
practicing,
Kimmel
said.
Thorp said he
had.
Kimmel
pulled
out a
deck
and
began
dealing
hands
to Thorp.
The
goal
in
blackjack
is to get a
hand
whose
cards
total
more
than the dealer's hand without
exceeding
21.
A
player
who
exceeds
21
loses.
82


## Page 87

Blackjack
In a
casino,
there can be one to
six
players.
Each
places
a bet and
is
dealt
two cards facedown. The dealer also deals
himself
a hand,
one card
faceup.
Numbered cards count as their face
value.
Tens and
all the face cards
count
as 10. Aces can
count
as I or II,
whichever
is
better.
Should
you
get a io-valuecardand an aceon the
initial
deal,
that is
"blackjack."
A
player
getting
blackjack
wins—unless
the
dealer
also
has
blackjack
for
a
tie.
A
winning
blackjack
pays
off
3
to
2.
Otherwise,
players
have
the
option
of
asking
for
more
cards,
one
at a
time.
These
additional
cards
arc
dealt
faceup.
A
player
may
keep
"hitting" as long as her hand is
less
than
21.
Once her hand totals
over
21,
she
loses.
The
trick
is to
know
when
to
stop.
The
decision
should
take
account
of
the
dealer's
faceup
card.
Unlike
the
players,
the
dealer
is
required
to
follow
a
fixed
strategy.
He
must
draw
cards
until his hand totals 17or more.
Say
you've
gota
queen
anda
six
for
a
total
of
16.
That'snot a
very
good
total.
By
drawing
another
card,
you
risk
going
bust (there are
all
those
tens,
and
a
ten
would
take
your
total
to
26).
Computer
studies
have
shown
what
to do
for
every
possible
point
total
and
faceup
dealer
card.
When
the
dealer
has
a
seven
showing,
you're
betteroff
hitting
your
16
hand.
A
normal
winning
hand
pays
even
money.
Kimmel
appeared
to be
interested
only
in
finding
out
whether
Thorp's
system
worked.
He
showed
no
interest
in
Thorp's
paper,
and as far as
Thorp
could tell, the math was "Greek" to Kimmel.
Kimmel
demanded that they
play
each other.
Thorp used a
"ten-count"
system,
different
from
the
five-count
detailed
in the
article.
Though
each
five
affects
the odds more than
each
ten, there are
16
"tens"
(including
the
face
cards)
in the
deck,
making
it easier to
identify
favorable
or
unfavorable
conditions.
They
played
the
rest
of the
day
and
had
a
rematch
the
following
day.
Kimmel
said he could
back
Thorp onlyon the condition that he
and his partner get a cut of the
profits.
Kimmel
said their cut would
be 90 percent.
Thorp
agreed
to that. He
was
more
interested
in
proving
the
concept
than in
making
a lot of
money.
Thorp
was
also
worried
83


## Page 88

FORTUNE
S
FORMULA
about
cheating.
FIc
had
concluded
that a
cheating
dealer
was
the
only
thing
that
might
upset
the
system.
Kimmel,
an
experienced
gambler,
assured
Thorp
thathe
was
an
expert
at
spotting
cheaters.
To
seal
the
deal,
Kimmel
dipped
into a deep
cashmere
pocket
and
pulled
out a
handful
of
jewels.
From
this
he
extracted
a
pearl
necklace
and presented it to
Vivian.
Thorp
flew
to
New
York
each
Wednesday
to
play
cards
against
Kimmel.
He won
regularly,
convincing
Kimmel
of his
playing
skills
and the merit of the
counting
system.
Kimmel
occasionally
pre
sentedThorp with the giftof a
salami.
During
one of
these
meetings.
Thorp
met
his
other
backer,
Ed
die Hand. Hand
was
a
dark-haired
heavyset
man in
his
late
forties,
maybe
five
feet
nine,
with
a
taste
for
flashy,
bright-colored
leisure
wear.
He owned a
trucking
business
that shippedcars and trucks for
Chrysler.
He did a lot of
negotiating
with
Teamsters.
Hand
had
a
perpetually
irritated,
cranky
tone
to
his
voice.
He
was
irresistible
to
women.
Hand had been married to "Gorgeous Gussie" Moran, a 1940s
tennis star who
shocked
Wimbledon
by wearing outfits that ex
posed
the
fringe
ofher
lace
panties.
Hand
was
a
decent
tennis
player
himself. Moran had said she was
astounded
that
Hand could play
tennis
all
day and then
have
sex
all
night.
Thorp
was
present
once
when
I
land
was
leafing
through
Time
magazine
on a
plane
and
suddenly
grew
choked
up
over
an item
about a
Chilean
copper
heiress
remarrying.
Hand
haddated
her.
There
was
a lot that Thorp didn't knowabout
Manny
Kimmel.
Kimmel
was
then one of the
biggest
bookies
in New
York
City.
"What was he a bookie
for?
For
everything!"
claimed Eddie Hand in
an
interview.
"Vegas,
football,
baseball,
the
horses.
Manny
was
great
at
talking
people
into
betting.
He
could
always
find
a
sucker."
Kimmel's
territory
covered
the
East
Coast horse
tracks
and the
sports
book
operations
at the
El
Rancho
Hotel
in
Las
Vegas.
"At
84


## Page 89

Blackjack
Saratoga
in
the
old
days
he
used
to
straighten
out
the
jockeys,"
ex
plained
Fland.
Straighten
out
the
jockeys
means
to
fix
the
race.
Kimmel
was
the
living
embodiment
of
John
Kelly's
new
interpretation
of
the
information
rate.
In
the
1960s,
Kimmel
took
bets
from
one
of
the
highest
rollers
of
all,
Texas
oil
tycoon
H.
L.
Hunt Hunt had won an oil
field
in a
poker
game.
As
a
billionaire
he
still
had
a
taste
for
risk,
reportedly
betting
as
much
as
a
million
dollars
on
a
football
game.
The
FBI
had
been
following
Kimmel's
career
for
years.
"Kimmel
is
known
to
be
a
lifetime
associate
of
several
internationally
known
hoodlums,"
read
one
1965
FBI
memo.
"Fie
is
an
admitted
gambler
and
consorts
with
many
well
known
gamblers
throughout
the
United
States."
Kimmel
also
knew
more
about
card-counting
than
he
let
on.
Kimmel
had
a
gambling
buddy
named
Joe
Bernstein.
In i960
Bern
stein found himself in a mob-run club in San
Francisco.
Bernstein
owed
his
bookie
$3,000.
He
had
Si.soo
in
his
pocket.
While
decid
ing
what
to
do.
Bernstein
watched
a
game
of
blackjack.
He
noticed
that three-quarters of the deck had been dealt and not one ace had
turned
up.
Bernstein
bet two
hands
of S500
each.
He won both
(one
was
blackjack),
and
had
enough
to
pay
off
the
bookie.
As a born
gambler,
Bernsteinfelt he had
discovered
the secret of
life
itself.
He
soon
determined
that
the
situation
he
had
happened
onto—having
all
the
aces
in the
last
quarter
of the
deck—was
ex
tremely
rare.
After
a
couple
of
days
of
mixed
luck
trying
to
exploit
the idea, Bernstein called Kimmel in New York to tell him
of
his
momentous
discovery.
Bernstein
and
Kimmel
went
to
Las
Vegas
and
experimented
with
various
counting
systems.
Then
Kimmel
heard
about
Thorp's
paper.
A
mathematician
was
just
what
they
needed
to
devise
a
practical
strategy.
Kimmel
divulged
nothing
of
this
to
Thorp.
He
also
had
his
peo
ple
run
a
background
check
on
Edward
and
Vivian
Thorp
to
make
sure theyweren't
grifters.
85


## Page 90

fortune's
formula
Reno
Kimmel
did
not
want
to
go
to
Las
Vegas.
He
intimated
to
Thorp
that
he
was
too
well
known
there.
So
during
MIT's
spring
recess,
Thorp
and
Kimmel
flew
to
Reno
for
the
experiment.
Kim
mel
was
accompanied,
again,
by
two
young
women.
They
checked
into
the
Mapes
Hotel
at
around
2:00
a.m.
Eddie
Hand
was
to
meet
them
ina
couple
of
days.
The
Mapes
was
the
first
Nevada
high-rise
offering
grand-hotel
luxury
in
a
state
of
motels.
Kimmel
insisted
on
a
huge
suite
for
himself
and the
women.
After
a
night's
sleep,
Thorp
and
Kimmel
drove
toa
small
casino
outside
of
town.
This
was
to be a
practice
session,
with
the
experi
ment
proper
not
beginning
until
Hand
arrived.
Thorp
played
with
minimal
bets,
winning
a
little
money
This
boosted
his
confidence
that he
was
able
to
count
cards,
adjust
bet
size,
and
play
under
real
conditions.
The
card-counter
must
adjust
the
size
of
bets
according
to the
deck's
composition.
For
the
most
part,
blackjack
is
a
game
of
even-
money
bets.
This
means
the
odds
are
I
(to
i).
The
Kelly
formula
of
edge/odds
reduces
simply
to
edge.
The
edge
varies
depending
on
what
cards
remain
in
the
deck.
It
may
be
positive,
zero,
or
negative.
The
Kelly
system
says
not
to
bet
at
all
unless
you
have
a
positive
edge.
Thorp
was
afraid
he'd
look
conspicuous
sitting
ata
table
and
watching
intently,
betting
only
oc
casionally.
He
concluded
he
would
have
to
place
at
least
a
minimal
bet on every hand.
In a
moderately
favorable
situation,
a
card-counter
might
have
a
86


## Page 91

Blackjack
51
percent
chance
of
winning.
Out of a
hundred
such
dollar
bets,
he
could
expect
to
win
51,
ending
up
with
S102.
The
edge
is
2
percent
(the
S2
profit
divided
by
the
Sioo
wagered).
When
the
deck
is
like
this,
the
Kelly
formula
says
to bet2
percent
of the
bankroll.
This
estimate
is
not
exact
because
of
the
features
of
splitting
pairs
and
doubling
down.
In
uncommon
situations
it is to the
player's
advantage
to
add
to
bets
already
placed.
The
effect
of
this
is
to
reduce
the
optimal
bet
somewhat.
The out-of-town
casino
closed
three hours in
observance
of
Good
Friday.
Thorp
and
Kimmel
drove
back
to
Reno,
scouting
small
casinos
in
which
to
practice.
Since
the
rules
vary
slightly,
they
wanted
to select casinos with the most favorable rules.
Kimmel
was
known
at
the
casino
they
chose.
He
excused
himself,
telling
Thorp
it
was
best
that
he
not
be
seen
there.
(Throughout
the
trip,
Kimmel
was
running
into
casino
people
he
knew:
neither
side
appeared
delighted
to
renew
the
acquaintance.)
Thorp
spent
the
rest
of
the
day
playing
alone,
much
ofit
on
a
losing
streak.
The
loss
was
onlyabout a hundred
dollars,
due to the
small
bets,
but this an
noyed
Thorp.
He
refused
to goto
bed.
At
about
5
a.m.,
Thorp
got
a
table
all
to
himself.
He
got
off
on
the wrongfoot with the
dealer.
Why
can't
I
play
two
hands?
Thorp
asked.
House
policy,
he
was told.
Eight
other
dealers
let
me
play
ftvo
hands.
It
can
hardly
be
house
policy.
It's
so
you
don't
crowd
the
other
players.
There's
no
one
else
here.
Your
reason
does
not
seem
to
apply.
The
dealer
dealt
as
quickly
as
possible.
Thorp
counted
just
as
fast.
The
deck
turned
sharply
favorable.
Thorp
let
several
bets
ride,
then bet $20 a
hand.
By
the end of the
deck,
he had
recovered
his
Sioo
loss.
On Saturdayafternoon Thorp had a
massive
brunch with
Kimmel.
He
had
a
story
to
top
Thorp's.
Using
the
count
system
ata
big
hotel,
Kimmel
had won
$13,000.
Then he'd lost $20,000.
Reason:
the
dealer
was
a
cheat.
87


## Page 92

fortune's
formula
The
casino
had
brought
in
a
"knockout
dealer,"
an
expert
card-
sharp
who
cheats
for
the
house.
The
cheat
was
a
stern
fortyish
woman
with
black
hair
going
gray.
Kimmel
saw
how
she
did
it.
When
dealing
her
own
hand,
she
would
sneak
a
peak
at
the
top
card.
If she didn't
like
what
she
saw,
she
dealt
the
second
card
instead.
Kimmel
had
the
impression
that
the
count
system
was
powerful
enough
to
overcome
this
type
of
cheating.
(It's
not.)
Kimmel
re
fused
to
leave
the
table.
Fie
poured
back
his
profit
and
$7,000
more.
Kimmel
demanded
to sec the
casino
owner.
He
accused
the dealer
of
cheating.
The
owner
justified
it
by
explaining
that
a
rich
Texan
had
won
$17,000
the
night
before.
They
couldn't
afford
any
more
losses.
After
the
meal,
Thorp
and
Kimmel
returned
to
the
out-of-town
casino
where
they'd
gambled
the
previous
day.
With
larger
bets.
Thorp
won
several
hundred
dollars
in
a
few
minutes
of
play.
This
whetted
Kimmel's
appetite.
He
sat
down
at
the
same
table.
After
two
hours
they
were
ahead
S650.
Then
the
dealer
began
shuffling
the
deck
early,
well
before
the
end
of
the
deck
had
been
reached.
That
was
bad.
Shuffling
erases
the
sometimes-profitable
concentra
tions
of
cards
that
card-counting
identifies.
They
could
hardly
com
plain,
so
Thorp
and
Kimmel
left.
Eddie
Hand
arrived
that
evening.
The
experiment
could
officially
begin.
Kimmel
and
Hand
had
originally
offered
a
bankroll
of
SlOO.OOO.
Thorp
talked
them
down
to
a
$10,000
bankroll.
With
a $100,000
bankroll,
the
Kelly
bets
would
have
been in the thou
sands of
dollars,
even with a moderate
advantage.
Thorp wasn't
comfortable
staking
that
kind
of
money;
it
was
more
than
the ta
ble
limits
of the
time
anyway.
Ten
thousand
was
enough
to test the
system.
To
simplify'
things
somewhat.
Thorp
decided
to
use
$50
as
the
minimum bet. Fiewould double it to $100 when the deck had about
a 1
percent
edge;
bet
S200
when
it
had
about
a 2
percent
advantage;


## Page 93

Blackjack
and
finally,
bet
$500
(the
usual
maximum
bet
in
1961)
when
the
edge
hit or
exceeded
5
percent.
Kimmel
pulled
out a
wad
of
bills
and counted out $10,000 for
Thorp.
Thorp
started
gambling
with
Hand
while
Kimmel
went
off
on
his
own.
They
began
at
Harolds
Club
in
downtown
Reno.
Run
by
a
family
of
carnics,
it
was
known
as
a
folksy,
low-pressure
place
where
dealers
advised
novice
bettors
and
tolerated
the
gamut
of
working-class
America's
darker
impulses.
It
was
said
that
manage
ment
occasionally
stepped
in
and
refunded
10
percent
of a
big
loser's
losses,
topping
it
off
with
the
friendly
advice
to
get
out
of
town pronto. Signs posted around the casino said NO ONE CAN
WIN
ALL
THE
TIME.
HAROLDS
CLUB ADVISES YOU TO
RISK
ONLY
WHAT
YOU
CAN
AFFORD.
Thorp
and
Hand
installed
themselves
at a
S500
maximum
table.
They
won
about
S500
in
fifteen
minutes.
Then
the
dealer
pressed
the
secret
button
on
the
floor.
Wheel
of
Fortune
The
button
was
connected
to
the
private
office
of Har
old
S.
Smith,
Sr.
Smith
worked
behind
double-thick
double-locked
doors,
connected
by
phone
line
to
the
security
catwalks,
where
an
army
of
unseen
operatives
inspected
the
play
from
behind
miles
of
one-way
mirrors.
Smith
kept
himself
alert
with
dozens
of
cups
of
hot
black
coffee
a
day.
Many
days,
he
never
went
home.
Dealers
at
Harolds
Club were
expected
to
inform
Smith
whenever
someone
89


## Page 94

FORTUNE'S
FORMULA
was
winning
too
much
too
fast.
Cheating
was
getting
more
scien
tific,
Smith
well
knew.
A
recent
operation
in the
club
had
used
cards
marked
withan ink
visible
only
in
infrared
light.
The
cheater
wore
special
contact
lenses
to
see
the
markings.
Then there
was
ESP.
Smith
suspected
that
some
players
were
us
ing
telepathic
powers
to
win.
Smith
had
made
a
lifelong
study
of
luck.
He
believed
ina
higher
force
that
governed
the
ebb
and
flow
of
fortune.
Smith
called
this
force
"Lady
Luck."
It
was
after
all
a
literal
wheel
of
fortune
that
started
the
Smith
family's
ascent
to
wealth.
Smith's
father,
Raymond
I.
Smith,
known
as
"Pappy,"
left
Vermont
for
the
lure
of the
mid
ways.
Pappy
operated
the
wheel
and
nail
game
at
carnivals.
The
marks
beton a
number,
and
Pappy
spun
the
wheel.
Should
a
chosen
number
come
up,
the
customer
won
a
pocketknife.
Through
long
hours
and
miserly
thrift,
Pappy
built
a
nest
egg.
Not
being
a
gambling
man
himself,
he
plowed
his
life
savings
into the
stock
market.
Pappy
lost
nearly
everything
in the
1929
crash.
As
an
out-and-out
game
of
chance,
the
wheel
of
fortune
was
ille
gal.
Pappy
needed
to
earn
enough
money
before
the
sheriff
closed
him
down
to
pay
the
fine
and
move
on
to
the
next
town.
When
Nevada
legalized
gambling,
Pappy
saw
a
chance
to
settle
down.
He
teamed
up
with
Harold,
the
twcnty-six-year-old
son
he
had
aban
doned,
and
bought
a
Reno
bingo
parlor
for
$500.
Father
and
son
opened
it
as
Harolds
Club
in
1936.
Harolds Club's theme
was
the Old
West.
The staff dressed like
cowpokes.
The
club
displayed
"the
world's
biggest
gun
collection"—
derringers,
pistols,
rifles,
cannons,
machine
guns—and
most
of
the
guns
had
drawn
blood.
That
firepower
came
in
handy
one
morning
in
1937
Harold
got
word
that
the
mob
intended
to
bust
up
Harolds
Club.
Organized
crime
already
ran
at
least
one
of
the
clubs
in
Reno
and
controlled
prostitution.
At
about
ten
in
the
morning,
when
the
club
was
nearly
empty,
seven
mob
enforcers
came
in,
brazenly
push
ingover
furniture.
Smith
pulled
a
loaded
.38
from
under
the
roulette
table.
"You're
not
going
to
shoot
any
dice,"
Smith
said,
"so
just
turn
around
and
90


## Page 95

Blackjack
walk
out
the
door."
According
to
Smith,
the
mobsters
turned
and
left
the
building,
never
to
bother
the
club
again.
As
Pappy
grew older, he fretted about
succession.
Harold, the
casino's
namesake,
was
an
alcoholic
and
compulsive
gambler.
He
would
go
on
weeklong
benders
in
which
he
would
gamble,
wear
a
cowboy
outfit,
ride
a
horse,
and
shoot
guns.
The
rival
casinos
eagerly
extended
Harold
credit.
They
would
have
liked
nothing
better
than
to
gain
control
of
Harolds
Club,
their
biggest,
most
successful
rival.
Pappy
was
afraid
Harold
would
gamble
using
his
stock
in
the
club
as
collateral.
Pappy
himself
did
not
own
stock
in
the
club,
taking
only
a
salary.
Harolds
Club had just three
stockholders:
Harold,
his
ex-wife
Dorothy,
and
his
older
brother,
Raymond.
Harold
had
resented
Raymond
since
childhood.
Well
into
mid
dle
age,
he
was
seething
over
a
boyhood
incident
in
which
Raymond
had
forced
Harold
to
eat
hen
manure.
Harold
especially
rued
his
own
decision
to
give
Raymond
a
one-third
share
of the
club
in re
turn for
helping
out.
Harold
never
dreamed
that the one-third
ownership
would
soon
make
Raymond
a
millionaire.
Harold
could
console
himself
with
the
thought
that
he
owned
twice
as
much
stock
as
Raymond—until
his
divorce.
Wife
Dorothy
wasa sucker for a man in
uniform.
Wartime Reno
was
full
of them.
In
due
course
the
Smiths
took
advantage
of
Reno's
second
industry.
Dorothy got the
house,
the
kids,
and half of her husband'sstock.
Dorothy
and
Raymond
were
just as
concerned
about
Harold's
drinking
as
Pappy
was.
In
1949
Pappy
came
up
with
a
solution.
It
was
a
stock
option.
The
Smith
family
forced
Harold
to
sign
a
doc
ument
giving
Pappy
the
right
to
buy
all
of
Harold's
stock for
$500,000
if
the stock were ever offered for sale in the next five
years.
The
stock
was
worth
much
more
than
that,
maybe
S8
million.
Bottom
line:
Harold
would
never
offerhis stockfor
sale,
not
unless
he
was
out
of
his
mind.
Even
then,
the
option
would
take
prece
dence
over
a
drunken
sale to an
outsider.
This
Machiavellian
experiment
in
family
finance
was
a
qualified
success.
Harold
didn't
gamble
his
patrimony
away.
The
option
ex
pired,
unexercised,
in
1954.
91


## Page 96

FORTUNE'S
FORMULA
All
the
while,
Harold
fumed
that he
was
being treated like an
irresponsible
child.
He
began
scarfing
handfuls
of
Miltowns,
a
prescription
tranquilizer
that
is
a
dangerous
mix
with
alcohol.
Flarold's
behavior
became
erratic.
On
August
9,
1956,
he
noticed
a
moth
fluttering
around
his
room.
Instead
of
being
drawn
to
the
light,
it
avoided
it.
This
impressed
Harold
as
an
almost
supernatural
manifestation.
A doctor talked Harold into
checking
into St.
Mary's
Hospital.
Not
until
a
nurse
took
his
temperature
with
a
metal
thermometer
did he
understand
exactly
where
he
was.
It
was
the
"psycho
ward."
After the nervous breakdown, Harold vowed not to touch an
other
drop
of
alcohol
for
four
years.
Fie
kept
this
oath.
At
its
com
pletion,
he
celebrated
with
a
thirteen-day
drinking
spree.
Smith
then
vowed
not to
drink
again
for
six
years.
Fie
was
still
on
that
pledge
when
the
bell
rang
informing
him
that
something
was
hap
pening
on the
casino
floor.
More
Trouble
Than
an
$18
Whore
BOTH
Smith
and
his
son,
Harold Junior, showed up at
Thorp
and
Hand's
blackjack
table.
After
getting
the
story
from
the
dealer,
there
was
some
polite
repartee.
Smith
Senior
explained
that
there
were
individuals
who
took
advantage
of
concentrations
of
cards that
sometimes
existedat the end of the
deck.
The telltalesign
was
someone
raising
the
bet
as
the
dealer
neared
the
end
of
the
deck.
92


## Page 97

Blackjack
A
guy
named
Joe
Bernstein
had
taken
the
Sahara
Hotel in
Las
Vegas
for
$75,000
with
an
"ace
count."
Word
got
out
that
Bernstein
was
headed
for
Harolds
Club.
Smith
had
warned
his
people
to
be
on
the
lookout.
He
was
not
notified
until
Bernstein
had
$14,000
of
Harolds'
money
sitting
in
front
of
him.
Bernstein
would
play
seven
hands
at
one
table,
leaving
no
room
for
anyone
else.
He
saw
every
card.
With
eight
hands
in
play
(including
the
dealer's),
a
deck
was
good
for
only
two
deals.
On
the
first
deal,
Bernstein
bet
$5
a
hand.
He
kept
track
of
how
many
aces
turned
up.
If
he
liked
what
he
saw,
he bet S500 a hand on the next deal.
Smith
Senior
instructed
Thorp
and
Hand's
dealer
to
shuffle
twelve
to
fifteen
cards
from
the end of the
deck.
The two
Smiths
re
mained
at
the
table
to
observe
the
results.
After Thorp won a
few
more hands, Senior told the dealer to
shuffle
twenty-five
cards
from
the
end.
Thorp
won
again,
and
Smith
said
to
shuffle
forty-two
cards
from
the
bottom.
They
would
use
only
the
top
ten
cards
of the
shuffled
deck.
There
was
not
much
Thorp and
Hand
could
do under
those
conditions. They left Harolds
Club.
Thorp
was
curious
to
see
the
cheating
dealer
Kimmel
had
met.
They
went
to
the
club
where
she
worked,
and
Thorp
bought
$1,000
in
chips.
FIc
made
a
bet
of
$30.
The
dealer
had
not
finished
dealing
the hand
when
the pit
boss
halted
her.
He
took
the
deck
and
handed
it to a
new
dealer.
She
was
the
grim-faced
woman
with
a
touch
of
gray.
Thorp
was
dealt
a
pair
of
eights.
The
rules
of
blackjack
allow
players
to
split
pairs.
This
means
to
turn
a
pair
of
same-value
cards
faceup
and
split
them
into
two
hands.
The
player
receives
a
new,
facedown
card
for
each
hand
and
plays
them
like
regular
hands.
The
player
who
splits
must
also
double
the
original
bet
as
he
is
playing
two
hands.
Thorp
put
down
another
S30
and
split
the
eights.
He
drew
cards
and
ended
up
with
totals
of20
and
18,
both
strong
hands.
93


## Page 98

FORTUNE'S
FORMULA
The
dealer
had
a
three
showing.
She
turned
up her
hole
card.
It
was
a ten.
She
had
to hit her
13.
Since
Thorp and
Hand
knew
what
to
look
for,
they
saw
what
happened
next.
The
dealer
held
the
deck
edge
up
and,
with
a
finger,
briefly
bent
back
one
corner
of
the
deck's
top
card.
It
was
the
queen
of
hearts.
That
would
have
busted
her.
With
imperceptible
sleight
of
hand,
she
dealt
the
second
card
to
her
hand.
It
was
an
eight.
She
had
21.
Eddie
Hand
bellowed
out
exactly
what
the
dealer
had
done.
Thorp
joined
in.
The
dealer
showed
no
emotion
save
a
blush.
The
pit
boss
listened
to
their
story
and
said
there
was
nothing
he
could
do. It was their word
against
hers.
After
each
gambling
session,
Thorp
met
Kimmel
and
emptied
his
pockets
onto
the
hotel
bed.
They
counted
the
chips
and
cash
to
de
termine
how
well
Thorp
was
doing.
"He'd
watch
me
like
a
hawk,"
Thorp
recalled.
"One
day
I
forgot
to
empty
one
pocket.
I
don't
know
why;
I
was
tired,
caught
up
in
the
excitement
of it
all.
He
got
this
funny
look
on
his
face.
'It
looks
like
we're
short
money'
'Oh,
I've
got
another
bunch
of
chips.'
I'm
sure
that
only
enhanced
his paranoia."
Paranoia
was
in
ample
supply.
The
day
after
the
experience
with
the
cheating
dealer.
Thorp,
Kimmel,
and
Hand
drove
to
the
small
out-of-town
casino.
Thorp
made
a
phone
call.
When
he
came
back,
Kimmel
and
Fland
told him theyhad beenbarred
from
the
casino.
The
floor
manager
said
Thorp
had
won
too
consistently.
They
con
cluded that a
system
was
involved.
Thorp
returned
to
the
Mapes.
Fie
played
alone,
betting
S5
and
up.
The
pit
boss
stepped
over
and
told
him
he
was
no
longer
wel
come.
That went
for
his
two
friends—and
any
other
friends
he
might
have.
The
next afternoon the three men drove to a casino at the south
end of
Lake
Tahoe.
Thorp
bought
$2,000 in
chips
and
pushed
his
way
to
one
of
the
few
seats
ata
blackjack
table.
Two
thousand
dol
lars
qualified
him
as
a
high
roller
at
this
place.
A
pit
boss
appeared
94


## Page 99

Blackjack
and
offered
a
free
meal
and
show.
Thorp
asked
if
his
two
friends
could
be
included
in
that
invitation.
The
pit
boss
agreed.
In
a
few
minutes'
play.
Thorp won
$1,300
and
Kimmel
S2.000.
They
ordered
filet
mignon
and
champagne
for
their
comped
dinner.
This
meal
inspired
such
a
spirit
of
gratitude
that
the
men
took
their
business
to a
neighboring
casino.
This
was
Harvey's
Wagon
Wheel.
Thorp
bought
another
$2,000
of
chips.
He
managed
to
get
a
S25
minimum
table
and
began
win
ning.
Kimmel
joined
him.
According
to
plan,
Thorp
did
the
count
ing
and
signaled
to
Kimmel.
It
took
thirty
minutes
to
clean
out
the
table's
money
tray.
That
is
a
rare
event.
The
money
is
supposed
to
flow
in
the
oppo
site
direction.
"Oh,
help
mc,
please
help
me,"
the
dealer
pleaded.
The
pit
boss
arrived
with
an
entourage.
As
Thorp
played,
the
pit
boss
attempted
to
account
for
his
luck
to
the
other
personnel.
The
pit
boss
prescribed
a
new
dealer.
This
did
not
stop
Thorp
and
Kim
mel's
winning
streak.
About
two
hours
and
five
dealers
later,
they
had
emptied
the
money
tray
a
second
time.
Thorp
had
won
S6,ooo
and
Kimmel
$11,000.
Thorp
told
Kimmel
it
was
time
to
quit.
He
was
tired.
As
Thorp
walked
to
cash
in
his
chips,
a
beautiful
young
woman
passed
by.
She
smiled
significantly.
Then
another,
equally
beautiful
woman
did
the
same thing.
Thorp
did
not
have
time
to
puzzle
over
his
sudden
popularity.
Kimmel
was
still
at the
blackjack
table.
Kimmel
told
him
he
had
a
good
reason
for
continuing
to
play.
The
cards
arc
hot,
he
said.
Thorp tried to
pull
him
away.
Kimmel
clutched
the
table.
"I
...
will. . . not. . .
leave
. ..
this
. ..
place!"
he
announced.
Thorp
sat
down
again.
He
continued
counting
and
telegraphing
the
counts
to
Kimmel.
As
long
as
he
was
counting,
Thorp
resumed
betting.
They
began
losing
quickly.
Thorp
kept
nagging
Kimmel
to
quit.
Forty-five
minutes
later he
gave
in.
The
two
of
them
had
lost
SlI.OOO.
95


## Page 100

FORTUNE'S
FORMULA
As Eddie Hand had said, Kimmelwas"more trouble than an $l8
This debacle still left them ahead about $13,000 for the trip. The
next
day,
after
losing
another
S2.000
downtown.
Thorp
was
on
another
winning
streak.
This
again
commanded
the
attention
ofa
casino
owner.
He
gave
the
dealer
instructions
to
shuffle
whenever
Thorp changed his bet
size.
This
is
fatal
to
any
viable
card-counting
system.
Thorp
tried
to
evade
the
owner's
remedy
by
playing
more
than
one
hand
when
the
deck
was
hot. The
dealer
shuffled
every
time Thorp
played
more
than
one
hand.
Thorp
scratched
his
nose.
The
dealer
shuffled.
Thorp
asked
if
the
dealer
was
going
to
shuffle
every
time
he
scratched
his
nose.
Yes,
the
dealer
said.
Thorp
scratched
his
nose
again.
The
dealer
shuffled.
He asked if she
intended
to shuffle whenever he made any
change
whatsoever
in
his
behavior.
Yes.
Thorp
was
playing
with
$20
chips.
He
asked
for
some
$50
or
$iOO
chips.
The
owner
refused
to
sell
him
any.
A
new
deck
was
brought
out.
It
was
displayed
faceup
and
facedown.
This
is
normally
done
to let
the
player
verify'
that
all
the
cards
are
present
and
the
backs have not been marked. This time, it was the casino people
who
scrutinized
the
backs.
The
dealer
saidthey
believed
that Thorp
had
such
sharp
vision
that
he
was
able
to
distinguish
unmarked
cards
from
their
backs.
He
was
memorizing
printing
defects.
Or dirt.
Thorp
stubbornly
continued
playing.
The
owner
successively
de
manded
that four
brand-new
decks
be brought in about
five
min
utes.
The dealer
now
theorized
that Thorp
was
memorizing
the
entire
deck.
He
knew
exactly
which
cards
remained
in the
deck
and
bet
accordingly.
Thorp
said
it
was
impossible
for
anyone
to do
that.
The dealer
insisted
that the pit
boss
could
do
that—he
could
memorize
the
whole
deck.
Thorp bet
$5
that the pit
boss
couldn't.
96


## Page 101

Blackjack
The pit bossand the dealer weresilent.
How about
$50?
Thorp
asked.
Fland
sweetened
the offer to
S500.
The
casino
people
would
not
accept.
Thorp
and
Hand
left.
They
tried
one
more
casino.
When
they
asked
for
a
private
table,
they
were
passed
to
another
manager,
who
appeared
to
hail
from
the
gay
Mafia.
He
too
said
he
knew
what
they
were
doing.
They
weren't
welcome.
This
terminated
the
experiment.
By
Thorp's
estimation,
they
had
built
$10,000
into
$21,000
in
about
30
person-hours
of
play.
(Had
it
not
been
for
Kimmel's
ill-fated
binge,
they
might
have
ended
upwith
$32,000.)
They
had
some
time
to
kill
before
leaving
for
the
airport.
Kimmel
wanted to visit a friend who ran the Primadonna
casino.
He instructed
Thorp
not
to
use
the
system
there.
Thorp
found
three
silver
dollars
in
his
pocket
and
played
them
anyway.
The
deck
turned
favorable,
and
Thorp
accumulated
$35
in about
five
minutes.
Had it not been for
Kimmel's
warning,
he
might
have
bet
fifties
ratherthan
dollars.
The
Kelly
Criterion,
Under
the
Hood
Martingale
and
many
other
betting
systems
purport
to
work
whether
there
is
a
house
advantage
or
not.
Not
so
the
Kelly
system.
When
the
edge
is
zero
or
negative
(as
it
almost
always
is
in a
casino)
the
Kelly
system
says
not to bet at
all.
97


## Page 102

fortune's
formula
You
might
say
that
this
is
the
difference
between
fantasy
and
re
ality.
The
reality
is
that
you
can't
expect
to
make
any
money
with
an
unfavorable
wager.
It
would
be
nice
if
things
were
otherwise,
but
the
world
doesn't
work that
way.
Given
a
favorable
betting
opportunity,
the
Kelly
system
promises
maximum
profit
and
protection
against
ruin.
These
goals
may
sound
antithetical.
It
is
worth
looking
at
how
the
Kelly
formula
works
in a
casino
situation.
The
Kelly
system
avoids
gambler's
ruin
quite
simply.
It
is
a
"pro
portional"
betting
system.
This
means
that
each
wager
is
scaled
to
the current
size
of the
bankroll.
Since
you
bet
only
a
prescribed
frac
tion
of
what
you've
currently
got,
you
can
never
run
out
of
money.
When
you
lose
repeatedly,
as
will
happen
in
any
game
of
chance,
bets
scale
down
in
proportion
to
your
diminished
wealth.
Casinos and
racetracks
have
a
minimum
bet
size.
One potential
problem
with
the
Kelly
system
is
having
a
losing
streak
erode
your
bankroll
to a
point
where
the
Kelly
bet
is
less
than
the
minimum
wager.
In
practice,
this
is
rarely
an
issue.
It
just
means
that
your
ini
tial
stake
has
to
be
large
compared
to
the
minimum
bet,
so
thatthe
chanceof this is
negligible.
The
exponential
growth
of
wealth
in
the
Kelly
system
is
also
a
consequence
of
proportional
betting.
As
the
bankroll
grows,
you
make
larger
bets.
Assuming
you
have
an
edge,
in
the
long
run
you
will
win
more
than
you
lose.
Winnings
will
parlay.
Imagine
making
a
series
of
even-money
bets
on
the
toss
ofa
coin
that
you
know
to
be
biased,
with
a
55
percent
chance
of
coming
up
heads.
Naturally,
you
will
bet on
heads
each time.
That itself
does
not
guarantee
a
profit.
Here's
a chart
showing
the
results
of
four
money
management
systems.
All
are
betting
on
the exactsamesequenceof 500
tosses.
The
simplest
"system"
of
all
is
betting
a
fixed
wager.
Here
the
bet
amountstarts at
IO
percentof the
initial
bankroll
and
does
not
vary
thereafter.
The
line
of the
fixed-wager
gambler's
wealth
climbs
slowly
upward.
However,
this
policy
carries
a
chance
of
ruin.
An
un
lucky
streak
could
bustthe
fixed-stake
bettor.
In the
three
other
systems,
the
wager
changes
as the
bankroll
98


## Page 103

Blackjack
Four
Money
Management
Systems
$80
55%chance of
winning
even-money
bets
$80
$40
Ar
$20
Bet-lt-AD
Martingale
_ -,
/
FixedWager
.
-----
-$20
-$40
does.
One
extreme
approach
is
to
bet
it
all.
You
bet
your
entire
bankroll
on the
first
toss.
If
you
win,
you
bet
everything
on the
sec
ond
toss.
You
keep
parlaying
as
long
as
you
can.
In 2004 a
London
man
named
Ashley
Revell
sold
all
his
posses
sions, including his clothes, and staked his entire net worth
of
$135300
on a
roulette
wheel
at the
Plaza
Hotel
in
Las
Vegas.
Revell
wore
a
rented
tuxedo
and
bet on
red.
He
won.
He
decided
against
going
for doubleor
nothing.
Revell
was
playing
an
unfavorable
game.
His
actions
would
hardly
have
been
less
reckless
had
he
had
an
edge.
The
bet-it-all
policy
works
only until you
lose.
In the chart
above,
the
bet-it-all
line
begins
with
the
small
uptick
at the
far
left.
The
first
two
tosses
were
heads,
allowing
the
bet-it-all
player
to
quadruple
his
money.
He let it ride on the third
toss,
tails,
andwent
bust.
Afterthat, the
bet-it-all's
player's
wealth
is
zero.
At
first
glance,
it
may
look
like
martingale
does
pretty
well.
The
general
slope
of the
martingale
line
beats
the other
systems
for hun
dreds
of
bets.
The
wicked-looking
downward
spikes
in the
martin-
99


## Page 104

fortune's
formula
gale
line
tell
a
different
story.
The
spikes
are
streaks
of
bad
luck.
The
martingale
bettor
is
required
to
double
his
wager
as
long
as
he's
los
ing.
This
can
lead
to
rapidly
escalating
losses.
These
same
unlucky
streaks
barely
dented
the other
systems'
lines.
For
the
martingale
bettor,
the
bum
luck
is
fatal.
In
this
simula
tion,
the
martingale
bettor
goes
bust
on
bet
19.
The
continuation
of
the
line
after
that
is
irrelevant.
The
line
representing
the
Kelly
system
stands
out in
two
ways.
No
tice
that
the
general
trend
of
the
fixed-wager
and
martingale
systems
are
straight
lines,
while
the
Kelly
system
is
an
upward
curve.
Notice
also
that the
Kelly
lineis
far
more
jittery
thanthe other
systems.
The
wealth
of the
fixed-wager
and
martingale
bettors tends to
grow
as
an
arithmetic
series.
The
fixed-wager
and
martingale
bet
tors are
essentially
earning
a
fixed
hourly
wage.
They do not
make
bigger
bets
as
their
wealth
grows.
They
arc
sitting
on
capital
that
could be put to use.
In
comparison,
the
Kelly
bettor's
wealth
grows
geometrically
be
cause
he is
making
optimal
use
of
capital.
It
takes
a
while
for the
Kelly
strategy
to getoffthe
ground.
Inthe lefthalfof the
chart,
rep
resenting
about
250
bets,
the
Kelly
bettor's
line
hugs
that of the
fixed-wager
bettor.
Much
of the
time,
the
fixed-wager
bettor
is
ahead.
Then the
Kelly
strategy
takes
off.
The
line
swoops
upward,
leaving
the
other
two
systems
far
behind.
In
this
particular
simula
tion,
the
Kelly
bettor
has
increased
the
original
bankroll
about
74-
fold in
500
bets.
The
Kelly
system
is not the
only
proportional
betting
system.
There are an infinity of such betting
systems.
You
could
always
bet
1
percent
of
your
bankroll,
or
10
percent,
or 99
percent.
You
could
bet
edge
squared
over
the-last-number-that-came-up
cubed
times
your
bank
roll.
What's
so
special
about
the
specific
system
that
Kelly
devised?
The
answer
is
simply
that the
Kelly
system
grows
wealth
faster
than
any other.
Below
is a chart
comparing
the
Kelly
system
to two other pro
portional
betting
systems.
The chart
tracks
the
same
series
of 500
biased coin tosses as above. The
Kelly
bettor
runs Si up into S74.46.
The line marked "undcrbet" is a proportional system where you
lOO


## Page 105

Blackjack
bet
exactly
half
the
prescribed
Kelly
bet.
The
undcrbcttor's
wealth
grows
much
more
steadily
than the
Kelly
bettor's. That is often a
good
thing.
But
the
underbettor
ends
up
with
significantly
less
money
($16.07).
The line marked
"overbet"
is a
system
of betting twice the
Kelly
bet. This
achieves
$35.88
in
this
simulation.
"Twice
Kelly"
is a
treacherous
system.
It
docs
well
in
lucky
streaks,
but
all
the
gain
is
temporary.
Notice
that the
overbettor
was
briefly
the best-
performing
of the
three
systems
early
on (the little
volcano-shaped
peak
at
lower
left).
Then
the
overbettor's
wealth
fell
back
to
nearly
zero and
stayed
there a
long
time
afterward.
Were
the
simulation
continued
indefinitely,
the
wealth
of the
twice-Kelly
bettor
would
fall
back
to the
original
$1
or
less
an
infinite
numberof
times.
Underbetting-
vs.
Over/betting-
It
could
be
worse.
Overbctting
can
lead
to
virtual
ruin,
even
with
a
proportional
betting
system.
A
line
representing
someone
betting
four
times
the
Kelly
bet
(40
percent
of
the
bankroll
each
time)
101


## Page 106

FORTUNES
FORMULA
would be
invisible
on this chart, for it
would
hug the
baseline.
Such
a
bettor
would run Si down to
$0.00000038
in 500 tosses. Were
bettingto
continue,
the
bankroll
would
plunge
endlessly
downward,
to
ever-smaller
millions
of
billionths
of
a
cent.
Strictly
speaking,
the
proportional
ovcrbettor
will
always
have
some
microscopic
fraction
of a cent to
his
name
(assuming
that
money
is
infinitely
divisible
and
there
are no
minimum
bets).
This
distinction
is
hardly
worth
bothering
over.
The
engine
driving
the
Kelly
system
is
the
"law
of
large
numbers."
In a
1713
treatise on
probability,
Swiss
mathematician Jakob Ber
noulli
propounded
a
law
that
has
been
misunderstood
by
gamblers
(and
investors)
ever
since.
It concerns the
tricky
notion of
expectation.
In American
roulette with a
perfectly
balanced
wheel,
a bet on red
has
an %
chance
of
winning.
Does
that
mean
that red is
guaranteed
to
come
up
18
times
out of
every
38
times?
No,
of
course
not.
(Who
would
be
offering
the
"guarantee"?)
Does
it
mean
that if the
wheel
has
been
coming
up
black
an
awful
lot
lately,
red
is
"due"?
No
(although
many
gamblers
think so).
What
does
expectation
mean
then?
Most
who
attempt
to
trans
late
the
math
into
plain
English
use
the
phrase
"in
the
long
run."
Peo
ple
say
things
like,
"Red
will
come
up
% of
the
time,
in
thclongrun."
This
is
only
a
figure
of
speech.
No
matter
how
many
times
you
spin
the
wheel,
there
is
never
any
certainty
of
achieving
the
ex
pected
number
of
reds.
Can you conclude that if you spin the wheel 38 trillion times,
18
trillion
will be red? No. Will the
number
of
reds be close to
18
trillion?
It
depends
on
what
you
mean
by
"close."
If
you
mean
"Will
it be
between
17999.999.999,995
and 18,000,000,000,005?"
the
answer
is
almost
surely
no.
In
fact,
the
difference
between
the
actual
and
expected
number
of
reds
tends
to
grow
with
the
number
of
spins.
Jakob
Bernoulli's
law
of
large
numbers
says
(only)
that the
per
centage
of
reds
will
tend
to
approach
the
expected
percentage
as
the
102


## Page 107

Blackjack
numberof
spins
increases.
After
trillions
of
spins,
the
percentage
of
reds
will
be veryclose to % or
47.37
percent.
Generations
of
innumeratc
gamblers
have
discovered
this result
to be
of
less practical value than they'd
like.
It is
of
no use in helping
anyone profit
from
a
negative-expectation
bet.
You
might
well
thinkthat,
provided
you're
lucky
enough
to
find
a
positive-expectation
bet, the lawof
large
numbers means
you'll
do
all
right in the long run. Not
necessarily!
As
we've
seen,
people
can
go bust in the short run.
Even
people
using
a
proportional
betting
system
can, for
all
intents and
purposes,
go
broke.
Shannon
invoked
the
law
of
large
numbers
throughout
informa
tion
theory.
In a
noisy
communications
channel
where
ever)'
bit is
uncertain, the one certain thing is playingthe percentages.
Kelly
used
an
analogous
approach
to
make
money
from
positive-
expectation
bets.The
Kelly
system
manages
money
so that the bet
tor
stays
in the
game
long
enough
for the
law
of
large
numbers
to
work.
Las
Vegas
Thorp
took
the
opportunity
to inspect the roulette
wheels
in
Reno.
They looked much like the one in Shannon's base
ment.
Many
were
slightly
tilted.
The roulette
computer
was
finished
by
late spring
1961.
In a dry
run
lasting
a
few
hours.
Shannon
and
Thorp
multiplied
a
virtual
bankroll
of
a few hundred into an
impressive,
though fictional,
$24,000.
103


## Page 108

FORTUNE
s
formula
Thorp did a
full-dress
rehearsal
in
Shannon's
workshop.
They
used the
finest
wire
practical,
barely
as thick as a
hair,
to connect the
earphone to the pocket unit. The wire
was
glued to his skin with
gum arabic. the all-purpose stickum
vaudevillians
used for fake
beards
and
pasties.
Then the
wires
were
painted
to
match
Thorp's
skin
and
hair.
In
June,
Ed
and
Vivian
Thorp hit
Las
Vegas,
later
joined
by
Claude
and
Betty
Shannon.
"Everybody
else
was
really,
really
ner
vous,"
Thorp
recalled.
Using
a
device
to predict roulette
was,
in
1961,
perfectly
legal.
But the group
was
well
aware
that
casino
peo
ple
would
take
a
dim
view
of their
experiment.
Unlike
the
blackjack
system,
this
scheme
used
a
device.
There
was
no
deniability
They
stayed
in a
motel
rather than a big
hotel-casino.
"We
didn't
trust the
casinos
not to
bug
our
rooms
or go
through
our
luggage,"
Thorp
said.
"If
you're
in their ownestablishmentyou
feel
a lot more
vulnerable."
All
four
worked
as
a
team.
First
they
"cased
the
wheels"
for
tilt.
When
they
found
a
promising
wheel,
Claude
posed
as
a
sys
tem
player.
He stood by the wheel and recorded the numbers that
came up on a piece of
paper.
This was a smoke screen. Claude was
timing
the
ball
and rotor
with
the toe
switches.
The
computer
re
layed
its
musical-tone
prediction
to
the
bettor
(Ed
or
Betty),
who
pretended
not to
know
Claude.
Betty
looked
the most
innocent,
and
her
hair
hid
the
wires
better
than
Ed's
crew
cut.
Vivian
took
lookout
duty.
In
deference
to
the
group's
jitters,
they
bet
ten-cent
chips.
When a number hit, theywon
$3.60.
The
thin
wires
kept
breaking.
Every
time
that
happened,
they
had
to
go
back
to their
rooms
for
repairs.
They
brought
soldering
irons
with
them.
These
problems
prevented
any
serious
gambling.
While
in
Las
Vegas,
Thorp
demonstrated
his
blackjack
system
to the
Shannons.
He
played
impeccably,
yet
could
not get
much
ahead.
It
was
as if the
system
no
longer
worked
-or
Lady Luck
was
against
him.
They
left
Las
Vegas
with
several
half-baked
plans.
They
would
build
a
roulette
computer
with sturdier
wires
(or the men
would
grow their hair
longer);
they
would
build
a computer to automate
the
counting
of
cards
in
blackjack
(possibly
Thorp
had
been
making
104


## Page 109

Blackjack
mistakes,
but he didn't think so and
questioned
the need for
such
a
device);
they
would
build
a
computer
for the
wheel
of
fortune.
Thorp
and Shannon saw a wheel of fortune and realized it is much
easier to predict than roulette. There is no ball, just the rotation of
the wheel to worry about, and there is nothing like the vanes to ran
domize
things.
Forall this
brave
talk.
Thorp
said,
"it
was
pretty clear
to me that this group wasn'tgoingto want to come
back."
The
First
Sure
Winner
in
History
The
COLLABORATION
between Shannon and
Thorp
ended
with the
Las
Vegas
trip.
The
same
month,
Thorp got a job offer
from the mathematics
department
of New Mexico State
University.
It was unclear whether
MIT
would renew Thorp's
appointment,
and New
Mexico
State offereda
salary
about 50 percent more than
Thorp
was
making.
Living
costs
would
be
much
less.
The
money
weighed
heavily
on Thorp, as he and
Vivian
were now raising a
family.
Thorp accepted the
offer,
transplanting himself and
Vivian
to
a
ranch
house
in Las
Cruces,
New
Mexico.
A mathematics professor must publish or perish.
Thorp's
field
was
functional
analysis.
He
was
publishing
learned articles with ti
tles like "The Relation Between a Compact Linear
Operator
and Its
Conjugate."
The
publication
for
which
he is best known came about
by accident, though.
In spring
1961,
a book
salesman
visited
MIT. Thorp found him
self describing his
blackjack
systemas a possiblebook.
The
salesman
105


## Page 110

fortune
s
formula
urged
Thorp to submitan
outline.
He did. A
small
New
York
pub
lisher
called
Blaisdell
took
the
book.
Released
as
Beat
the
Dealer
in fall
1962,
it
became
an instant
classic
of
gambling
literature.
Blaisdell
was
gobbled
up
by
Random
House.
Despite
that apt
name, the new corporate owner
was
reluctant to promote the book,
judging
it too
mathematical.
Even
without
much
backing,
the book
made
the
best-seller
lists.
Thorp
became
a minor
celebrity
promoting
the
book.
One TV
talk
show
reunited him with a
defiant
Harold
Smith,
Jr.
"System
players!"
huffed
Smith.
"We
senda
taxi
for them at the
airport!"
Smith
was
trying
to
equate
Thorp's
system
to
martingale
and
all
the other
time-honored
and
worthless
systems.
He couldn't
have
believed
that. The
Smith
family
had been barring
card-counters
even before Thorp
showed
up.
Like
everyone
elsein the casinobusi
ness, they had plenty of reason to be worried. The casinos were al
ready takingactions to
make
it
difficult
for card-counters.
In his more
rambunctious
days,
Harold
Smith
had
begged
a line
of credit
from
every major
casino
in
Nevada.
That is an excellent
way
to get to know
people.
In the
social
network running
Nevada,
Smith
was
one
degree
of
separation
from
everyone
who
mattered.
Within
hours
of
Thorp's
confrontation
with
Smith,
word
had
got
ten out that a
man
in
horn-rimmed
glasses
and
crew
cut
had
paired
with the
unmistakable
Eddie
Hand
in a
card-counting
operation.
On a winter 1962
gambling
trip, Thorp took along an expert on
card
cheating,
Michael
MacDougall.
a
former
investigator
for the
Nevada
Gambling
Control
Board.
Thorp
learned
far more about
cheating from
MacDougall
than he had from
Kimmel.
The two men
spent six
days
in
Las
Vegas
and two in
Reno.
MacDougall
concluded
that Thorp
was
not
paranoid—everyone
really
was
out to get
him.
Many
of the
dealers
were
second-dealing,
the
trick
Kimmel
had
spotted
in Reno.
In the
1966
revision
of
Beat
the
Dealer.
Thorp
described
a superior
"point count"
strategy.
(Still
popular
today,
this
system
is alsoknown
as
"high-low")
You
count
< I
for
every
low
card
you
see
played
(2,
3,
4,
5,
or 6) and -1 for
every
high
card
(10or
ace).
This is easierthan
it
sounds.
High
and
low
cards
can
be
mentally
paired
off (and
cancel
106


## Page 111

Blackjack
out). This
system
is better than the ten-count at
gauging
deckcon
ditions.
A surprising
conclusion
of later computer studies, also reported
in Thorp's book,
was
that the
Baldwin
group had
miscalculated
the
house advantage. Instead of the claimed 0.62 percent in favor of the
house,
it
was
about
O.IO
percent
in
favor
ofthe
player.
This is without
counting cards.
The
Baldwin
group's
basic
strategy
was
not quite right, cither.
Thorp's
slightly
improved
strategy
bumped up the
advantage
of the
noncounting
player to
0.13
percent. For years casinos had unknow
ingly
offered
a
game
that
was
favorable
to the
player.
In
Beat
the
Dealer,
Thorp mentions his two
financial
backers
only
as "Mr. X" and "Mr.
Y."
(Shannon makes a brief appearance as an
unnamed "famous scientist.") After the book's
success,
Kimmel pre
sented
himself
to
friends
as
the
true
mastermind
behind
the
book's
card-counting
system.
When
fellow
gambler
Jack
Newton
called
Kimmel's
bluffand
asked
why
he
had
let Thorp writeabout
his
sys
tem, Kimmel replied,
"Jack,
I didn't think it would be worth two
cents. I thought that what Thorp
was
going to do
was
produce a
pamphlet,
and it
wouldn't
amount
to much, and no one would be
lieve
it. So I let him go aheadand even helped him word someof it."
Thorp disputes these
claims.
He
recently
told gamblingjournal
ist Peter Ruchman that he remembered
Kimmel
as "a
promoter
who
manipulated people using whatever stories it took.
You
can under
stand this from his
background;
it
was
a
way
to
survive
and ad
vance." Had he known
of
Kimmel's mob
connections
in 1961,
"there
would have been no trip to Nevadawith X and
Y."
Thorp
and his book were responsible for creating a subculture hero.
Want to get rich without
working?
Like
disguises,
glamour, and
neon
lights?
Thousands
have
answered
that
call.
Yet
the card-
counter is an often
lonely
figure
whose
appeal
rests on the masquer
ade as much as the
all-too-hard-earncd
money.
"The
typical
counter,
as the
casinos
see him, is
young,
male,
serious and
introverted,"
reported
one journalist. "To
enter
a casino
107


## Page 112

FORTUNES
FORMULA
with the
ability
to beat the
house,
knowing
the casino
will
be doing
everything
it can to
identify
and
eliminate
such
a threat,
gives
a
James-Bond-Spy-vs.-Spy
flavor
to the experience," wrote counter
Arnold Snyder. "The feeling is not unlike that which I recall from
my childhood when all the kids in my neighborhood would choose
up sides for 'cops and
robbers.'
I'd
forgotten
how much fun it was to
hide, sneak, run, hold your breath in anticipation."
For a
couple
of
years,
Thorp
was
one of this
group.
A
1964
Life
magazine
feature
described
Thorp as
one of those young men who can
manage
to look just like thou
sands of
other
young men. His cropped dark hair, his horn
rimmed
glasses,
his
quick
and
faintly
diffident
mode
of
speech,
and his dark suits arc all somehow
deceptive;
he could be a shoe
salesman, a young
executive
or a
television
repairman. He does
everything in his power to capitalizeon this
anonymity.
He reg
isters
in
Nevada
under
assumed
names,
wears
contact
lenses
and
usually
attempts to dress as
much
as
possible
like
a
vacationing
LosAngelesbarber.
One summer Thorp grew a
beard.
After two
days
of
successful
play
in
Las
Vegas,
word got out.
All
players
with beards were sus
pect. Thorp went to
Lake
Tahoe
and found that the
casinos
there
already knew about the beard.
Thorp
discovered he could use peripheral vision to count while
his
eyes
remained on the
dealer.
On the theory that the
walls
have
eyes,
he took a vowof
poverty
each time he went to
Nevada,
eating
bargain breakfastsand stayingin cheap
motels.
He got good at spot
ting cheats and learned to
leave
promptly.
Through these measures.
Thorp beganwinning
again.
By
1966,
after a dozen trips to
Nevada,
he was said to be
ahead
about
$25,000.
By Las
Vegas
standards, that
was
a trifle,
less
than a high roller
might win in a streak of dumb
luck.
It is
possible
to argue that card-
counting is the greatest shill ever invented. Not everyone who read
Thorp's book
was
able to
apply
the
system
consistently
enough to
108


## Page 113

Blackjack
gain an
advantage.
For
every
successful
counter,
there were hun
dreds
who
merely
thought
they
could
count
cards
successfully.
Card-counting of coursecommandedmuch more attention than
the
more
abstract
Kelly
formula.
The
1966
Life
profile
of
Thorp
contained
probably
the
first
mention
of
the
Kelly
system
in a
gen
eral publication:
One of the
most
ingenious
aspects
of
Thorp's
strategy
today
in
volves
his
application
of the
Kelly
System—a
mathematical
the
ory
for
the
management
of
capital
conceived
by
a
Bell
Telephone
labs
research
scientist... It isthis
element
of
play
which
insures
him
against
going
broke
(the
man
who
consistently
overbets,
even
in
favorable
situations,
is
certain
todo
so)
and
which
made
him the firstsure
winner
in
history.
Nevertheless,
people
who
skimmed
Thorp's
book
probably
did
not understand the
importance
of
scaling
their bets to their bank
roll.
It is a
natural
impulse
to
make
large
wagers
when
the
deck
is
hot.
For
many,
this
must
have
been
a
costly
mistake.
Deuce-Dealing
Dottie
"Flow
the
HECK
do I
know
howhe
docs
it? I
guess
he'sgot one
of
them
mathematical
minds
or
photographic
memories,
or
some
thing."
The topic
was
Ed Thorp. The speaker
was
Cecil
Simmons,
ca-
109


## Page 114

FORTUNES
FORMULA
sino boss at the Desert Inn. Simmons wasspeaking by phone to one
of his
competitors,
Carl
Cohen
of the
Sands.
"All
I
know,"
Simmons went on, "is he wrote a book that teaches
everyone
how
to
win
every
time
they
play
blackjack.
I'm
just
telling
you,
this
book-learning
SOB
has
ruined
us."
Simmons
said
they
were
"outof the
blackjack
business."
Another
Las
Vegas
veteran
said
Beat
the
Dealer
was
the worst thing to hit the
gambling
business
since
the
Kefauvcr
hearings.
Simmons
organized
a
conclave
of
casino
bosses
and
representa
tives
of Eastern crime
families.
It
was
held in a private room at the
rear of the Desert Inn.As
casino
manager
Vic
Vickrey
remembered
it, one
hard-boiled
type
had no doubt about the
solution
to their
mutual
problem:
"Break
a
few
legs,
and
I'll
betcha
the
word
will
get
out
real
quick
that it
just
ain't
healthy
to tryto
play
that countthing
in our
joints
...
that
is,
unless
they
like
hospital
food."
The
meeting's
chairman
objected
that
they
didn't do
things
that
way
anymore.
They
were
legitimate
businessmen
and
needed
to
think like
legitimate
businessmen.
Another
suggestion
was
to
call
in
"Deuce-Dealing
Dottie."
She
was
the
best
second-dealer
in
the
business.
The calmer minds present
appreciated
that it
was
no longer
practical
for
casinos
to
identify'
every
counter.
There
were
too
many.
Instead
the group
resolved
to
change
the
rules
of
blackjack.
The
change
applied
to
"doubling
down,"
an often
favorable
op
tion
many
casual
tourists
don't
understand
well
enough
to
use.
Un
der the
revised
rules,
the
player
could
double down only on "hard"
totals
of
IO
or n
("hard"
meaning
no
aces).
Doubling
down after
splitting a pair
would
be
forbidden.
These
changes
would
give
the
house
an
edge
over the
basic
strategy
player
and
make
it more
difficult for card-counters to
achieve
an
advantage.
In
April
1964,
the
Las
Vegas
Resort
Hotel
Association
an
nounced the new
official
rules of
blackjack.
The new rules were
like
breaking
everyone's
legs.
People
who had
no intention of
counting
cards
understood
that the
game
was
less
no


## Page 115

Blackjack
advantageous
than
it
had
been.
Blackjack
play
was
down,
tips
to
dealers
were
way
down.
Dealers
grumbled
to
management.
Within
weeks casinos
reverted
to the old rules.
The
casinos
continued
to
experiment.
Most
settled
on a
solution
originally
known
asthe
"professor
stopper."
That
term
was
in
honor,
more
or
less,
of
Thorp.
The
professor
stopper,
or
"shoe,"
is
a
holder
that
allows
dealers
to
shuffle
multiple
decks
together.
Anywhere
from
two
to
eight
decks
arc
shuffled
together.
Cards
arc
dealt
from
the
combined
deck.
The
dealer reshuffles when she comes to a
faceup
card
that
has
been
placed,
typically,
about
fifty
cards
from
the
bottom.
Use
of
multiple
decks
makes
counting
more
difficult
and
less
profitable.
Because
the end cards are never dealt, the
concentrations
of
good
cards
that
occasionally
occur
at the end of the
deck
never
come into
play.
Thorp
once
computed
that
he
could
make
$300,000
a
year
playing
blackjack
under
ideal
conditions.
That's
assuming
he
could
play
forty
hours
a
week,
raising
and
lowering
his
bets
between
the
table
limits
with
no
interference
from
the
casinos.
No
interference
was
becoming
an
unrealistic
assumption.
While
playing
at one
Las
Vegas
strip
casino,
Thorp
was
offered
a
drink.
He
asked
for
coffee
with
cream
and
sugar.
After
drinking
it, he
noticed
he
was
having
problems
concentrating.
Thorp
staggered
up
from
the table and got to
his
room.
His
eyes
were
dilated.
It took about
eight hours for the effect to wearoff.
The next dayThorp returned to the same
casino.
He
was
offered
another
drink.
He
asked
for
water
this
time.
He
sipped
it
carefully.
"It tasted
like
they'd
dumped
a
box
of
baking
sodain it.
Flad
I drunk
more
I
would
have
been
finished
because
just
the
few
drops
on
my
tonguewere
enough
to
wipe
me out for the
night."
"I knowof three
beatings,"
Thorp
said.
"One
well-known
black
jack
card-counter
had
a lotof
his
face
caved
in.
A
guy
I
know
had
his
arms
held,
and
every
time
he
tried
to
catch
his
breath
they'd
punch
him in the solar
plexus
again."
in


## Page 116

FORTUNES
FORMULA
The latter
player
had
been
told
to
leave.
He
ignored
the
warning
and
continued
playing.
Thorp
made
it a
policy
to
leave
when
asked
on the
hopeful
theory
that the
thugs
would
always
give
one
"fair"
warning
before
getting
violent.
Ed Reid and Ovid
Demaris's
The
Green
Felt
Jungle,
an
expose
of
casino
corruption
published
the
year
after
Beat
the
Dealer,
confirms
that the
casinos
settled
disputes
with
gangland
violence
well
into
the
1960s.
Beatings
often
took
place
in the
counting
room,
a
sound
proof
room
"ideal
for
such
torture."
Reid
and
Demaris
tell
of a
cheating
dealer
at
the
Riviera.
Two
casino
enforcers
forced
him
to
place
his
closed
fists
on a
table.
Another
used
a
lead-encased
base
ball bat to
smash
the
man's
fists.
He was
dragged
past the tourists in
the
casino.
A mobdoctor
bandaged
but did not set the
hands.
The
man
was
driven
to the
edge
of
town.
The
thugs
took
his
shoes
off
and
pushed
him
out of the
car.
"Now
you
sonof a
bitch,"
one thug
said,
"walk
to
Barstow.
No
goddamn
hitchhiking,
cither. We're
gonna checkon youall the
way."
Bicycle
Built
for
Two
John
Kelly,
Jr.,
published
nothing moreabout
gambling.
As far
as
anyone
knows,
he
never
tried to
use
G - R to
make
money.
His
close
friend
Ben
Logan
is not
even
certain
that
Kelly
ever
used
his
football circuits to place bets.
Kelly
had
become
an important man at
Bell
Labs.
He was pro
moted to head of the information coding and programming depart
ment.
He
applied
Shannon's
theory
to the
problem
of
correcting
for
112


## Page 117

Blackjack
echo
effects
in
satellite
transmissions.
Kelly
devised
a
block
diagram
compiler
that
took
a
simple
logic
diagram
and
produced
working
code.
And
he
taught
a
computer
to
sing.
This
was
an
IBM
704,
the
model
Thorp
had
used
for
his
first
blackjack
studies.
In
1961
Kelly
and
Carol
Lochbaum
demonstrated
their
new
voice
synthesis
sys
tem
by
making
a
recording
of
the
machine
reciting
a
passage
from
Hamlet
and
singing
the
song
"Daisy
Bell,"
better
known
as
"Bicycle
Built
for
Two."
An
occupational
hazard
of
voice
synthesis
research
is the"parrot
effect."
Through
long
exposure,
the
researcher
is better
able
to
understand
his
pet
creation's
words
than
anyone
else
is.
Manfred
Schroeder
recalled
proudly
demonstrating
a
voice
synthesis
system
to
two
Bell
Labs
executives
in
the
mid-1950s.
"They
were
very
polite,
but
I'm
pretty
sure
that
what
my
machine
was
saying
was
unintelligible to them."
Flaving
a
computer
"sing"
a
popular
song
is
cheating
slightly—
the
familiar
tune
cues
listeners
to
the
words.
It
is
thus
easier
to
syn
thesize
an
acceptable
singing
voice.
This
fact
was
lost
on
journalists,
who
judged
the
singing
computer
more
newsworthy.
John Pierce knew the British science fiction
writer
Arthur
C.
Clarke.
Clarke
visited
Bell
Labs
in
the
mid-1960s,
trying
to
get
AT&T's
cooperation
for
the
film
that
would
become
Stanley
Kubrick's
2001:
A
Space
Odyssey.
It
was
Clarke
and
Kubrick's
idea that
the
film
would
show
futuristic
technology
branded
with
logos
of
contemporary
companies,
such as an
AT&T
videophone.
Pierce
amused
Clarke
by
playing
Kelly's
recording
of
"Bicycle
Built
for
Two."
AT&T's
ever-cautious
executives
decided they didn't want to
have
anything to do with the
film.
Their concern
was
that the tech
nology
shown
might
be
wrong
or
never
come
to
pass,
and that
could
embarrass
AT&T.
Clarke
remembered
the
Kelly
recording
when
he
was writing the
screenplay
for
2001.
In the
movie,
the
homicidal
computer
HAL is
unplugged
and
reverts
to a
childish
state,
singing
the
same
song
Kelly's
computer
did.
Clarke
and
Kubrick
assumed
that
by
the
year
2001,
people
like
113


## Page 118

FORTUNE
S
FORMULA
Kelly
would
have
achieved
their
goal
of
synthesized
voice
indis
tinguishable
from
a
human's.
They
reasoned
that
FIAL
should
not
sound like a
movie
robot. Actor
Douglas
Rain was cast to
voice
FIAL's
lines,
including
the
rendition
of
"Bicycle
Built
for
Two."
By
the
year
2001,
digital
speech
was
ubiquitous
on
computers,
telephones,
and
the
Internet.
It
provided
a
voice
for
one
of the
world's
most
distinguished
physicists.
In a
way,
the
AT&T
execu
tives
were
right,
though.
The
quality
of
those
voices
had
advanced
slowly.
It
still
couldn't
be
mistaken
for
a
human
speaker.
A
legend
has
arisen
that
Clarke
created
the
name
"HAL"
by
rolling
each
letter's
place
in
the
alphabet
one
position
back
from
"IBM."
It
was
to
IBM
that John
Kelly
was
going.
On
March
18,
1965,
he and
several
colleagues
took the
Bell
Labs
limo into
Man
hattan
for
a
meeting
at the
computer
company's
offices.
Walking
along
the
street,
Kelly
held
his
hand
to
his
head.
"Wait
a
minute!"
he
cried out.
Moments
later,
he
slumped
to the
sidewalk.
Fie
was
dead
of a brain
hemorrhage
at the
age
of
forty-one.
Kelly
would
thereafter
be
known
for
an
incidental
connection
to
a
movie
he
never
saw—and
for the
gambling
formula
that
would
carry his name on to
posterity.
114


## Page 119

PART
THREE
Arbitrage


## Page 120

4
Paul
Samuelson
Paul Samuelson loved
Harvard.
The
love
was
not
entirely
requited.
By
the
age
of
twenty-five,
Samuelson
had
published
more
journal
articles
than
his
age.
This
distinction
seemed
to count little
at
Flarvard,
where
Samuelson
was
boxed
into
a
low-paying
post
as
an
economics
instructor.
Tenure
was
a
remote
prospect.
One of
Samuelson's
colleagues
had
been
passed
over
for
tenure
because
he
had
a
disability.
The
disability
was
that
he
came
from
Kansas.
Samuelson
came
from
Gary,
Indiana.
The
Kansas
guy
was
not
Jew
ish.
Samuelson
was.
In 1940
Samuelson
accepted
an offerto
move
three
miles
to the
other
end
of
Cambridge.
As
some
saw
it,
MIT
was
a
step
down
from
Harvard.
MIT
was
a
science
and
engineering
school,
hardly
known
for
its
economics
department,
nor
for
training
America's
economic
and
political
leaders.
In
an
era
when
Ivy
League
schools
wereoften
quietly
anti-Semitic,
it
was
an
index
of MIT's outsider
status
that
they
were
willing
to
hire
a
Jew
just
because
he
was
smart.
MIT's
technical
focus
was
a
good
match
for
Samuelson's
gifts.
Samuelson
chose
to
view
economics
asa
mathematical
science.
That
was
an
unconventional
approach
at the time.
From
Adam Smith
through
John
Maynard
Keynes,
economics
had
been
mostly
talk.
At
Flarvard,
economics
was
talk.
At MIT,
Samuelson
made it math.
Samuelson
was
as
comfortable
with
differential
equations
as
a
physicist.
His
papers
are
full
of
"theorems,"
as
he
called
his
results.
To this
Samuelson
wedded
an
incisive
wit that set his
lectures
and
117


## Page 121

fortune's
formula
publications
apart
from
the
great,
gray
mass
of
economist-speak.
Samuelson
was
a
superb
teacher.
Probably
no
other
economist
of
the
day
produced
such
a
succession
of
brilliant
followers
as
Samuel
son did at MIT. His
influence
wentfar
beyond
Cambridge.
In
1948
Samuelson
channeled
his
encyclopedic
knowledge
and
verbal
flair
into an
"Economics
101"
textbook.
Titled
simply
Economics,
it
has
been
a
perennial
bestseller.
"Let
those
who
will,
write
the
nation's
laws,"
Samuelson
once
said,
"if I
can
write
its
textbooks."
Samuelson
was
a
Democrat.
He
gave
economic
tutorials
to
pres
idential
candidate
Adlai
Stevenson
and
President
John
Fitzgerald
Kennedy.
He
remained
a
trusted
adviser
throughout
the
Camelot
era.
By
the
mid
1960s,
Samuelson's
influence
on
the
economic
pro
fession
was
unrivaled,
and
he
had
almost
single-handedly
raised
the
prestige
of
MIT's
economics
department
up
to
his
own
lofty
level.
About
1950,
Samuelson
became
interested
in
warrants.
A
warrant
is
a
stock
option
issued
by
a
company
to
allow
purchase
of
its
own
shares. Some believed it was easier to make money in warrants
than
stocks.
Samuelson
shelled
out
S125
for a
yearly
subscription to
The
R.FIM
Warrant
and
Low-Price
Stock
Survey.
This purported to
give
profitable
market
tips.
Samuelson
figured
that
if
he
could
make
just
one
decent
killing
a
year,
he'd
bein
fine
shape.
The
service
did
not
prove
to
be
the
lazy
man's
road
to
riches.
Samuelson
learned much
from
his
failure
to strike it
rich.
If the war
rant
tips
were
any
good,
he
reasoned,
the
service
would
sell
for
a
lot
more
than
S125.
And
why
should
the
tips
be
any
good?
Why
would
the
owner
of a
warrant
sell
it to
you
for
anything
less
than its true
value?
In
1953
a
British
statistician
named
Maurice
Kendall
gave
a
talk
to
the
Royal
Statistical
Society
in
London.
The
subject
was
a
dry
one
even
for a
statistical
society:
the
weekly
wheat
prices
in the
Chicago
commodity
markets
(from
1883
through
1934.
excluding
1915
to
1920).
Kendall
wanted
to
see
how
well
one
could
predict
fu
ture wheat
prices
from
past
history.
Kendall's
unexpected
conclusion
was
that
you
couldn't
predict
118


## Page 122

Arbitrage
wheat
prices
at
all.
He
said
that
wheat
prices
wandered
aimlessly,
"almost
as
if
once a
week
the
Demon
of
Chance
drew a
random
number
. . .
and
added
it
to
the
current
price
to
determine
next
week's price."
Kendall
suggested
that
the
same
principle
might
apply
to
stock
prices.
The
people
who
thought
they
could
predict
the
stock
market
(that
would
be
just
about
any
broker,
adviser,
or
money
manager)
were
deluding
themselves.
Kendall's
words
were
branded
"nihilism."
They
were
said
to
"strike
at the
very
heart of
economic
science."
Deconstruction:
Eco
nomic
science
is
about
showing
how
things
are
predictable.
Things
have
to be
predictable.
Samuelson
heard
of
Kendall's
ideas
through
a
friend
who
at
tended
the
lecture.
As
a
natural
contrarian,
Samuelson
delighted
in
Kendall's
nihilism.
He
decided
to
see
how
far
he
could
go
with
the
hypothesis
that
stock
and
commodity
prices
aren't
predictable.
He
was
reinforced
in
this
project
by
a
postcard
he
received
from
Leonard
("Jimmie")
Savage.
Savage
was another
statistician,
an
American
one, with Coke-
bottle-thick
glasses
and
a
taste
for
bow
ties.
He
was
then
working
at
the
University
of
Chicago.
Savage
used
"Leonard"
in
his
publica
tions.
Everyone
knew
him
as
"Jimmie."
He
was
also
known
for
living
up
to
his
last
name.
Anyone
who
substantially
disagreed
with
Savage
was,
in
his
freely
offered
opinion,
stupid.
It
was
rumored
that
Sav
age's
peripatetic
career
had
something
to do
with
his
habit
of in
forming
associates
of
their
stupidity.
In
1954
Savage
was
looking
for
a
book
ona
library
shelf.
He
came
across
a
slim
volume
by
Louis
Bachelier.
The
thesis
of
Bachclier's
book
was
that
the
changes
in
stock
prices
are
completely
random.
Savage
sent
postcards
to
a
number
of
people
he
thought
might
be
interested,
including
Samuelson.
On
the
cards
Savage
wrote,
"Ever
hear of this
guy?"
The
answer
was
no.
The
world
had
forgotten
Louis
Bachelier.
His
1900
thesis,
"A
Theory
of
Speculation,"
argued
that
the
day-to-day
119


## Page 123

fortune's
formula
changes
in
stock
prices
are
fundamentally
unpredictable.
When
a
stock's
price
reflects
everything
known
about
a
company
and
all
reasonable
projections,
then
future
changes
in
price
should
be,
by
definition,
unpredictable.
A
stock
does
not
go
up
just
because
it
lives
up
to
everyone's
expectations.
It
goes
up
when
it
does
better
than
people
anticipated.
It
goes
down
when
it
docs
worse
than
predicted.
A
stock's
price
should
therefore
vary
randomly,
subject
to
the
buf
feting
of a
constant
stream
of
unpredictable
news
events,
good
and
bad.
This
implies
that
someone
who
buys
a
stock
and
sells
it
almost
immediately
is
as
likely
to
have
a
loss
as
a
gain.
Bachelier
wrote
that
"the
mathematical
expectation
of the
speculator
is
zero."
The
thesis
got
a
middling
grade.
Bachelier
spent
the
rest
of
his
career
in
such
obscurity
that
virtually
nothing
is
known
of
his
life,
save
that he
was
born in
1870
and died in
1946.
Bachelier
died a
decade
before
his
rediscovery
by
Savage
and
(especially)
Samuelson
would
make
him one of the most
influential
figures
in twentieth-
century
economic
thought.
Ironically,
the
unpredictability
of
stock
prices
makes
them
some
what
predictable—in
a
statistical
sense.
Bachelier
believed
that
stock
prices
follow
a
random
walk.
This
term
refers
to
a
classic
exer
cise in statistics
classes.
A drunk has
fallen
asleep
at a
lamppost.
Every
now
and
then
he
rouses
himself,
staggers
a
few
steps
in
a
ran
dom
direction,
and
collapses
for
a
nap.
The
process
repeats
indefi
nitely.
After
many
stages
of
this
aimless
journey,
how
far
is
the
drunk
from the lamppost?
You
might
think
there's
no
possible
way
of
telling.
And
of
course,
there's
no
way
of
telling
exactly.
You
can
however
calculate
how
far
the
drunk
gets
from
the
lamppost,
on the
average.
Imagine
a
crowd
of
drunks,
all
starting
at
the
same
lamppost
and
all
moving
randomly
as
described
(ignoring
collisions).
The
overall
distribution of the crowd will remain centered on the lamppost.
That's
because
nothing
is
"pushing"
the
wandering
drunks
in
any
particular
direction.
All
directions
are
the
same
to
them.
Over
time,
the crowd diffuses outward in all directions. This is nothing more
than the
familiar
observation
that
when
you're
lost and
wandering
120


## Page 124

Arbitrage
aimlessly,
you
tend
to
get
farther
and
farther
from
where
you
started.
Should
you
follow
the
paths
of
particular
drunks,
you
find
that
they
do
a
lot
of
backtracking
and
moving
in
"circles."
The
few
drunks
who
end
up
far
from
the
lamppost
do
so
because
they
hap
pen
to
move
in
about
the
same
direction
for
many
legs
of
their
jour
ney,
approximating
a
straight-line
journey
Since
each
leg's
direction
is
chosen
at
random,
this
is
unlikely,
like
a
run
of
the
same
number
in
roulette.
The
crowd's
average
distance
from
the
lamppost
increases
with
time.
More
exactly,
this
average
distance
increases
with
the
square
root
of
time.
If it
takes
an
hour,
on
average,
for
a
drunk
to
wander
a
block
away
from
the
lamppost,
it
will
take
four
hours
on
average
to
wander
two
blocks
from
the
lamppost,
and
about
nine
hours
to
wander
three
blocks.
Random
walks
happen
in
many
contexts.
As
we've
already
seen,
the
fluctuations
ofa
bettor's
bankroll
in
a
game
of
chance
constitute
a
random
walk
(a
one-dimensional
random
walk,
since
wealth
can
only
move
up
or
down).
With
time,
the
gambler's
wealth
strays
fur
ther
and
further
from
its
original
value,
and
this
eventually
leads
to
ruin.
At
about
the
time
Bachelier
was
writing,
Albert
Einstein
was
puzzling
over
Brownian
motion,
the
random
jitter
of
microscopic
particles
suspended
in
a
fluid.
The
explanation,
Einstein
surmised,
was
that
the
particles
were
being
hit
on
all
sides
by
invisible
mole
cules.
These
random
collisions
cause
the
visible
motion.
The math
ematical
treatment
of
Brownian
motion
that
Einstein
published
in
1905 was similar to, but less advanced than, the one that Bachelier
had
already
derived
for
stock
prices.
Einstein,
like
practically
every
one
else, had
never
heard
of
Bachelier.
121


## Page 125

fortune's
formula
♦
The
Random
Walk
Cosa
Nostra
Samuelson
adopted
Bachclier's
ideas
into his
own
thinking.
Characteristically,
he
did
everything
he
could
to
acquaint
people
with
Bachelier's
genius.
Just
as
characteristically,
Samuelson
called
Bachelier's
views
"ridiculous."
Huh?
Samuelson
spotted
a
mistake
in
Bachelier's
work.
Bache
lier's
model
had
failed
to
consider
that stock
prices
cannot
fall
be
low
zero.
Were
stock
price
changes
described
by
a
conventional
random
walk,
it
would
be
possible
for
prices
to
wander
below
zero,
ending
up
negative.
That
can't
happen
in
the
real
world.
Investors
are
pro
tected
by
limited
liability.
No
matter
what
goes
wrong
with
a
com
pany,
the
investors
do
not
end
up
owing
money.
This
spoiled
Bachelier's
neat
model.
Samuelson
found
a
simple
fix.
He
suggested
that
each
day,
a
stock's
price
is
multiplied
by
a
ran
dom
factor
(like
98
or
105
percent)
rather
than
increased
or
de
creased
by
a
random
amount.
A
stock
might,
for
instance,
be
just
as
likely
to
double
in
price
as
to
halve
in
price
over
a
certain
time
frame.
This
model,
called
a
log-normal
or
geometric
random
walk,
prevents
stocks
from
taking
on
negative
values.
To
Samuelson,
the
random
walk
suggested
that the
stock
market
was
a
glorified
casino.
If
the
daily
movements
of
stock
prices
are
as
unpredictable
as
the
daily
lotto
numbers,
then
maybe
people
who
make
fortunes
in the
market
are
like
people
who
win
lotteries.
They
are
lucky,
not
smart.
It
follows
that
all
the
people
who
advise
clients
122


## Page 126

Arbitrage
on
which
stocks
to
buy
are
quacks.
The
favored
analogy
was,
you
might
as
well
choose
stocks
by
throwing
darts
at
the
financial
pages.
This
skepticism
became
formalized
as
the
efficient
market
hy
pothesis.
It
claims
that
the
market
is
so
good
at
setting
fair
prices
for
stocks
that no one
can
achieve
better
returns
on their
invest
ment
than
anyone
else,
save
by
sheer
luck.
University
of
Chicago
economist
Eugene
Fama
developed
the
idea
both
theoretically
and
empirically.
There
is
much
truth
in
the
efficient
market
hypothesis.
The
con
troversy
has
always
been
over
just
how
far
the
claim
can
be
pressed.
Asking
whether
markets
are
efficient
is
like
asking
whether
the
world
is
round.
The
best
way
to
answer
depends
on
the
expectations
and
sophistication
of
the
questioner.
If
someone
is
asking
whether
the
world
is
round
or
fiat,
as
fifteenth-century
Europeans
might
have
asked,
then
"round"
isa better
answer.
If
someone
knows
that and is
asking
whether
the
earth
is
a
geometrically
perfect
sphere,
the
an
swer
is
no.
The
stock
market
is
more
efficient
than
many
small
investors
think.
Studies
show
that
most
actively
managed
mutual
funds
do
worse
than
the
market
indexes.
Yet
people
put
money
into
these
funds
believing
that
the
fund
management
must
be
worth
the
fees
they
charge.
The
more
difficult
question
is
whether
some
extremely
talented
investors can beat the market.
Samuelson
claimed
an open
mind
on
this.
"It is not
ordained
in
heaven,
or
by
the
second
law
of
thermodynamics,"
he
wrote,
"that
a
small
group
of
intelligent
and
informed
investors
cannot
achieve
higher
mean
portfolio
return
with
lower
average
variabilities."
Still,
Samuelson
didn't
see
any
convincing
evidence
that
such
people
existed.
You
might
compare
his
position
to
that
ofa
present-day
"skeptic
society"
on
psychics
or
UFOs.
Samuelson
challenged
the
hotshot
money
managers
to
prove
their
superior
abilities.
Fama
and
other
economists
such
as
Jack
Treynor,
William
Sharpe,
Fischer
Black,
and
Myron
Scholes
earnestly
tried
to
find
investors
or
investment
techniques
that
really
and
truly
beat
the
market.
It
seemed
that
(like
other
practitioners
of
the
paranormal)
123


## Page 127

fortune's
formula
superior
portfolio
managers
had
a
convenient
habit
of
touting
their
successes
and
forgetting
their
failures.
In
the
majority
of
cases,
claims
of
beating
the
market
evaporate
when
subjected
to
scrutiny.
It
is
worth
spelling
out
exactly
what
kind
of
performance
the
economists
were
looking
for—and
what
the
efficient
market
theo
rists
were
not
saying.
They
were
not
saying
that
no
one
makes
money
in
the
market,
obviously.
Most
long-term
investors
do
make
a
nice
return,
as
well
they
should—otherwise,
why
would
anyone
invest?
Nor
were
they
saying
that
no
one
makes
better
than
average
re
turns.
"Average"
return
is
measured
by
indexes
like
the
Dow
Jones
Industrial Indexor the Standard&
Poor's
500. These track the per
formance
ofa
group
of
representative
stocks.
Plenty
of
investors
do
better
than
the
indexes,
for
a
few
years.
A
handful
do better
for
decades.
The
theorists
were
not
even
saying,
necessarily,
that
all
the
market-beaters
are
simply
lucky.
There
arc
ways
to
boost
return
by
accepting
greater
risk.
One
is
to
use
leverage.
A
very
aggressive
in
vestor
might
borrow
money
to
buy
more
stock
than
he
could
other
wise.
This
multiplies
the
expected
return—and
also
multiplies
the
risk.
For
these
reasons,
the
notion
of a
superior
investor
needs
to be
carefully
qualified.
The
hallmark
has
to
be
a
market-beating
risk-
adjusted
return,
achieved
not
through
luck
but
through
some
logical
system.
It
was
concrete
evidence
of
this
that
the
economists
failed
to
find.
A
name
that
occurs
to
many
people
today
is
Warren
Buffett.
"Ed
be a
bum
in the street
with
a tin
cup
if the
markets
were
efficient,"
Buffett
once
said.
Buffett
had
already
made
a
name
for
himself
with
a
successful
hedge
fund
and
had
founded
Omaha-based
Berkshire
Flathaway
when
Samuelson
wrote
that
"a
loose
version
of
the
efficient
market'
or
'random
walk'
hypothesis
accords
with
the
facts
of
life."
Samuelson added: "This truth, it must be emphasized, is a
truth
about
New
York
(and
Chicago,
and
Omaha)."
Samuelson
apparently
felt
that
Buffett's
success
was
best
filed
124


## Page 128

Arbitrage
with
a
small
minority
of
"unexplained
cases."
Skeptics
cannot
possi
bly
investigate
every
claimed
psychic,
UFO
abductec,
or
market-
beating
investor.
After
so
many
investigations
with
no
proof,
a
certain
cynicism
is justified.
Samuelson,
however,
hedged
his
personal
bets—by
putting
some
of
his
own
money
in
Berkshire
Hathaway.
The
claim
that
the
market
is
efficient
is
a
disturbing
one
to
many
people.
It
is
disturbing,
most
obviously,
to
the
professional
stock-
pickers
who
run
mutual
funds
or
manage
wealthy
people's
invest
ments.
If
the
efficient
market
hypothesis
is
true,
these
people
provide
no useful service.
The
dissatisfaction
runs
beyond
Wall
Street.
Many
an
American
dream
entails
making
more
money
for
less
effort
in
shorter
time
than
the
other
guy.
At
the
Kefauver
hearings,
Willie
Moretti
sup
plied
a
telling
definition
of
the
word
mob:
"People
are
mobs
that
make
six
percent
more
on
the
dollar
than
anyone
else
does."
It is not just criminalswho cherish the belief that there is an eas
ier
way
of
getting
rich.
The
small
investor
has
long
been
inundated
by
mutual
fund
and
brokerage
ads
implying
that
you'd
be
a
sap
to
settle
for
"average"
returns.
It
is
an
American
credo
that
you
can
pick
a
"good"
mutual
fund
from
Morningstar
ratings.
"Good"
pre
sumablymeans that it
will
earn morecents on the dollar than an in
dex
fund.
It
is
a
more
astonishing
credo
that
the
small
investor
can
pick
market-beating
stocks
him-
or
herself
just
by
doing
a
little
re
search
on the
Internet
and
watching
pundits
on
CNBC.
This
raises
an
important
point,
the
connection
between
market
information
and
return.
"In
an
efficient
market."
Eugene
Fama
wrote,
"competition
among
the
many
intelligent
participants
leads
to a
situation
where,
at
any
point
in
time,
actual
prices
of
individual
securities already reflect the effect of information based both on
events
that
have
already
occurred
and on
events
which,
as
of
now,
the
market
expects
to
take
place
in the
future."
Fama's
words
recall
Shannon's
perfect
cryptographic
system.
Ci-
125


## Page 129

fortune's
formula
pliers
are
broken
through
telltale
patterns.
Therefore,
all
codes
as
pire
to
the
condition
of
noise.
Predictable
patterns
in
the
market
would
allow
excess
returns.
The
"competition"
of
second-guessing
the
market's
next
move
effectively
erases
any
such
patterns.
Hence
the random walkand an efficient market no one beats.
Fama
did
not
presume
to
measure
the
market's
information
in
bits,
as
Kelly
did.
Information
was
nonetheless
a
key
feature
of
Fama's
analysis.
Ina
1970
article,
Fama
used
information
sources
to
distinguish
three
versions
of
the
efficient
market
hypothesis.
Fama's
"weak
form"
of the
hypothesis
asserts
that
you
can't
beat
the
market
by
predicting
a
stock's
future
prices
from
knowledge
of
its
past
prices.
This
takes
aim
at
technical
analysts,
people
who
look
at
charts
of
stock
prices
and
try
to
spot
patterns
predictive
of
future
movements.
The
weak
form
(in
fact,
all
the
forms
of
the
efficient
market
hypothesis)
says
that
technical
analysis
is
worthless.
The
"semistrong
form"
says
that
you
can't
beat
the
market
by
us
ing
any
public
information
whatsoever.
Public
information
includes
not
only
past
stock
prices
but
also
every
press
release,
balance
sheet,
Bloomberg
wire
story,
analyst's
report,
and
pundit
comment.
No
matter
how
intently
you
follow
the
news,
and
no
matter
how
good
you
are
at
drawing
conclusions
from
news,
by
gut
instinct
or
fancy
software,
you
can't
beat
the
market.
Fundamental
analysis
(the
study
of
company
finances
and
other
business
and
economic
fac
tors) is
worthless,
too.
Finally,
the
"strong
form"
adds
private
information
to
the
mix.
It
says
that
you
can't
beat
the
market
even
if
you
have
access
to
com
pany
news
that
has
not
yet
been
made
public.
"Insider
trading"
is
worthless!
Fama
was
not
going
quite
that
far.
Fie
was
just
laying
out
the
log
ical
possibilities.
There
are
of
course
many
cases
of
company
insid
ers
profiting
from
advance
knowledge
to
buy
or
sell
stock.
There
have
also
been
studies
offering
evidence
that
private
information
leaks
into the market and
affects
prices
before public announce
ments.
Insiders
may
find
that
the
market
has
already
priced
in
their
private
knowledge.
The common element to all of
Fama's
three versions is the claim
126


## Page 130

Arbitrage
that
no
one
has
a
usable
"private
wire"
on
the
stock
market.
There
is
no
way
to
achieve
consistently
bcttcr-than-market
returns.
No
one
raised
criticism
of
the
opposing
view
to
a
higher
art
than
Paul
Samuelson.
His
most
famous
rant,
published
in
the
first
issue
of
the
Journal
of
Portfolio
Management
(1974),
runs
in
part:
A
respect
for
evidence
compels
mc
to
incline
toward
the
hy
pothesis
that
most
portfolio
decision
makers
should
go
out
of
business—take
up
plumbing,
teach
Greek,
or
help
produce
the
GNP by
serving
as
corporate
executives.
Even
if this
advice
to
drop
dead
is
good
advice,
it
obviously
is
not
counsel
that
will
be
eagerly
followed.
Few
people
will
commit
suicide
without a
push.
Through
the
spirited
advocacy
of
Fama
and
Samuelson,
the ef
ficient
market
hypothesis
swept
the
academic
community
in
the
1960s
and
1970s
(a
time
that
happened
to
be
boom
years
for
"star"
portfolio
managers,
actively
managed
mutual
funds,
and
media
cov
erage
of
stock
investing).
Its
influence
was
endorsed
by
the
Nobel
Prize
committee.
Samuelson
took
home
the
first
economics
prize
awarded
to
an
American
(in
1970),
and
Fama
seems
to
be
on
every
one's
short
list
of
likely
future
Nobelists.
A
sizable
proportion
of
economics
prizes
have
gone to students and
associates
of
Samuel
son's,
who
shared
his
views
on
market
efficiency.
The
influence,
and
attitude,
of this
clique
was
captured
in one
nickname:
the
"Random
Walk
Cosa
Nostra."
To
some
it
seemed
that
an
MIT
"Mafia"
made
it
difficult
to
pub
lish
dissenting
views
in
The
Journal
of
Finance
and
other
prestigious
pub
lications.
In the
mid-1980s,
MIT
information
theorist Robert Fano
wrote
a
paper
arguing
that
stock
price
changes
are
not
exactly
a
ran
dom
walk
and
are
subject
to
predictable
cycles.
He
showed
it to
some
MIT
economists
for
comment.
The
reaction
to
the
paper's
mere
premise
was
brutal.
"Unless
you're
working
ina
certain
way,
with
cer
tain
views,
you're
wrong,"
is how
Fano
described it. He was told that it
127


## Page 131

fortune's
formula
would
be
pointless
to
seek
publication.
The
referee
"would
call
some
oneat MIT and
they'd
say,
'Oh,
yes,
he's
a
crackpot.'
"
This
Is
Not
the
Time
to
Buy
Stocks
After
she
divorced
ClaudeShannon, Norma
Levor
moved
to
Hollywood
and
joined
the
Communist
Party.
Claude
did
not
see
her
for
over
twenty
years.
Norma
and
her
second
husband,
Ben
Barzman,
were
blacklisted
screenwriters
during the
McCarthy
era.
When
it
appeared
that
the
U.S.
government
would
force
them
to
name
fellow
Communists
or
face
prison,
they
fled
the
country
for
France.
In
1963
Norma
visited
Cambridge
to
help
her
daughter
furnish
a
Harvard summer
school
dorm
room.
Norma took the initiative of
contacting Shannon.
They
met
at
the
Commander
Hotel
bar
and
compared
lives.
"I
have a nice wife, wonderful
kids,"
Claude told her. "I teach, do re
search.
I
have
a
collection
of twenty-three
cars.
I
tinker."
At the
word
"tinker,"
he
laughed
in
spite
of
himself.
Norma
put
out her hand. Claude took it and
kissed
her palm.
They
went
up
to
Norma's
room
and
made
love.
Afterward,
Claude asked,"Areyou
happy?"
"Reasonably.
And
you?"
"Reasonably."
128


## Page 132

Arbitrage
Shannon
told
Norma
that
their
marriage
would
have
been
doomed
in any
case:
her
radical
politics
would
not
have
mixed
with his secret
cryptographic
work.
No
less
an odd match
was
communism
and
Shannon's latest
research
interest, the stock
market.
Shannon's
attitude
toward
money
was
an
enigma
to
the
people
around
him.
Growing
up
in
Michigan,
he
never
wanted
for
necessi
ties,
nor
had
much
ofa
chance
to
spend
a
dollar
foolishly.
As
a
grad
uate
student,
Shannon
was
"entirely
without
funds,"
as
Vannevar
Bush
wrote.
This
changed
with
his
first
marriage.
Norma's
wealthy
mother
hired a decorator and
furnished
the
Shannons'
modest
Princeton
apartment
with smart modern furniture. Claude never felt
comfort
able
with
the
makeover,
said
Norma,
complaining
that
it
was
like
living
in a
stage
set.
It
was
Betty
who
nudged
Claude
toward
an interest in
invest
ments.
Before
his
second
marriage,
Shannon
kept
his
life
savings
in
a
checking
account,
earning
no
interest.
Betty
suggested
that
it
might
be
a
good
idea
to
put
some
money
in
bonds—or
stocks,
even.
The
adult
Shannon
cultivated
the
image
ofa
disinterested
seeker
of
truth,
disdaining
the
values
of
the
marketplace.
"I've
always
pur
sued
my
interests,"
he
told
one
journalist,
"without
much
regard
for
financial
value
or
value
to
the
world."
"When
he
was
working
on
a
theory,"
explained
Betty,
"he
was
thinking
of
things
that
were
beau
tiful
mathematically."
Flaving
solved
the
abstract
problem
that
in
terested
him,
he
was
ready
to
move
on.
"Once
he
was
done with
something,"
Betty
said,
"he
was
donewith
it."
Claude
admittedwhat
was
clear
to
anyone
who
ever
laid
eyes
on
the
Toy
Room:
"I've
spent
lots
of
time
on
totally
useless
things."
Stories
tell
of
Shannon's
otherworldly
indifference
to
money.
Bell
Labs
long
had
a
policy
of
keeping
salaries
secret.
In
1955
a
bio-
physicist
named
Bob
Shulman
made
a
list
ofa
hundred
employees
and
went
to
each
with
an
irresistible
offer.
Put
your
salary
on
this
list,
Shulman
said,
and
I'll
let
you
see
everyone
else's.
Most
of
the
hundred
accepted,
among
them
Shannon.
The list
revealed
that
Shannon
was
making
no
more
than
a
lot
of
other
people
of
no
great
129


## Page 133

fortune's
formula
reputation.
Bell
Labs
was
sufficiently
shamed
to
give
Shannon
a
50 percent
raise.
A
colleague
who
borrowed
Shannon's
MIT
office
while
he
was
away
found
a
large
uncashed
check
made
out
to
Shannon.
It
was
a
year
old.
This
incident
appears
to
be
the
grain
of
truth
behind
an
MIT
legend
of
piles
of
uncashed
checks
languishing
in
Shannon's
office.
In the
late
1950s,
Shannon
began
an
intensive
study
of the
stock
market
that
was
motivated
both by
intellectual
curiosity
and
desire
for
gain.
He
filled
three
library
shelves
with
something
like
a
hun
dred
books
on
economics
and
investing.
The
titles
included
Adam
Smith's
The
Wealth
of
Nations,
John
von
Neumann
and
Oskar
Mor-
genstern's
Theory
of
Games
and
Economic
Behavior,
and
Paul
Samuelson's
Economics,
as
well
asbookswith a more
practical
focus
on
investment.
One
book
Shannon
singled
out
as
a
favorite
was
Fred
Schwed's
wry
classic,
Where
Are
the
Customers'
Yachts?
At the
time
he
was
designing
the
roulette
computer
with
Thorp,
Shannon
kept
notes
in
an
MIT
notebook.
Part
of the
notebook
is
devoted
to the
roulette
device
and
part to a
wildly
disconnected
set
of
stock
market
musings.
Shannon
wondered
about
the
statistical
structure of the market's random walk and whether information
theory
could
provide
useful
insights.
He
mentions
such
diverse
names
as
Bachelier.
(Benjamin)
Graham
and
(David)
Dodd,
(John)
Magec,
A.
W
Jones,
(Oskar)
Morgenstern,
and
(Benoit)
Mandel
brot.
FIc
considered
margin
trading
and
short-selling;
stop-loss
orders
and the
effects
of
market
panics;
capital
gains
taxes
and
transaction
costs.
Shannon
graphs
short
interest
in
Litton
Indus
tries
(shorted
shares
vs.
price:
the
values
jump
all
over
with
no
evi
dent
pattern).
He
notes
such
success
stories
as
Bernard
Baruch,
the
Lone Wolf, who ran about
Sio.ooo
into a million in about ten
years,
and
Hetty
Green,
the
Witch
of
Wall
Street,
who
ran
a
million
into a
hundred
million in thirty years.
Shannon once went into the
office
of
MIT
grad student Len
Kleinrock
to
borrow
a
book.
(Kleinrock
would
later
have
a
measure
130


## Page 134

Arbitrage
of
fame
for
his
role
in
starting
up
the
great
wire
service
of
our
age,
the Internet.) The book
Shannon
wanted
to borrow
contained
ta
bles
of
wealth
distribution
in
the
United
States.
It
told
how
many
millionaires
there
are,
how
many
people
with
a net
worth
of
Sioo.ooo,
and so on. Puzzled, Kleinrock asked
Shannon
what
he
needed
it
for.
Shannon
said
he
was
devising
a
system
for
investing
in
the
stock
market.
Still
puzzled,
Kleinrock
asked,
"You're
interested
in
making
money
in
the
stock
market?"
"Yes,
aren't
you?"
Shannon
replied.
When
friends
tactfully
asked
Shannon
what
he
was
doing
with
his
time,
he
would
often
speak
of
using
mathematical
methods
to
invest in the stock market. It was rumored that Shannon
had
made a
lotof
money
through
his
investments.
Not
everyone
took
these
sto
ries
at
face
value.
"Usually
in
my
experience
the
very
few
who
some
how develop a knack for
risk-corrected
excess
total return do
become
rich
very
quickly
and
do
reveal
that in
their
observable
life
style,"
Paul
Samuelson
told
mc.
"I
do
not
remember
any
gossip
at
the
MIT
watercoolers
that the Shannons had levitated out of the
academic
class."
Others
suspected
that
the
talk
of a
stock
market
"killing"
was
an
excuse
for dropping out of the
scientific
world.
"You
weren't
affected
by
your
success
in
the
stock
market,
were
you,
taking
away
the
necessity
to
work
so
hard?"
asked
journalist
Anthony
Liversidge
in a
1986
interview.
Shannon's
answer
was
"Certainly
not."
He
con
tinued,
I evendid some
work
on the
theory
of
stocks
and the stockmar
ket
which
is
among
other
papers
that I
have
not
published.
And
everybody
wants
to
know
what's
in
them!
...
I
gave
a
talk
at
MIT on the
subject
some
twenty
years
ago
and
outlined
this
material
. . . but
never
wrote
it up and
published
it, and to this
day people ask about it.
Despite
the
fact
that he
never
published
a
word
on the
subject,
the
stock
market
became
one of
the
great
enthusiasms
of
Claude
131


## Page 135

FORTUNE
s
formula
Shannon's
life,
and of
Betty's
as
well.
Soviet
mathematician
Boris
Tsybakov
recalls
a
1969
visit
to
America
in
which
Shannon
flew
off
into an
enthusiastic
tangent,
outlining
market
theories
on
napkins
at the MIT
faculty
club.
Shannon
apologized
for
the
fact
that
Tsy
bakov
would
not be
able
to put
these
ideas
into
practice
in the
So
viet
Union.
Shannon
was
not the
first
great
scientific
mind
to
suppose
that his
talents
extended
to the stock market. Carl Friedrich Gauss,
often
rated
the
greatest
mathematician
of
all
time,
played
the
market.
On
a
salary
of
1,000
thalers
a
year,
Euler
left
an
estate
of
170,587
thalers
in cash and
securities.
Nothing is
known
of
Gauss's
investment
methods.
On the other hand,
Isaac
Newton lost some
20,000
pounds in
vesting
in
the
South
Sea
Trading
Company.
Newton's
loss
would
be
something
like
S3.6
million
in
today's
terms.
Said
Newton:
"I
can
calculate
the
motions
of
heavenly
bodies,
but not the
madness
of
people."
Shannon told one of his
Ph.D.
students, Henry Ernst, that the
way
to
make
money
in
the
market
was
through
arbitrage.
That
term
was
in the
process
of
being
redefined
by
the
information
age.
Originally
it
referred
to a
scheme
for
profiting
from
small
price
differences
between
geographically
remote
markets.
Gilded
Age
fi
nancier
Jay
Gould
discovered
that
the
price
of
gold
varied
slightly
between Londonand New
York.
Gould boughtgoldwhereverit was
cheaper
and
shipped
it to
wherever
it
was
more
expensive,
selling
it
for a quick profit.
Instantaneous electronic communication has mostly erased geo
graphic
price
disparities.
Today
"arbitrage"
is
used
to
describe
al
most
any
attempt
to
profit
from
irrationality
in
the
market.
Much
like
Gould,
today's
arbitrageurs
usually
buy
and
sell
nearly
the
same
thing
at
nearly
the
same
time
in
order
to
make
a
profit.
Because
ar
bitrage
profits
can
be
quick,
the
return
on
investment
may
be
far
more than with more conventional stock or bond investing.
"Arbitrage"
is
a
charged
word.
Those
of
leftish
political
convic-
132


## Page 136

Arbitrage
tions
often
see
arbitrage
as
money
for
nothing,
the
epitome
of
Wall
Street
"greed"
and
fortunes
made
while
providing
little
or
no
visible
social
benefit. To efficient market
theorists,
arbitrage is perhaps no
lessan affront.
By
definition,
arbitrage
opportunities cannot exist in
an
efficient
market.
The
strongly
theoretical
slantof
much
academic
finance
is
well
illustrated
bythe adoption of "no arbitrage"as an ax
iom.
Financial
"theorems"
are
proved
with
Euclidean
rigor by as
suming
that no
arbitrage
opportunities
exist.
This
circular
logic
has
given
rise
to a
joke.
An
MIT
(University
of
Chicago)
economist
says
there's
no
point
in
looking
for
hundred-
dollar
bills
in the
street.
Why?
Because,
were
there
any
hundred-
dollar
bills,
someone
would
already
have
picked
them up.
This is not quite the
paradox
it
appears.
Whether there are
hundred-dollar
bills
in the street depends on how
frequently
people
drop
them
and
how
quickly
other
people
pick
them
up.
The
effi
cient market theorists
claim
that
picking
up is easy There is a race
between
the
picker-uppers
to
snatch
up
the
bills
before
anyone
else
does.
This
competition
promptly
clears
the
streets
of
hundred-
dollar
bills.
The
free
money
vanishes
like
snowflakes
on a hot grid
dle.
One
may
then
say,
to
good
approximation,
that
there
is
no
free
money
lying
around.
The
critics
of the
efficient
market
hypothesis
make
a more mod
est
case,
that
sometimes
people
drop
bills
faster
than the
picker-
uppers
collect
them.
In
some
places,
the
hundred-dollar
bills
remain
on
the
street
for
a
while.
Shannon
apparently
saw
the
Kelly
formula
as
the
mathematical
essence
of
arbitrage.
In the
spring
term
of
1956,
Shannon
gave
a
class
at
MIT
called
Seminar on Information
Theory.
One lecture
was
titled
"The
Portfolio Problem."
The
lecture is
documented
only
by
a
mimeographed
lecture
handout
saved
by
student
W
Wesley
Peterson
(now
a
prominent
information
theorist)
and
housed
with
Shannon's papers at the
Library
of
Congress.
This
handout
would
mystify
anyone
looking
for
investing
advice.
The
lecture
is on
John
Kelly's
gambling
system.
It
mentions
The
$64,000
Question
and a
wire
service
giving
horse
tips.
Aside
from
the
title, it docs
not
mention portfoliosor the stock
market.
133


## Page 137

FORTUNE
S
FORMULA
Presumably,
Shannon made the connection in the lecture itself.
His
point
was
that a
horse
race
is
like
a
particularly
fast-paced
and
vicious
stock
market.
It
would
be
alarming
to
visit
a great
stock
ex
change and find the floor
littered
with worthless stock certificates.
Try
visiting
a
racetrack.
Most
wager
tickets
become
worthless
within
minutes.
It
is
folly
to
bet
everything
on a
favorite
(horse
or
stock).
The
only
way
to
survive
is
through
diversification.
Someone
whobetson
every
horse—or
buys
an
index
fund—will
at
least
enjoy
average
re
turns, minus transaction costs.
"Average"
isn't so hot at the race
track,
given
those
steep
track
takes.
"Average"
is
pretty
decent
for
stocks,
something
like
6
percent
above
the
inflation
rate.
For
a
buy-
and-hold
investor,
commissions
and
taxes
are
small.
Shannon
was
more
interested
in
above
average
returns.
The
only
way
to
beat
the
market
(of
stocks
or
horse
wagers)
is
by
knowing
something
that other
people
don't. The stocktickeris
like
the tote
board. It
gives
the
public
odds.A trader whowants to beat the mar
ket must
have
an
edge,
a more
accurate
view
of what bets on stocks
are reallyworth.
There are of
course
many
differences
between
a
racetrack
and a
stock
exchange.
A
horse
must
win,
place,
show,
or
finish
out of the
money:
those are the only distinct
outcomes.
For
stocks
and other
securities,
the rangeof
outcomes
is a continuum.A stock can rise or
fall
by
any
amount.
It
may
pay
dividends,
split,
or
merge.
Time
at
the
track
is
divided
into
discrete
races. Time in the
market
is
contin
uous.
An investor can stay
invested
for as long or short a time as
desired.
These
differences
are
not
fundamental.
Any
type
of
random
event
has
a
"probability
distribution."
This
is
an
accounting
of
every
possible
outcome
and
its
probability.
For
a
simple
casino
game,
there
may
be
just
two
outcomes
(win
and
lose)
with
associated
probabili
ties
and
payoffs.
You
could
represent
this
distribution
as
a
bar
graph
with
two
bars
for
"win"
and
"lose."
Fora stock
investment,
the
probability
distribution
is more
like
a
134


## Page 138

Arbitrage
bell-shaped
curve
whose
shape
changes
gradually
with
time.
You
tend to end up
somewhere
in the
middle
of the
curve,
with a
mid
dling
degree
of
profit.
There isa
small
chance
of
doing
much
better,
or much worse, than usual. Statisticians arc at home with
both
types
of
probability
distributions,
and
both
arise
in
information
theory.
Kelly's
tale of a
gambler
with
inside
tips
presupposes
exactly
what the
efficient
market
theory
denies.
No one is
supposed
to
have
advance
knowledge
of what the
market
is
going
to
do.
In the sim
plest
conception
of an
efficient
market,
everyone
gets
all
financial
news
simultaneously
and
acts
on it
all
at
once.
This isn't
literally
true,
of
course. More realistic models
of
the efficient
market
admit
that it takes minutes, hours, or days for people to act on news.
Throughout
this
process,
there
must
be
people
who
are
temporarily
better
informed
than
others.
Some
economists
hold
that
even
though
some
people
do
have
an
informational
edge,
they
are
unable
to
profit
from
it.
Transaction
costsare often
mentioned
as a
reason.
The
gains
from
inside
infor
mation
may
be
smaller
than
the
commissions.
It
may
also
bethat the
arbitrageur
is
taking
unacknowledged
risks.
Whathe
believes
to bea
"sure
thing"
is
not.
The
usual
small
profit
comes
at the
expense
of
accepting
a
small
risk
ofa
catastrophic
loss.
And
one
way
or
another,
no one beats the market in the long run.
Kelly's
analysis
raises
doubts
about
this
tidy
conclusion.
If
the
only
limit
to
profit
is
the
information
rate
of the
private
wire,
then
it is hard to see
why
transaction
costs
must
always
be larger than
profits.
With a
sufficiently
informative
private
wire,
an
investor
could
overcome
costs
and
beat
the
market.
"You
know
the
economists
talk
about
the
efficient
market
where
everything
is
equalized
out and
nobody
can
make
any
money
really,
it's all
luck
and
so on,"
Shannon
once
said. "I
don't
believe
that's
true
at
all."
Shannon
had
already
tasted
his
first
market
success.
This had noth
ing
to do
with
arbitrage
and
everything
to do
with
social
networks.
In 1954 Charles William Harrison, a Bell Labs
scientist
Shannon
135


## Page 139

FORTUNE
s
formula
knew,
started
his
own
company.
Harrison
Laboratories
made
power
supplies for the
promising
new
field
of color
television.
Shannon
bought
a
block
of
stock.
Harrison
Labs
isnot a
familiar
name
today
because
it
was
acquired
by
Hewlett-Packard
in
1962.
The
stock's
price
zoomed,
and Shannon got a
handsome
chunk of
Plewlett-
Packard
stockin the
merger.
The
size
of the paper profit
convinced
him that there
was
real
money
to be
made
in
stocks.
The
experience
with
Harrison
made
Shannon
receptive
when
another
friend,
Henry
Singleton,
spoke
of
starting
his
own
com
pany.
Singleton
was
a
close
friend
of
Shannon's
from
MIT
graduate
school.
They
played
chess
together.
For
a
while.
Singleton
lived
in
Greenwich
Village
near
Bell
Labs.
Then he
moved
west to work
in the
booming
defense
industry.
In
i960
Singleton
and
George
Kozmetsky
founded
Tcledyne,
a
defense
contractor
selling
digital
navigation
systems
to a
still-analog
Pentagon.
Shannon
bought
a
couple
thousand
shares
at the
initial
price
of Si a
share.
It
became
one of the red-hot
stocks
of the
1960s.
By
1967
it hit
S24.
As
the
company's
shares
skyrocketed,
Singleton
used
the
inflated
market
value
to
buy
other
companies.
He
bought
about
130.
Tele-
dyne
came
to
own
insurance
companies,
offshore
oil
wells,
and the
manufacturer
of
Water
Pik
teeth
cleaners.
In
1962
an MIT
group
founded
Codex
Corporation
to
provide
coding
technology
to the
military.
Shannon
bought
Codex
stock.
Codex
marketed
the
first
modem
for
mainframe
computers
(9,600
baud,
for
523,000).
Few
businesses
could
use
it
because
it
was
illegal
to attacha third-party
modem
to
AT&T's
phone
lines.
A
1967
FCC
ruling
overturned
AT&T's
equipment
monopoly,
and
Codex's
mo
dem
business
surged.
Codex
merged
into
Motorola,
giving
Shannon
another
success
story.
These
three
savvy
choices
were
not
the
only
new
technology
of
ferings
the
Shannons
bought.
Some
of
the
new
issues
they
bought
fizzled.
In at
least
one
case,
they
sold
too
early.
They
bought
Xerox
and
sold
at a
profit,
losing
out on
what
could
have
been
a
vastly
larger gain.
In his early yearsas an
investor,
Shannon tried to do market tim
ing.
One day in
1963
or
1964,
Shannon
warned
Elwyn
Berlckamp
136


## Page 140

Arbitrage
that it was
not
the time to buy
stocks.
Like
most grad students.
Bcrlekamp
barely had
money
for rent. When
Bcrlckamp
politely
asked
why.
Shannon
explained
that he had invented an
electrical
device that
mimicked
the
flow
of
money
into and out of the stock
market.
It
was
an
analog
feedback
circuit
that must
have
been
something
like
Kelly's
football
circuit.
(No one I
spoke
with
remembers
whether
Shannon's or
Kelly's
circuit
was
first.)
One of the
puzzles
of the
market is that stock
prices
are more
volatile
than corporate earn
ings.
This is often attributed to
feedback
effects—the
phenomenon
that
causes
the head-splitting shriek of the
principal's
microphone
in the high
school
auditorium.
When people put money into the
market,
the
buying
pressure
causes
prices
to
rise.
The
people
who
have
made money talk about it.
Envy
motivates
friends into buying
stock too. This continues the positive
feedback—for
a while.
Prices
can't go up
forever,
not
when
earnings
haven't
increased
apace.
At some point, bad
news
triggers
a
panic
selling
(negative
feedback).
The "bad
news"
does
not
have
to be
all
that bad. It is
only
a
catalyst,
the
pinprick
that
bursts
the
bubble.
Shannon
evidently
had a
way
of
adjusting
the
inputs
to his
electrical
circuit to
match
the
flows
of
investment
funds.
He
concluded
the
market
was
over
due
for
a
correction.
The
market
was
then
in
the
midst
of
a
bull
market
that
lasted
through
1965.
This
was
followed
by a
13
percent drop in the
S&P
500 in
calendar
year
1966.
Neither the
timing
nor the
magnitude
of
the
1966
pullback
supplies
much
evidence
in support of
Shannon's
device.
On
one
of
his visits to the
Shannons'
home, Ed
Thorp
saw an
equation on a blackboard in the
study.
It read:
2"=2048
Thorp
asked
what it
meant.
Both
Claude
and Betty turned
silent. After a moment's
hesitation,
they
explained
that they had
been trading hot new stock
issues.
They had been
doubling
their
money about every month. They were
figuring
how much money
137


## Page 141

FORTUNE
s
formula
they would
have.
Ever)'
dollar invested would turn into 82,048 after
eleven
doublings.
*
IPO
Shannon
was
not
the
only
one turning
spectacular
profits
from
new
issues.
At the
time
Thorp met
him,
Manny
Kimmel
was
planninga stock offeringof his parkinglot
business—an
IPO of his
slice
of
Murder,
Inc.
The
idea
that
chance
or
chaos
determines
the
fates
of
markets
and
corporations
is one
many
find
hard to
accept.
Surely
God
docs
not play dice with the stock market. The talc of
Kimmel's
stock
of
fering
may
serve
asan
amusing
counterexample.
The
first
thing
to
remember
is
that
Kimmel
got
into
the
parking
lot
business
literally
ona
lucky
roll
ofthe
dice.
Kimmel
incorporated
that
business
in
1945,
calling
it the
Kinney
System
Parking
Corpora
tion, after
Kinney
Street in
Newark,
where the first lot
was
located.
Ownership of
Kinney
was
unclear,
however.
Longy
Zwillman
left no
will.
In i960 a
man
named
Howard
Stone
happened
to be
dating
Zwillman's
daughter.
Zwillman's
widow told Stone that the Zwill
man
family
owned
Kinney
Parking
and
several
Las
Vegas
hotels.
If
he
married
into the
family,
it
could
all
be
his
someday.
The
February
1962
prospectus
for
the stock
offering,
to be
called
Kinney Service
Corporation,
did not
mention
Emmanuel Kimmel
or Abner
Zwillman.
It
claimed
that the
largest
block
of stock
was
owned
by
Kimmel's
firstborn
son,
Caesar.
The
younger
Kimmel
138


## Page 142

Arbitrage
reportedly
owned
169,500
shares,
making
up
10.8
percent of the
company.
In March1962
Kinney
began
tradingon the AmericanStockEx
change with the
symbol
KSR. The offering price was S9 a share.
This made Caesar
Kimmel's
(whocvcr's?)
shares worth
S1.5
million.
Kinney Service Corporation began publishing
glossy
annual re
ports like any
other
American
company.
The first annual report
boasted, "Service is our middle name." The corporate culture re
tained tracesof the old
days.
"One
day,
a
black
guycame in and tried
to steal a car,"said Judd
Richheimer,
who worked for Kinney in the
early 1960s.
"Butchie
[the
garage
foreman]
turned the air compres
sor on so there would be a lot of
noise;
then he took the guy down
stairs and broke both his arms and both his
legs
and threw him out
on
the
street."
Kinney
had recently entered a new line of
business:
funeral
homes.
Just
before
the stock
offering,
it
merged
with
Riverside
Memorial
Chapel in New
York.
The
funeral
parlor
was
doing better
than the parking lot
business
was.
A further
advantage
of the
merger
was
that
Kinney
gained
the
talents
of a
young
undertaker
named Steve
Ross.
Despite his
unlikely
background,
Ross
was
a ca
pable manager and brilliant deal
maker.
It
was
Ross
and not the
Kimmcls who was soon running the
company.
Ross
was a natural
gambler.
He read
Beat
the
Dealer,
and
Manny
Kimmel
gave
him
lessons
in
card-counting.
Ross
was
willing
to take
gambles
in
building
the
company,
too.
The
sixties
was
the
age
of
conglomerates.
Ross
diversified
into
businesses
that had no
visible
connection to the
already
odd
marriage
of
caskets
and parking
spaces.
He bought
office
cleaning
services,
DC Comics (publishers
of
Superman),
MAD
magazine, and a
talent
agency.
In 1969
Ross
made a daring bid for Warner Brothers, the
film
studio and
record
company.
It is a
reflection
of those
giddy
times
that two other
conglomerates
were also trying to buy
Warner.
Ross
narrowly
prevailed
in the
bidding
war.
Kinney
acquired
Warner for
S400
million.
By
1969
Kinney
stock
was
selling
for over S30a share.
That represented about a
19
percent annual return from the offer-
139


## Page 143

FORTUNE
S
FORMULA
ing
price.
The year after the
merger,
Caesar
Kimmel's
shares were
worth
over
S6
million.
The merger put
Kinney
in the
spotlight.
In 1970
Forbes
magazine
called
it a
"Market
Mystery"
that
Kinney
was
selling
for twenty
times
earnings.
It
alleged
dubious
accounting
practices.
To top this
off,
the
magazine
ran a
sidebar
mentioning
rumors
linking
Kinney
to the
Mafia.
A reporter asked Caesar Kimmel for comment.
The
younger
Kimmel,
shown in a
photograph,
was
a clean-cut guy who
could have stepped out of a
Brooks
Brothers ad. "I've lived with this
over the years—the charge that we are run by the
Mafia,"
Kimmel
told the
magazine.
"It just isn't true. We don't wear shoulder hol
sters.
We've
never been under the
influence
of any underworld
group."
He told the
magazine
that he
was
the headof the
company's
ac
quisition committee. "We could have acquired a lot
of
businesses
which in our opinion were corrupt. We didn't touch them with a
ten-foot
pole."
Asked
whether his
father,
Manny
("a
big
gambler"),
had
owned
the parking lot
company,
Kimmel
answered,
"Never."
He
attributed
the stories to the incidentsin the late 1940sin
which
the
company's
midtown
lot had been
used
for
limousines
taking
players
to crap
games in New
Jersey.
The
Forbes
reporter was
incredulous.
"And
that's the event that is
responsible
for the rumor about the
Mafia
popping
up
again
and
again?
The game that your father was
involved
with from 1948 to
1950?"
"To put it
bluntly,
I am not myfather's
keeper,"
Kimmel
replied.
"He hashisworld
...
and I
have
mine.
Print what you want.The ru
mors
are
not
true."
After the
Warner
merger
and the
Forbes
article,
Steve
Ross
recog
nized that
Kinney's
past could be an impediment to his future
140


## Page 144

Arbitrage
empire-building.
He
renamed
the
company
Warner
Communica
tions.
At theendof
1971,
the
company
spun
off
the
parking
lot
busi
ness.
The
funeral
home
business was sold, too.
In
1990
Warner
merged
with
publishing
giant
Time-Life
to
create
Time-Warner.
Warner's
shares
rose to S70.
Time-Warner
be
came
the
world's
largest
media
corporation,
with about Sio
billion
annual
revenue
and
Si5 billion in stock
market
value.
This
deal was
itself
dwarfed
by
the
S350
billion
merger
between
Time-Warner
and
America
Online
in
2000.
A
note
in
the
interest
of
full
disclo
sure:
One of
Time-Warner's
smaller
subsidiaries
published
my
last
book.
Manny Kimmel died in Boca Raton, Florida, in 1982. He left
behind an
attractive
young
Swedish
wife,
Ivi,
who had been in her
twenties
when
she
married
him.
Bet
Your
Beliefs
Blackjack
had
ceased
to be as
profitable
or fun as it had once
been for Ed Thorp. "I
realized
that if I
pushed
it, sooner or later
some unpleasant
physical
things
would
happen in
Nevada,"
he said.
By
1964he
decided
to directhis
talents
toward
the
biggest
casino
of
all:
the
stock
market.
Thorp
had
accumulated
about
$25,000
in
blackjack
winnings
plus
anotherSi5,000 in
savings,
mainly
from
book
royalties.
During
the
New
Mexico
summer
breaks
of
1964
and
1965,
he
made
a
sys
tematic
effort
to
educate
himself
on
the
market.
One
of
the
books
141


## Page 145

FORTUNES
FORMULA
he read
was
Paul
Cootner's
The
Random
Character
of
Stock
Market
Prices
(1964).
This
was
published
by
the
MIT
Press
and
collected
key
ar
ticles
on
the
random-walk
model.
Thorp
read
a
news
article
saying
that
some
people
were
buying
silver.
The demand for
silver
had long been greater than the
supply.
The difference had been made up by melting down and
reclaiming
old
jewelry
and
other
silverware.
Stores
of
reclaimablc
silver
were
running
low.
Using
his
savings,
Thorp
bought
some
silver
at
about
S1.30
an
ounce.
It went up to about
S2.
Fie
bought more
silver
on
margin
(with
borrowed
money).
The
price
fell.
Thorp
couldn't
meet
the
margin
calls
and lost
about
$6,000,
a
crushing
sum
at the
time.
"I
learned an
expensive
lesson,"
he
said.
The
lesson
was:
You
are un
likely
to get an
edge
out of what
you
see in the
news.
A
couple
of
Texas
investors
contacted
Thorp.
They
had
heard
of him
through
the
blackjack
publicity.
They
identified
themselves
as
experts
in
picking
life
insurance
stocks
and
wanted
to
know
if
Thorp
might
be
able
to
help
them.
Thorp met with the
investors
in
Dallas.
He studied the life insurance industry and grew confident
enough
to put
some
of
his
own
money
into
companies
the
pair
rec
ommended. The stock
"promptly
went down the
tubes."
All Thorp
gotoutof the
experience
was
asetof
defective
steak
knives
the
pair
sent him as a gift.
Back
in Las Cruces, New
Mexico,
Thorp
did what many small
investors
do. Fie
checked
out the "get rich
quick"
ads in
financial
magazines.
There
were
hundreds
of
stock
market
systems
for
sale.
An ad in
Barron's
caught his
eye.
It
was
for a
company
called
RFIM
Warrant
Service.
The
service
Paul
Samuelson
had
subscribed
to
was
still
in
busi
ness.
It
was
run bya
certain
Sidney
Fried
who
claimed
it
was
possi
bleto
buy
warrants
for
pennies
and
sell
them
for
dollars.
Thorp sent
away
for the
book.
As
he
read
it,"I got
thinking
aboutwhatit is that
determines
the
price
of a
warrant,"
Thorp
said.
"In about an hour of
thinking
and
sketching
on
scratch
paper,
I
realized
that there
was
almost
un
doubtedly a
simple
way
to price these
things."
142


## Page 146

Arbitrage
Warrants
were
the
only
kind
of
widely
traded
stock
option
then.
One
of
the
warrants
Thorp
began
following
was
issued
by
Sperry
Rand,
the
company
that
made
the
first
mass-produced
digital
com
puter. On March 17
1958,
Sperry Rand
issued
a warrant that enti
tled
the
owner
to
buy
one
share
of
Sperry
Rand
stock
for
the
price
of
$25
(the
"strike
price").
The
warrant
expired
on
September
16,
1963,
meaning that at the close of business on that date, it became
worthless.
What is a fair price for a
warrant?
The warrant would be imme
diately
valuable
if and
when
Sperry
Rand
stock
traded
for
more
than
S25
a
share.
Should
Sperry
Rand
be
selling
for
S29
a
share,
the
warrant
would
be
worth
at
least
$4,
for
you
could
use
it to
buy
a
share
of
Sperry
Rand
at a
$4
discount
from
the
going
price.
That
does
not
mean
the
warrant
would be
worthless
when
Sperry Rand
was
selling
for
less
than
S25.
You
can still sella warrant
to
someone
who
thinks
that
stock
will
rise
above
the
strike
price
be
fore the expiration date.
The
newspaper
listings
quoted
prices
for
warrants,
just
as
they
listed
handicapper's
odds
for
horse
races.
The
people
pricing
war
rants
factored
in a lotofgut
instinct.
When
you
say
that a
warrant
is
worth
such
and
such,
you
are
essentially
quoting
odds
that the
stock
will
rise
above
the
strike
price
before
the
expiration.
You
are further
guessing
by
how
much
it
might
rise
above
that
price.
This isa
com
plex
judgment
call.
The warrant
price
must
reflect
such
scenarios
as
the
failure
of a newproduct
launch,
the
resolution
of a
lawsuit,
or an
executive
selling
a big
block
of
stock
to
pay
for
a
Matisse.
The but
terfly
whose
flapping
causes
a
hurricane
could
lead
to
the
sinking
of
a
yacht
full
of
Sperry
executives,
pummcling
the
stock's
price.
How
can anyone predict such
contingencies
systematically?
Then Thorp thought of the random
walk
model.
Assume that
there
is no
possible
way
of
predicting
the
events
that
move
stock
prices.
Then
buying
a
stock
option is
placing
a bet on a
random
walk.
Thorp
knew
that
there
were
already
precise
methods
for
cal
culating
the
probability
distributions
of
random
walks.
They
de
pend on the
average
size of the random
motions—in
this
case,
how
much
a
stock's
price
changes,
up or
down,
per
day.
143


## Page 147

FORTUNE
S
FORMULA
Thorp did
some
computations.
He
found
that
most
warrants
were
priced
like
carnival
games.
They
cost
too
much,
given
what
you
can
win
and
your
chance
of
winning
it.
This
was
especially
true of
warrants that were within a couple of years of expiring. Traders
were
too
optimistic
about
the
prospect
of
stock
prices
rising
in that
time.
There is nothing
you
cando abouta
carnival
game
that coststoo
much
except
to
refuse
to
wager.
But
should
you
find
a
warrant
that
costs
too
much,
you
can
sell
it
short.
This
flips
the
unfavorable
odds
in your
favor.
A trader who
sells
short is
selling
a
security
he doesn't yet
own.
The trader borrows the
security
from
a third parryand
sells
it at to
day's
price.
He
agrees
to
deliver
the
same
security
to the third
party
at a future
date.
The trader is
hoping
that the
price
of the
security
will
fall
in the
meantime.
He
will
then be able to buythe securityfor
less
money
than he
received
in the
sale.
Selling
short
carries
an
unpleasant
risk.
When
the
price
of a
company's
stock
shoots
up,
the
value
of its
warrants
goes
up,
too.
Theoretically,
there
is no
limit
to
how
much
a
stock's
(or
warrant's)
price
might
rise.
That
means
that
there
is no
limit
to
how
much
a
short-seller might lose.
Compare this to the more
usual
situation
of
buying
a stock or
warrant
("buying
long").
You
cannot
lose
more
than
you
paid
for
the
securities.
That is a
painful
enough
prospect,
but at least the
losses
are
capped.
The
short-seller
is
liable,
potentially,
for
infinite
losses.
There is a time-honored
way
of
reducing
this
risk.
It is to buy and
sell
short
nearly
the
same
thing
simultaneously.
Jay
Gould
bought
"underpriced"
gold
and soldit
where
it
was
"overpriced."
Gould
did
not
have
to
know
which
price
was
"correct"
or
even
whether
such
words
have
meaning.
He did not
have
to
predict
whether the
price
of
gold
was
going
to go up or
down.
By
buying
and
selling,
Gould
eliminated
practically
all the risk of owning
gold.
He
locked
in the
"irrational"
price
difference
as a sure profit.
Most forms of
arbitrage
loosely
follow
Gould's
design.
An arbi-
144


## Page 148

Arbitrage
trageur
buys
an
underpriced
security
and
simultaneously
sells
short
a
closely
related
security
that
is
overpriced.
Here
"closely
related"
means
a
security
whose
price
has
to
rise
or
fall
apace
with
the
origi
nal
security.
In the
case
of
warrants
or
options,
the
"closely
related"
securityis the
company's
stock
itself.
This
scheme
may
sound
confusing
on
first
hearing.
It
is
much
like
Kelly's
"bet
your
beliefs"
horse
race
system.
In a
race
with
just
two
horses,
one
horse
has to win and the
other
has to lose. Because
of
this
obvious
correlation,
it
is
possible
to
eliminate
the
usual
risk
of
betting
on
horses.
By
betting
on
both
horses,
you
can't
lose.
The
value
ofan
option
or
warrant
goes
up
as
the
price
of the
un
derlying
stock
does.
By
buying
the
stock
and
selling
the
option,
you
create
a
"horse
race" where one side
of
the
trade
has to win
and
the
other side
has
to
lose.
And if
you
know
the
"true"
odds better than
everyone
else
and
use
your
beliefs
to
adjust
your
bets,
you
can
expect
a profit.
It
can
be
shown
that
these
long-short
trades
are
Kelly-optimal.
They
were
in
use
in
the
stock
market
long
before
Kelly,
though.
Thorp's
innovation
was
to
calculate
exactly
how
much
of the
stock
he
had
to
buy
to
offset
the
risk
of
short-selling
the
warrant.
This
technique
is
now
called
"delta
hedging,"
after the
Greek
letter
used
to
symbolize
changein a
quantity.
In
delta
hedging,
the
paper
profit
(or
loss)
of
any
small
change
in
the
price
of the
stock
is
offset
by
the
change
in the
price
of the war
rant.
You
make
money
when
the
"irrational"
price
of the warrant
moves
into line with the price of the
stock.
John
Maynard
Keynes
is
famous
for
remarking
that the
market
can remain irrational longer than you can remain solvent. It does
little
good
to
buy
something
at an
irrational
price
unless
you
are
sure you can
sell
it for profit at the
"reasonable"
price.
You
have
to
know
when
all
those other
"irrational"
people
will
come to their
sensesand agreewith
you.
That
was
the
beauty
of
Thorp's
scheme.
The
market
can't
persist
in its
irrational
valuations
of
warrants.
On the
expiration
date, the
warrant
goespoofl—and
with it.
any
irrational
notion of its
value.
Someone
who
holds
a warrant to the bitter end winds up with
145


## Page 149

FORTUNE
S
FORMULA
either
(a)
nothing
at
all,
if the
stock
is
selling
for
less
than
the
warrant's
strike
price;
or
(b)
an
immediate
profit,
ifthe
stock
is
sell
ing
for
more.
Any
irrational
sentiment
about
the
warrant's
worth
is
a
memory.
(The
stock
itself
may
be
"irrationally"
priced—who
knows?—but
that's beside the point.)
Beat
the
Market
Summer
1964
brought
CHANGES
in Thorp's
life.
The grant
supporting
his
appointment
at
New
Mexico
State
had
run
out.
It
looked
like
the
math
department
would
fall
into the
hands
of a
"clique
of
group
theorists."
Thorp
began
a
job
search.
The
Univer
sity of
California
was
starting a new
campus
at
Irvine
in Orange
County.
Both
Ed
and
Vivian
had
fond
memories
of
Southern
Cali
fornia,
soThorp
interviewed
there.
Hegotan offerand tookit.
On
Thorp's
first
day
at UC
Irvine,
he
happened
to
mention
his
interest in warrants to
Julian
Feldman,
the head of the computer
sciences
department.
Oh,
Feldman
said,
we've
got a
guy
who's
doing
the same thing.
He
was
talking
about
an
economist
named
Sheen
Kassouf.
Kas-
souf had written his
Columbia
University
Ph.D.
thesis
on how to
determinea fair
price
for
warrants.
Kassouf
had not comeup with a
rigorous
answer,
but he
had
a
good
practical
sense
of the
problem.
He was already trading warrants.
Feldman
introduced Thorp to
Kassouf.
They
resolved
to do a
weekly
research
seminar
on the
subject.
There
were
no
students;
Thorp and
Kassouf
simply
met
weekly
to
figure
out howto get
rich.
146


## Page 150

Arbitrage
Thorp
began
trading
warrants
too.
His
hedging
system
worked
as
he'd
hoped.
By
1967
Thorp
had
parlayed
his
original
$40,000
into
Sioo.ooo.
The
system
was
not
bulletproof.
There
were
relatively
few
war
rants out there, so the
market
was
illiquid.
Someone
who
sells
short
too many warrants may find it
difficult
to buy them when needed.
The
"artificial"
demand
created
by
the
deal
itself
can
drive
up the
prices
of
these
warrants.
That
is
bad
because
Thorp
was
betting
the
warrants would get cheaper.
The delta
hedging
scheme
protects
against
only
small
move
ments
in the
stock's
price.
Should
the
stock's
price
change
greatly,
it is
necessary
to
readjust
by
buying
or
selling
more stock or war
rants.
This
means
the
trader
must
watch
stock
and
warrant
prices
closely.
Sometimes
a
company
would
change
the terms of a warrant, and
this could be disastrous for the trade. For these and
other
reasons,
not
every
warrant
deal
turned
a
profit.
Unlike
many
young
traders,
Thorp
understood
the
concept
of
gambler's
ruin.
He
was
able
to es
timate the
chances
of profitand
use
the
Kelly
formula
to
make
sure
he
was
not
committing
too
much
money
to
any
one
deal.
By
the end of
1965,
Thorp
was
up
for
a
full
professorship
at UC
Irvine.
He
wrote
Shannon
for
a
letter
of
recommendation.
In
his
re
quest. Thorp reported that
after
several
false
starts,
I
have
finally
hit
pay
dirt
with
the
stock
market.
I
have
constructed
a
complete
mathematical
model
for a
small
section
(cpsilon
times
"infinity"
isn't
so
small,
though)
of the
stock
market.
I
can
prove
from
the
model
that the
expected
re
turn is
33?o
per
annum,
and that the
empirical
assumptions
of
the
model
can
be
varied
within
wide
limits
(well
beyond
those
dictated
by
skepticism)
without
affecting
this
figure
much.
Past
records
corroborate
the
33%
figure.
It
assumes
I
revise
my
port
folio
oncea
year.
With
continuous
attention
to the
portfolio
the
rate of return
appears
to
exceed
50%
gross
per
year.
But I
haven't
147


## Page 151

FORTUNE
S
FORMULA
finished
with the
details
of that,so I canonlybe sureof the lower
rate
at
present.
A
major
portion
of
my
modest
resources
has
been
investedfor
several
months. We once "set"as a tentative first goal
the
doubling
of
capital
every
two
years.
It isn'tfar
away
now.
While
the
33
percent
figure
was
optimistic.
Thorp
was
beating
market returns. In the
margin
of this letter,he drew an arrow point
ing
to the
phrase
"the
stock
market"
and
added
the
question
"Have
you
continued
attacking
it?
And
how
have
you
made
out?"
Paul
Samuelson
coined the term
"PQ/^
or performance quotient.
Like
IQ^
this
supposedly
measures
a
portfolio
manager's
ability.
A
PQ_of
lOO
is
average.
The
question
is,
does
anyone
have
a
PQ_of
over
100?
Samuelson
theorized that if such people
existed,
they would be
all
but
invisible.
You
would
not find them working for investment
banks
or the
Ford
Foundation.
"They
have
too high an I.Q^for
that,"
Samuelson
wrote.
"Like
any race track tout, they
will
share
[their
talents]
for
a
price
with
those
well-heeled
people
who
can
most
benefit
from
it."
Samuelson
concluded
that the
high-PQs
would
operate by
stealth,
investing
their
own
money
or that of
friends.
They
would
keep
their
"systems"
to
themselves.
Otherwise,
the
efficient
market
would
copy
what
they
were
doing,
nullifying
the
system's
advantage.
For
a
few
years,
Thorp
was
the
model
of a
high-PQjrrader.
He
operated
his
warrant
system
quietly,
investing
his
own
money
and
that
of
a few
relatives
who had bugged him to invest for them. Soon
he
was
investing
over
a
million
dollars
of
friends'
money.
Then Thorp did what
Samuelson
said
wouldn't
happen.
He told
Kassouf
they
should
reveal
their
system
to the
world.
Thorp
was
looking
two
calculated
moves
ahead.
He
was
thinking
of
manag
ing
money
professionally.
By
writing
a
book
on the
warrant
hedge
system,
"we'd
get a
certain
cachet,"
Thorp
recalled,
"which
would
make
it a lot easier to
raise
investment
money."
Thorp felt that
he had
such
a
steady
stream
of
profitable
ideas
that he
could
afford
148


## Page 152

Claude
Shannon
with
"Theseus,"
his
maze-solving
robotic
mouse.
In
the
1960s,
Shannon
turned
his
universal
genius
to
beating
Las
Vegas
and
the
stock
market.
Shannon's
"Toy
Room."
The
roulette
wheel
is
the
one
Shannon
and
lid
Thorp
used
to
design
a
prediction
device.
(Arthur
Lewbel)


## Page 153

John
L.
Kelly,
Jr.
Texas-born
Kelly
was
agun
col
lector
who
predicted
football
results
by
computer.
Friends
rated
him the
second
smartest
man
at Dell
Labs—next
to
Shannon
himself.
Bell
Labs,
Murray
Hill,
New
Jersey,
1942
(Library
of
Congress.
Prints
and
Photographs
Division.
Gottscho-Schleisner
Collection)


## Page 154

Kelly
(right)
and
colleague
Louis
Gerstman,
listening
to
a
computer
speak
The $64,000
Question.
Kelly's
scientific
betting
system
was
inspired
not
only
by
Shannon's
theory
but
also
by
rigged
betting
on
this
1950s
quiz
show.
(Getty
Images)


## Page 155

New
Jersey
mobster
Longy
Zwillman,
head
of
an
illegal
gambling
empire.
Bookies
got
race
results
on
wires
leased
from
Shannon
and
Kelly's
employer,
AT&T.
(©
Bettmann/Corbis)
FBJ
director
J.
Edgar
Hoover
(right)
and
Clyde
Tolson
at
Pimlico
racetrack.
1954.
The
mob
gave
them
advance
word
of
fixed
races.
(<,
Bettmann Corbis)


## Page 156

Edward
Thorp,
early
1960s.
The
circular
object
in
his
left
hand
is
a
memory
aid
for
Thorp's
blackjack
system.
Thorp
didn't
need
it,
having
a
photographic
memory.
Thorp
at
the
Tropicana
I
lotel.
Las
Vegas,
1963.
Thorp
used
Kelly's
betting
formula
to
make
maximum
profits
at
the
blackjack
tables,
and later in the stock market.


## Page 157

Daniel
Bernoulli
came
from
a
dysfunctional
family
of
eighteenth-century
geniuses.
His
173S
article
anticipated
the
"Kelly
criterion"jor
balancing
risk
and
return.
Nobel
laureate
Paul
Samuelson
questioned
whether
anyone
beats
the
market.
Calling
the
Kelly
system
a
"fallacy,"
he
helped
persuade
most
economists
to
reject
it.
(Courtesy
MIT
Museum)


## Page 158

U.S.
Attorney
Rudolph
Giuliani
filed
RICO
charges
against
Ed
Thorp's
hedge
fund,
Princeton-Newport
Partners—the
first
time
the
organized
crime
law
was
used
against
Wall
Street.
(AP Wide World Photos)
Junk
bond
king
Michael
Milken.
Princeton-Newport
was
charged
with
illegally
"parking"
securities
for
Milken's
opera
tion.
Saidone
Princeton-Newport
employee:
"I
couldn't
stand
all
the
crimes
they
were
committing."
(AP
Wide
World
Photos)


## Page 159

Robert
C.
Merton
was
the
son
ofa
famous
sociologist
and
the
protege
of
Paul
Samuelson.
Merton shared the
1997
Nobel
Prize
in
economics
with
Myron
Scholes
and
partnered
with
him
in
the
ill-fated
hedge
fund
Long-Term
Capital
Management.
(Courtesy
MIT
Museum)
Myron
Scholes
segued
from
efficient
mar
ket
economist—one
of
the
"Random
Walk
Cosa
Nostra"-
-to
pitchman
for
a
hedge
fund
touting
market-beating
returns.
The
fund
would
succeed,
he
told
one
skepti
cal
investor,
"because
of
fools
like
you."
(Courtesy
MIT
Museum)
Claude
Shannon
beat
the
market
and
99.9
percent
of
mutual
fund
managers.
Through
19S6
the
average
compound
return
on
Shannon's
portfolio
was
28
percent—vs.
27
percent
for
Warren
Buff'ett's
Berkshire
Hathaway.
(Courtesy
MIT
Museum)


## Page 160

Arbitrage
to
give
away
the
warrant
hedges,
much
as
he
had
the
blackjack
system.
Kassouf
consented.
They
got a
$50,000
advance
for
the
book.
To
Kassouf
that
was
"staggering."
The
advance
was
about
five
times
his
annual
salary
The
book
was
called
Beat
the
Market
(1967).
It
described
a
sim
plified
version
of
the
warrant
hedge
system
for
small
investors.
No
one
had
home
computers
then.
Overpriced
warrants
had
to
be
identified
by
drawing
charts
on
graph
paper.
The
book
seems
to
have
been
the
first
discussion
in
print
of
delta
hedging.
Yet
as one of the
hundreds
of
books
of
advice
for the
small
investor
that
come
out
every
year,
the
book
received
little
notice
from
most
academics.
One
exception
was
the
prolific
Paul
Samuelson.
He
reviewed
the
book
for
the
Journal
of
the
American
Statistical
Association.
"Just
as as
tronomers
loathe
astrology,"
Samuelson
began
unpromisingly,
"sci
entists
rightly
resent
vulgarization
of their craft and
false
claims
on
its
behalf."
Though
Samuelson
allowed
that
a
minority
of
readers
might
make
some
money
from
the
system,
he
feared
that
it
would
require
too
much
work
and
mathematical
sophistication
to
satisfy
the
majority
of
readers,
who
were
doubtless
looking
for
a
get-rich-
quick
scheme.
"The
Pure
Food
and
Drugs
Administration
should
enjoin
the
authors
from
making
such
misleading
claims,"
Samuelson
carped,
"or
at
least
require
them
to
take
out
of
the
fine
print,
so
to
speak,
the
warning
showing
they
know
better."
Thorp
and
Kassouf
kicked
around
the
idea
of
starting
an
invest
ment
partnership.
Kassouf
proposed
an
arrangement
where
the
principals
would
be
Thorp,
Kassouf,
and
Kassouf's
brother.
Thorp
worried
that
that
would
shift
the
balance
of
power
too
much
toward
the
Kassoufs.
There
was
a
philosophical
difference,
too.
Kassouf
be
lieved
that he
could
sometimes
predict
in
which
direction certain
stocks
were
going
to
move.
Kassouf
was
willing
to
buy
stocks
he
thought
were
going
up
and
sell
short
stocks
he
thought
were
going
to go
down.
Thorp
wasn't.
He
was
unconvinced
that
Kassouf,
or
149


## Page 161

FORTUNE
S
FORMULA
anyone,
could
predict
the
market
that
way.
As
Thorp
told
me,
"We
had
a
different
degree
of
daring
about
what
we
wanted
to
do
in
the
marketplace.
I
was
not
daring."
Thorp
wanted
to
start
a
"market
neutral"
investment
partner
ship,
meaning
that
its
returns
would
be
independent
of
what
the
stock
market
did.
A
bad
year
for
the
stock
market
could
be
a
good
year
for
the
partnership—that
was
the
idea,
anyway.
This
would
it
self
be
a
great
selling
point.
The
big
investors
Thorp
hoped
to
at
tract
would
be
placing
just
part
of
their
money
in
the
partnership.
If he
could
show
that the
partnership's
performance
was
not cor
related
with
the
stock
market's,
people
who
already
had
large
stock
holdings
could
reduce
their
overall
risk
by
investing
in
the
partnership.
Thorp
asked
an
attorney
about
starting
an
investment
partner
ship.
The
attorney
told
him
the
idea
was
impractical.
Thorp
ob
jected
that
Warren
Buffett
had
a
partnership.
The
attorney
replied
that
Buffett
hadn't
been
incorporated
in
California.
The
state
had
too
many
regulations
to
permit
the
type
of
freewheeling
operation
Thorp had in
mind.
The
attorney
billed
Thorp
for
20
hours'
work.
That
came
to
$2,000,
a
good
fraction
of
Thorp's
salary.
Thorp
negotiated
the
fee
down,
but the
experience
left
him
disillusioned
and
poorer.
♦
James
Regan
James
"Jay"
REGAN
was
one
of
the
relatively
few
finance
profes
sionals
who
read
Thorp
and
Kassouf's
book
and
appreciated
its
im-
150


## Page 162

Arbitrage
portance. In 1969
Regan
contacted Thorp and asked if he could
meet
him.
Regan,
a
decade
younger
than
Thorp,
was
a
Dartmouth
philoso
phy
major
turned
stockbroker.
Regan
had
worked
for
three
broker
ages,
most
recently
the
Philadelphia
firm
of
Butcher
&
Sherrerd.
He
decided
he
was
bored
with
merely
executing
orders.
At
the
meeting,
Regan
told
Thorp
that
he
intended
to
start
an
investment
partner
ship.
He
had
a
list
of
four
names
of
potential
partners.
By
coinci
dence,
all
four
lived
on
the
West
Coast.
Thorp
was
one
of
the
candidates.
Regan
held
the
list
carefully,
like
a
hand
of
cards.
When
Regan
got up to
use
the
bathroom,
he left the list on the
table.
Thorp
turned
the
list
around
and
read
it.
It
was
Thorp,
Kas
souf,
and
two
other
names.
Thorp
believed
that
Kassouf
wouldn't
be
interested
and
concluded
that
Regan
was
almost
certain
to
choose
him.
This
prediction
was
correct.
Regan
was
a
natural
promoter
and
extrovert.
"He
was
going
to
do
the
things
I
didn't
want
to
do,"
Thorp
explained,
"which
were:
in
terface
with
brokers,
accounting,
run
around
Wall
Street
getting
information,
that
sort
of
thing.
What
I
wanted
to do
was
think—
work
out
theories
and
try
to
put
them
into
action.
We
were
actually
happy
being
separate
because
we
had
different
styles
and
very
dif
ferent personalities."
"Being
separate"
was
one
of
the
oddest
parts
of
the
arrangement.
Thorp
did
not
want
to
give
up
his
UC
Irvine
post
or
California.
It
was
agreed
from
the
outset
that
it
would
be
a
bicoastal
partnership,
connected
by
a
wire—phone
and
data
lines.
Thorp
andastaff
would
do the
math
in
California.
They
would
transmit
trade
instructions
to Regan and
staff
on the East Coast.
The
East
Coast
branch
would
handle
the
business
end
of
things,
including
most
ofthe
recruitment
of
investors.
Thorp
had
come
from
the
working
class,
and
most
of
his
friends
were
mathematicians.
With
the
possible
exception
of
Claude
Shan
non,
mathematicians
did
not
have
piles
of
money
sitting
around.
Regan
came
from
a
comfortable
East
Coast
background.
Through
151


## Page 163

fortune's
formula
family,
Dartmouth,
and
his
brokerage
career,
he
knew
wealthy
peo
ple.
He
also
had
a
practical
sense
of
the
markets
that
Thorp
still
lacked.
Regan
was,
like
Kimmel
had
been
in the
casinos,
someone
who knew the ropes.
Thorp
and
Regan
offered
a
"hedge
fund."
That
term
goes
back
to
1949.
Alfred
Winslow
Jones,
a
sociologist
and former
Fortune
maga
zine
writer,
started
a
"hedged
fund."
The
final
d
in
hedged
was
later
dropped.
When
Jones
liked
a
stock,
he
would
borrow
money
to
buy
more
of
it.
The
leverage
increased
his
profits
and
risk.
To
counter
the
risk,
Jones
sold
short
stocks
that
he
felt
were
overpriced.
This
was
"hedg
ing"
the
fund's
bets.
Jones
called
the
leverage
and
short-selling
"speculative
tools
used
for
conservative
ends."
By
1968
there
were
about
two
hundred
hedge
funds
competing
for
the
finite
pool
of
wealthy
investors.
Many
who
became
well-
known
managers
had
started
hedge
funds,
among
them
George
Soros,
Warren
Buffett,
and
Michael
Stcinhardt. In the
process,
the
term
"hedge
fund"
drifted
from
its
original
meaning.
Not
all
hedge
funds
hedge.
The
distinction
between
a
hedge
fund
and
a
plain
old
mutual
fund is now
partly
regulatory
and partly
socioeconomic.
Mutual funds, the
investments
of
the
U.S.
middle class, are heavily
regulated
and
generally
cannot
sell
short
or
use
leverage.
Hedge
funds
are
restricted
to the
wealthy
and
institutions.
Regulators
give
hedge
fund
managers
much
more
latitude
on
the
hopeful
theory
that their
wealthy
investors
can
look
out
for
themselves.
Hedge
fund
investors
are
thumbing
their
nose
at
the
efficient
market
hypothesis.
A
typical
hedge
charges
its
investors
20 percent
of
profits
(as
did
Thorp
and
Regan).
Today,
funds
often
tack
on an
extra
I
percent
(or
more)
of
asset
value
each
year
for
expenses.
In
vestors
would
not
pay
that
unless
they
believed
the
hedge
fund
would
beat the
market,
net of the
high
fees.
It
might
seem
it
would
be
easy
to
determine
whether
hedge
funds
live
up
to
this
somewhat
incredible
promise.
It's
not.
Unlike
mutual
funds,
hedge
funds
are
not
required
to
make
performance
figures
public.
About
all
that
152


## Page 164

Arbitrage
economists
have
established
is
that
the
public
database
for
hedge
funds,
known as
TASS,
is rife with
survivor
bias.
The funds that re
port
their
returns
to
TASS
do
so
voluntarily.
Thorp
and
Regan
called
their
new
hedge
fund
partnership
Con
vertible Hedge
Associates.
"Convertible"
referred to convertible
bonds,
a
new
type
of
opportunity
Thorp
had
discovered.
They
be
gan
recruiting
investors.
The
dean
of
UC
Irvine's
graduate
school,
Ralph
Gerard,
hap
pened
to
be
a
relative
of
legendary
value
investor
Benjamin
Graham.
Gerard
was
then
looking
for
a
place
to
put
his
money
because
his
current
manager
was
closing
down
his
partnership.
Before
commit
ting
any
money
to
Thorp,
Gerard
wanted
his
money
manager
to
meet
Thorp and
size
him
up.
The
manager
was
Warren
Buffett.
Thorp
and
wife
met
Buffett
and
wife
for
a
night
of
bridge
at
the
Buffetts'
home
in
Emerald
Bay,
a
community
a
little
down
the
coast
from
Irvine.
Thorp
was
im
pressed
with
Buffctt's
breadth
of
interests.
They
hititoff
when
Buf
fett
mentioned
nontransirive
dice,
an
interest
of
Thorp's.
These
arc
a
mathematical
curiosity,
a
type
of
"trick"
dice
that
confound
most
people's
ideas
about
probability.
At the end of the
evening,
Ed
told
Vivian
he
believed
that Buf
fett
would
one
day
be the
richest
man
in
America.
Buffctt's
verdict
on
Thorp
was
also
positive.
Gerard,
who
had
done
quite
well
with
Buffett,
decided
to
invest
with
Thorp.
Regan
went
to
the
courthouse
and
looked
up
the
names
of
peo
ple
who
were
already
partners
in
hedge
funds.
He
did
a lot of
cold
calling
and
got
some
leads.
One
was
two
wealthy
brothers,
Charles
and
Bob
Evans.
Charles
had
made
a
fortune
selling
women's
slacks.
His
brother.
Bob,
was
an
actor
who
became
head
of
production
at
Paramount
Studios.
Thorp and
Regan
met the
Evans
brothers
in
New
York.
The
Evanses
were
intrigued
by
the
story
of
Thorp's
suc
cess at blackjack.
Bob
Evans
knew
something
of
that
milieu.
One
of
his
first
coups
as
studio
head
was
to
buy
the
rights
to
Mario
Puzo's
Mafia
saga.
The
Godfather.
Puzo's
life
was
alarmingly
close
to
his
art.
He
told
Evans
that
he
owed
the
mob
SiO.OOO
in
gambling
debts
and
they
were
153


## Page 165

FORTUNE
S
FORMULA
about to break his arms if he didn't comeup with the
money.
Evans
paid
Puzo
SI2.500
to
write
the
screenplay.
Both
Evans
brothers
invested
in the
fund.
At one meetingat
Bob
Evans's
house
in
Beverly
Hills,
Evans
lounged
in the
pool
while
Thorp,
dressed
in
stiff
business
clothes,
followed
him
around
and
tried
to
explain
his
investment
results
from
the
side.
Evans
tossed
outa
string
of
questions
and
seemed
to
approve
of
Thorp's
answers.
Every
time
they
met
after
that,
Evans
would
ask
nearly
the
same
list
of
questions
and
Thorp
would
supply
nearly
the
same
answers.
The
money
began
rolling
in.
Thorp and
Regan
got a
major
cor
porate
pension
fund
account
and
raised
money
from
Dick
Salomon,
the
chairman
of
Lanvin-Charles
of
the Ritz, and Don Kouri, presi
dent
of
Reynolds
Foods.
By
November
1969,
Convertible
Fledge
Associates
was
in
business.
*
Resorts
International
The
fund's
West
Coast
office
became the conceptual
antipodes
of the
efficient
market
school
at MIT
and
Chicago.
As
Thorp
recalls
those
days,
"The
question
wasn't
'Is
the
market
ef
ficient?'
but
rather
'How
inefficient
is the
market?'
and
'How
can we
exploit this?' "
The
fund's namesake was convertible bonds. Like any
other
bonds,
these
are
loans
paying
a
fixed
rate
of
interest.
A
convertible
bond
is
special
because
it
gives
the
holder
the right to
convert
the
loan
into
shares
of the
issuing
company's
stock.
This
feature
be
comes
valuable
when
the
stock
rises
greatly
over
the
term
of the
154


## Page 166

Arbitrage
bond.
A
convertible
bond
is
essentially
a
bond
with
a
"bonus"
stock
option
attached.
It is
easy
to
figure
out
what
a
regular
bond
ought
to
sell
for.
That
depends on the current interest rate and the
issuer's
credit. It was
the
"stock
option"
part
ofa
convertible
bond
that
threw
people.
Evaluating
that
was
still
guesswork.
Unknown
to
the
academic
community,
Thorp
had
just
about
solved
that
problem.
By
1967
Thorp
had
devised
a
version
of
what
are
now
called
the
Black-Scholes
pricing
formulas
for
options.
The
value
of
an
option
depends,
obviously,
on
the
strike
price,
the
stock's
current
price,
and
the
time
to
expiration.
It
also
depends
strongly
on
the
volatility'
of the
stock's
price.
The
more
volatile
the
stock,
the
more
likely
it
is
that
the
stock
price
will
rise
enough
to
make
the
op
tion
valuable.
Of
course,
it's
also
possible
that
the
stock
will
go
down.
In
that
case,
you
can't
lose
any
more
than
you
paid
for
the
op
tion.
Therefore,
greater
volatility
means
the
option
should
be
worth
more.
The
pricing
formulas
were
complicated
enough
that
a
computer
was
vital
to
use
them.
Computer-sawy
Thorp
had
a
real
edge
over
most
options
traders
of
the
time.
Thorp
was
thereby
able
to
find
mispriced
convertible
bonds
and
hedge
the
deals
with
the
underly
ing stock.
Thorp
was
successful
from
the start. In the few last
weeks
of
1969,
the
fund
posted
a
3.20
percent
gain.
In
1970,
the
first
full
year,
the
fund
returned
13.04
percent,
after
the
hefty
fees
had
been
sub
tracted.
The
S&P
500
returned
only
3.22
percent
that
year.
In
1971
the
fund
earned
26.66
percent,
nearly
double
the
S&P
performance.
The
fund
was
prospering
enough
to
hire
new
people.
While
the
Princeton
office
hired
a
typical
mix
of
Wall
Street
people,
the
New
port
Beach
office
recruited
largely
from
the
math
and
physical
sciences
departments
at
UC
Irvine.
In
1973
Thorp
hired
Steve
Mizusawa,
a
former
physics
and
computer
science
major.
Mizusawa
was
quiet,
self-effacing,
and
hardworking.
He
slept
only
five
hours
a
day
(a
one-hour
nap
around
5
p.m.
and
four
hours
from
I
to
5
a.m.).
This
came
in
handy
when
trading
on the
New
York,
London,
and
Tokyo
exchanges.
155


## Page 167

FORTUNE'S
FORMULA
As
the
fund
grew,
the
salaries
increased
exponentially.
Thorp
told
another
UC Irvine hire, David Gelbaum, that he could proba
bly
increase
his
salary
fivefold
in
five
years.
After
this
came
to
pass,
Gelbaum
asked
about
the
future.
Thorp told
him
he
thought
he
could
expect
another
fivefold
increase
in
five
years.
"But
I
don't
think
I'll be able to do that again."
In
1972
the
fund's
computer
model
determined
that the
warrants
of
Resorts
International
were
incredibly
underpriced.
The com
pany
was
building
a
casino
in
Atlantic
City,
and
its
stock
had
dropped
to
about
$8
a
share.
The
warrants
had
a
strike
price
of
S40.
Since
the
chance
of
the
stock
rising
above
S40
was
a
long
shot,
the
warrants
were
deemed
to
be
just
about
worthless:
27
cents,
to
be
exact.
Thorp's
model
computed
that
the
warrants
ought
to
be
worth
about
$4.
This
was
due to the
stock's
history
of
high
volatility.
Thorp
bought
all
the
warrants
he
could—about
10,800.
The
war
rants
cost
him
about
$2,900.
Thorp
simultaneously
sold
short 800
shares of Resorts International stockas a
hedge.
The
stock
slumped
to
S1.50
a
share.
Thorp
took
advantage
of
the
low
prices
to
buy
the
800
shares
he'd
already
sold
at
the
$8
price.
The
shares
cost
Thorp
about
$1,200,
for
which
he
received
$6,400,
a $5,200 profit.
The
stock's
plunge
also
depressed
the
price
of the
warrants.
But
the
$5,200
gain
covered
the
price
of
the
warrants
and
left
Thorp
$2,300
ahead.
And
Thorp
still
had
the
warrants.
Six
years
later,
in
1978,
things
were
looking
up
for
Resorts
International.
Its
stock
price
had
risen
to
SiS-
That
was
still
a
long
way
from
the
$40
strike
price.
People
of
fered
Thorp
as
much
as
$4
per
warrant.
That
was
nearly
15
times
what
he'd
paid.
Thorp
checked
his
computer
model
and
concluded
that the warrants should
have
then been worth almost $8. They
were still underpriced.
Thorp
turned
the
offers
down
and
bought
more
warrants,
selling
short
the stock again.
156


## Page 168

Arbitrage
By
the
mid-1980s,
Thorp
sold
his
warrants
for Sioo
each.
That
was
370
times
what
he
paid.
It
amounted
to
about
an
80
percent
annual
return
over
the
decade,
not
counting
the
profit
on
the
common-stock
short
sale.
An irony of the deal was that
Resorts
International was the de
fendant
in
a
lawsuit
on
the
legality
of
card-counting
in
blackjack.
The
newly
opened
casino
had
barred
card-counter
Ken
Uston
and
his team
of
Czech
"shuffle-trackers."
In
trades
like
this,
the
size
of
Thorp's
investment
was
limited
by
the
market
itself,
rather
than
concerns
about
overbetting.
The
optimal
position
was
"all
you
can
get"—in
this
case,
a
mere
$2,900
worthof
warrants.
This
was
typical.
In
practice,
Thorp's
use
of
the
Kelly
phi
losophy
rarely
required
elaborate
calculations.
He
could
make
a
quick
estimate
to
confirm
that a
position
size
was
well
under
the
Kelly
limit.
It
usually
was,
in
which
case
no
more
exact
calculations
were
necessary.
The
Kelly
formula
says
to
bet
all
you've
got
on
a
"sure
thing."
In
the
real
world,
nothing
is
quite
a
sure
thing.
There
were
a
few
cases
where
Thorp
had
a
virtual
"sure
thing"
trade
in
readily
available
se
curities.
On
occasion,
Thorp
committed
as
much
as
30
percent
of
the
fund's
assets
to
a
single
trade.
In
the
most
extreme
case.
Thorp
invested
150
percent
of
the
fund's
assets
in
a
single
"sure
thing"
deal.
That
was
everything
the
fund
had
and
half
again
as
much
borrowed
money.
Thorp
said
that
the
real
test
of
these
aggressive
positions
is
"whether
you
can
sleep
at
night."
He
scaled
back
his
position
sizes
when
it
bothered
him
too
much.
The
card-counter
must
worry
about
the
invisible
eye
in
the
ceiling.
The
successful
trader
must
worry
about
other
people
copying
his
trades.
Had
others
known
of
Thorp's
success
andthen
learned
ofhis
intention
to
buy
Resorts
International
warrants,
for
instance,
they
might
have
bought
up
the
warrants
before
Thorp
did.
157


## Page 169

FORTUNE'S
FORMULA
One
risk
in
keeping
trades
confidential
is
the
broker
executing
those
trades.
Some
traders
prefer
to
establish
a
strong
relationship
with
a
single
broker
who
can
be
trusted
not
to
divulge
anything.
Others
attempt
to
spread
trades
among
many
brokers.
They
might
place
an
order
to
sell
short
warrants
with
one
broker,
and
an
order
to
buy
the
stock
with
another.
No
broker
sees
the
full
trade.
Thorp
and
Regan
decided
it
made
more
sense
to
use
a
single
broker.
Powerful
brokers
have
leeway
in
helping
favored
customers.
They
can
make
sure
trades
are
executed
quickly
and
offer
attractive
rates.
A
broker
can
also
pass
on
information
ranging
from
research
reports
to
rumors.
The
important
thing
was
that
the
broker
be
someone
of
unquestioned
honesty
and
discretion.
Regan
found
someone
who
seemed
just
about
perfect.
His
name
was
Michael
Milken.
Michael
Milken
In
HIS
OWN
WAY,
Milken founded his career on the less-than-
perfect
efficiency
of
the
market.
As
a
Berkeley
business
student,
Milken
came
across
a
study
by
W
Braddock
Hickman
on the
bonds
of
companies
with
poor
credit
ratings.
Hickman
determined
that
a
diversified
portfolio
of
these
neglected
bonds
was
in
fact
a
rela
tively
safe
and
high-yielding
investment.
His
study
examined
the
period
from
1900
to
1943.
No
one
paid
much
attention
to
Flick-
man's
study
except
for
Milken
and
a
certain
T.
R.
Atkinson,
who
ex
tended
it to
cover
the
period
1944-65
and
came
to
much
the
same
conclusion.
158


## Page 170

Arbitrage
What
Milken
did
with
this
finding
was
entirely
different
from
what
Thorp
was
doing
with
market
inefficiencies.
Milken
was
a
salesman.
He
christened
these
unloved
securities
"junk
bonds."
He
began
selling
them
aggressively
at
his
employer,
the
investment
bank
Drexel
Burnham
Lambert.
Milken
was
such
a
superb
salesman
that
in
time
he
largely
nullified
Hickman's
reason
for
buying
junk
bonds.
At
the
height
of
Milken's
influence,
junk
bonds
had
become
so
popular,
and
were
selling
at
such
elevated
prices,
that the
conclusions
of the
Hickman
and
Atkinson
studies
probably
no
longer
applied.
Milken
had
ideas
of
his
own.
One
was
that
companies
with
doubtful
credit
could
issue
their
own
"junk
bonds"
at
high
interest
rates.
The
companies
would
use
the
capital
to
buy
other
companies
and
sell
offtheir
assets
to
pay
the
bond
interest.
This
was
called
cor
porate
raiding.
When
successful,
it
was
a
form
of
arbitrage.
The
ac
quired
companies
were
sometimes
worth
more
than
the
irrationally
low
value
the
market
assigned
to
them.
Corporate
raiding
made
Milken
unpopular
with
the
press
and
many
corporate
executives.
It
also
made
him
wealthy
and
powerful.
Milken
was
so
powerful
at
Drexel
Burnham
that
he
was
able
to
open
his
own
office
in
Beverly
Hills.
He
liked
the
freedom
of
being
a
con
tinent
away
from
the
Drexel
Burnham
leadership
in
New
York.
It
was
said
that
Milken
purposely
surrounded
himself
with
hardwork
ing
loyal
people
of
mediocre
talent.
He
wanted
people
who
would
owe everything to him.
"No
one
who's
been
with
me
for
five
years
is
worth
less
than
twenty
million,"
Milken
reportedly
told
Drexel's
Robert
Wallace
in
1983.
Quotes
of
people
in
Milken's
circle
showed
an
almost
creepy
level
of
devotion:
"Michael
is
the
most
important
individual
who
has
lived
in
this
century,"
said
Drexel
employee
Dort
Cameron.
An
other
felt,
"Someone
like
Mike
comes
along
once
every
five
hundred
years."
Milken
spoke
of
wanting
to
make
his
family
the
wealthiest
in
the
world.
Yet
if
his
whole
life
was
devoted
to
making
money,
he
seemed
not
to
care
much
about
spending
it.
He
lived
in
a
relatively
unpretentious
Encino
home
that
had
once
been
the
guesthouse
on
159


## Page 171

FORTUNE'S
FORMULA
the estate
of
Clark Gable and Carole Lombard. Milken ate lunch
off
paper
plates,
wore
a
reasonably
priced
toupee,
and
drove
an
Oldsmobile.
Thorp
and
Regan
began
using
Milken
as
their
hind's
primary
broker
in
the
early
1970s.
In
all
the
time
that
Thorp's
fortunes
were
connected to
Milken's,
the two men never met.
Thorp
once met
Milken's
attorney
brother,
Lowell,
who
had
an
office
in the
same
Beverly
Hills
building
and
who
handled
Michael's
legal
affairs.
Thorp's
closest
approach
to
Michael
Milken,
however,
was
seeing
him
across
Drexel's
Beverly
Hills
trading
floor—behind
a
pane
of
glass.
In
the
early
1970s,
Steve
Ross
and
Caesar
Kimmel
believed
that it
might
make
sense
to
take
Warner
Communications
private.
They
wanted
to
buy
back
most
of the
stock
issued,
limiting
ownership
to
the
few
biggest
shareholders.
To
get
the
necessary
money,
Warner
Communications
would
have
to
issue
junk
bonds.
Ross
asked
Michael
Milken
for
advice.
Milken
devised
a
plan
and
met
with
Ross
in
New
York
to
discuss
it.
Milken
explained
that
Ross
would
have
to
give
up
40
percent
of
Warner's
stock
as an
inducement
to get
people
to
buy
the junk
bonds.
This
was
a
standard
equity
kicker.
People
would
not buy
these
junk
bonds
unless
they
also
got
stock.
Drexel
would
get
another
35
percent
cutof the
company's
stock
as
payment
for
services
rendered.
That
left
a
mere
25
percent
of
the
company for
Ross's
group.
"What
are
you
talking
about?"
Ross
said.
"All
you're
doing
is
financing
this
deal,
and
you
get
35
percent?"
Milken—who
genuinely
admired
Ross
and
told
one
friend
he
saw
Ross
as a
kindred
spirit—would
not
back
down
on these
terms.
Ross
had no intentionof
giving
away
75
percentof the
company.
He
dropped
the
plan
to
take
the
company
private.
Milken
repeated
this
pitch
to
clients,
with
variations,
many
times.
Many
of
them
accepted
Milken's
terms.
What
the
clients
160


## Page 172

Arbitrage
didn't
know
was
that
the
equity
kicker
was
rarely
if
ever
offered
to
bond
buyers.
Milken's
salespeople
were
able
to
sell
the
bonds
with
outit.
Instead,
the
stock
allotted
for
bond
buyers
quietly
went
into
Milken's
private
accounts.
Robert
C.
Merton
The
ACADEMIC
WORLD
was
starting to
show
interest in war
rantsand
options.
One of the
key
figures
was
Paul
Samuelson's
most
brilliant
protege,
Robert C. Merton. Merton
was
the son of a
famous
Columbia
University
sociologist,
Robert
K.
Merton.
The
elder
Merton
was
known
for
inventing
the
focus
group
and
popular
izing
the
terms
"role
model"
and
"self-fulfilling
prophecy."
Robert
K.
taught
his
son
about
the
stock
market
and
poker.
The
younger
Merton
was
always
trying
to
find
an
edge
in
both.
In
poker,
Robert
C.
believed
he
could
achieve
that
by
staring
at
lightbulbs
during
games.
The
light
contracted
his
pupils,
making
his
reactions
harder
to
read.
In
1963
it
was
announced
that
Singer
Company,
which
made
sewing
machines,
was
going
to
buy
the
Friden
Company,
which
made
calculators.
The
nineteen-year-old
Merton
bought
Friden
stock
and
sold
short
Singer,
making
a
nice
profit
when
the
merger
went through.
After
graduating
from
Columbia,
Robert
C.
started
graduate
work
in
math
at
Caltech.
But
Merton
had
been
hooked
by
his
ama
teur
success
in the
market.
He
found
himself
haunting
a
Pasadena
161


## Page 173

FORTUNE
S
FORMULA
brokerage
before
classes
started
in
order
to
check
prices
on
the
New
York
exchanges.
Merton
resolved to switch to economics. His Caltech adviser,
Gerald
Whitman,
thought
it
was
very
odd
that
someone
would
want to
leave
mathematics.
Whitman
helped
Merton
apply
to halfa
dozen
schools.
Onlyone
accepted
him.
It
was
MIT. It
offered
a
full
fellowship,
and
Merton
transferred
in fall 1967.
One of his
first
MIT
courses
was
taughtby
Samuelson.
Samuel
son
was
immediately
impressed
with
Merton.
The
following
spring,
Samuelson hired him as his research assistant, an
incredible
honor
for
someone
whohad
only
recently
decided
to study
economics.
Samuelson
encouraged
Merton
to
tackle
the
still-unsolved
prob
lem
of
pricing
options.
Samuelson
had
worked
on
this
problem
himself
and
had
come
close to a
solution.
He
sensed
that
Merton
might
be the one to
succeed.
Other
people
at MIT
were
working
on the
problem.
Merton
soon
became
aware
of the work of MIT's
Myron
Scholes
and
Fischer
Black,
then
employed
at the
consulting
firm
of Arthur
D.
Little.
Merton
reasoned
that the
"correct"
price
for options is the
one where no one can
make
a profitby
buying
them or
selling
them
short.
This is the
assumption
of "no
arbitrage."
From
this,
and the
assumption
that
stock
prices
move
in a
geometric
random
walk,
Merton derived
Black
and
Scholes's
pricing
formulas.
All
three
men were
curious
about
how well
their
new
formulas
reflected
reality.
The
option
traders
ofthe
day
were
bottom-feeders,
existing
on the
fringe
of the
securities
business.
Would
these
people
from
the
wrong
side
of
Wall
Street's
tracks
instinctively
arrive
at the
mathematically"correct" option
prices?
Black, Scholes, and
Merton
examined
ads for
over-the-counter
options
in
Sunday
newspapers
and
compared
them
with
their
for
mula's
predictions.
Some
options
traded
close
to the
formula's
price.
Some weren't so
close.
Occasionally
they found options that were
real
bargains.
Did that mean that it
was
possible
to beat the market after
all?
On
Monday
mornings,
Scholes
called
the
dealers
who had
adver-
162


## Page 174

Arbitrage
tised
the
bargain
options.
He
was
always
told
that
they
had
just
sold
out
of
the
cheap
options.
But
they
had
another
option,
just
as
good . . . Scholes realized it was bait and switch.
Scholes
later
had
one
of
his
students
analyze
the
options
offered
by
one
dealer.
The
student
concluded
that
some
options
were
mis-
priced,
but
dealers
charged
such
high
transaction
costs
that no one
could
make
a
profit.
Then
the group discovered warrants.
Because
warrants were traded
on the
regular
stock
exchanges,
there
was
no bait and
switch.
The
price
quoted
is
the
price
you
get.
Of
the
warrants
then
being
traded,
those of a
company
called
National
General
were the most under-
priced
relative
to
the
formula.
National
General
was
a
conglomerate
that
had
just
failed
in
a
bid
to
acquire
Warner
Brothers,
losing
out
to the
company
that
owned
Kinney
parking
lots.
Black,
Scholes,
and
Merton
dipped
into
their
savings
and
bought
a block of National General warrants. "For a
while,"
Black
recalled,
"it
looked
as
if
wc
had
done
just
the
right
thing."
In
1972
American
Financial
announced
plans
to
acquire
Na
tional
General.
As
partof the
deal,
it
changed
the
terms
of the war
rants,
and
the
change
was
bad
for
warrant
holders.
The MIT
group
lost everything
they'd
invested.
Black
theorized
that the
warrants
had
been
cheap
because
insid
ers
had
advance
word
of
the
takeover
bid.
The
insiders
sold
early,
tricking
Black,
Scholes,
and
Merton
into
buying
what
they
con
cluded
was
a
cheap
warrant.
"Although
our
trading
didn't turn out
very
well,
this event helped
validate
our
formula,"
Black
said. "The
market
was
out of line for a
very
good
reason."
It
took
a
while
for
Black
and
Scholes
to get
their
paper
into
shape
for
publication.
When
it
was
about
ready,
Black
sent
a
preprint
to
someone
he thought
might
be
interested:
Ed Thorp.
Black
knew
of the delta
hedging
technique
described
in
Beat
the
Market.
Fie
explained
in the
cover
letter
that he
had
taken
Thorp's
163


## Page 175

FORTUNE'S
FORMULA
reasoning
a
step
further.
In a
perfectly
rational
world,
no
risk-free
investment should be worth more than any other. A delta hedge is
(theoretically)
a
risk-free
investment.
Ergo,
it
should
offer
the
same
return as other
risk-free
investments
like treasury
bills—when
options
are
priced
"correctly."
As
Thorp
scanned
it,
it
looked
like
Black
and
Scholes
had
de
rived
his
own
option-pricing
formulas.
He
couldn't
be
sure
because
the
equations
were
structured
differently.
One of
Thorp's
prized
"toys"
at
the
time
was
a
Hewlett-Packard
9830A.
This
was
one of the
first
small
computers.
It cost just under
$6,000,
had
7,616
bytes
of
memory,
a
full
typewriter
keyboard,
and
was
programmable
in
BASIC.
In
lieu
ofa
monitor,
it
had
a
single-
line
text
display
and a plotterthat
drew
graphs
in
color.
Thorp
quickly
programmed
Black
and
Scholes's
formulas
into
the
machine
and had it plot a
pricing
graph.
He
compared
it to a
graph
produced
with
Thorp's
own
formulas.
They
were
the
same
except
for
an
exponential
factor
incorporating
the
risk-free
interest
rate.Thorp had not
included
this
because
the over-the-counterop
tions he traded did not credit the trader with the short-sale pro
ceeds.
The
rules
were
changed
when
options
began
trading
on the
Chicago
Board
of
Exchange.
Black
and
Scholes
accounted
for
this.
Otherwise, the formulas were equivalent.
The
Black-Scholes
formula,
as
it
was
quickly
christened,
was
pub
lished
in
1973.
That
name
deprived
both
Merton
andThorp of
credit.
In Merton's
case,
it was a matter of
courtesy.
Because
he had
built on
Black
and
Scholes's
work,
he
delayed
publishing
his deriva
tion until their
article
appeared.
Merton
published
his
paper in a
new
journal
that
was
being
started
by
AT&T,
the
Bell
Journal
of
Eco
nomics
and
Management
Science.
This
journal
was
an
acknowledgment
of
how
profoundly
quantitative
methods
from
information
theory
and
physical
science
were
transforming
formerly
alien
fields
like
finance.
Thorp
considers
the Merton paper "a
masterpiece."
"I never
thought
about
credit,
actually,"
Thorp
said,
"and
the
reason
is
that I
came from outside the economicsand finance profession. The great
164


## Page 176

Arbitrage
importance
that
was
attached
to
this
problem
wasn't
part of
my
thinking.
What I
saw
was
a
way
to
make
a lot of
money."
Man
vs.
Machine
Few
theoretical
findings
changed
finance
so
greatly
as the
Black-Scholes
formula. Texas
Instruments
soon
offered
a
handheld
calculator
with the
formula
programmed
in. The marketin
options,
warrants, and convertible bonds became more efficient. This made
it harder for
people
like
Thorp to
find
arbitrage
opportunities.
Of
necessity,
Thorp
was
constantly
moving
from
one
type
of
trade
to
another.
In
1974
Thorp
and
Regan
changed
the
name
of
their
fund
to
Princeton-Newport
Partners,
a
name
steeped
in the
Ivy
League
and
East
Coast
old
money
The
Newport
was
not
the
one
in
Rhode
Island,
of
course,
but
Newport
Beach,
California.
The
Prince
ton
was
not the
university
but the
town.
Regan
preferred
the
com
mute into Princeton to the more hectic one into
Manhattan.
Thorp
and
Regan
also
set up a
firm
called
Oakley
Sutton
Management
(after
the
partners'
middle
names)
to
hire
employees
and
create
a
brokerage
subsidiary
in order to
save
on
some
commission
costs.
In
1972,
1973,
and
1974,
the fund posted net returns on invest
ment
of
12.08
percent,
6.46
percent,
and
9.00
percent.
This
dem
onstrated
the
value
of
being
market
neutral.
The
stock
market
declined
steeply
in
1973
and
1974-
By
theendof
1974.
the
fund
was
just
shy
of
having
doubled
its
original
investors'
money.
Thorp
and
Regan
were
then
managing
S20
million
in
assets.
It
was
hard
to
keep
that
kind
of
success
under
wraps.
On
Sep-
165


## Page 177

FORTUNE
S
FORMULA
tember
23.
1974,
The
Wall
Street
Journal
ran a
front-page
profile
of
Thorp
and
Princeton-Newport.
It
began
with
the
idiosyncratic
po
etry
of
Journal
headlines:
Playing
the
Odds
Computer
Formulas
Are
One
Man's
Secret
to
Success
in
Market
Hunches, Analysts'
Reports
Are Not for Ed
Thorp;
He
Relies on Math,
Prospers
'I Call It
Getting
Rich Slow'
The
Journal
writer
was
amazed
at
Thorp's
disregard
of
funda
mental
analysis
and
his
reliance
on
computers.
In
1974
the
Journal's
average
reader
had
as
much
hands-on
experience
with
computers
as
with
moon
rockets.
A
computer
was
something
you
saw
in a
movie
(often
it
went
berserk
and
killed
people).
In
some
cases,
the
funds'
trading
is
dictated
completely
by
com
puter
printouts,
which
not
only
suggest
the
proper
position
but
also estimate its probable annual return. "The more we can run
the
money
by
remote
control
the
better."
Mr.
Thorp
declares.
The
Journal
linked
Thorp's
operation
to
"an
incipient
but
grow
ing
switch
in
money
management
to a
quantitative,
mechanistic
approach."
It
mentioned
that
the
Black-Scholes
formula
was
being
used
by
at
least
two
big
Wall
Street
houses
(Goldman
Sachs
and
Donaldson,
Luflcin
&
Jenrette).
The latter's
Mike
Gladstein
offered
the
defensive
comment
that
the
brainy
formula
was
"just
one
of
many
tools"
they
used.
"The
whole
computer-model
bit is
ridiculous
because
the
real
investment world is too
complicated
to be reduced to a
model,"
an
166


## Page 178

Arbitrage
unnamed mutual fund
manager
was
quoted as
saying.
"You
just can't
replace
the
money
manager
using
security
analysis
and
market
feel
with
a
machine."
Yet
the
Journal
reported that Thorp's
"machine"
outperformed
all
but one of the
400-some
mutual funds tracked by Standard &
Poor's.
Said
Thorp, "The better one
was
one of those
crazy
funds
that invested in onlygold
stocks."
Thorp
computed
that out of 200
hedged
trades
he
completed
for a
pension
fund
client,
190
made
a
profit,
6 broke
even,
and
4
lost.
The
losses
ranged
up to
15
percent of the
value
of the long
side of the deal. One of the worst things that can go wrong is for the
company
to go
bankrupt.
Thorp had a $250,000
convertible
bond
hedge
involving
U.S.
Financial
Corp.
When
the
company
filed
for
Chapter II, Thorp's fund lost $107,000.
Another
problem
was
the one that
sunk
Merton,
Black,
and
Scholes's
warrant
experiment.
Princeton-Newport
took a
proactive
approach,
phoning
companies'
attorneys
to try
and
get a
line
on
whether they were planning to
change
the
rules.
Why
Money
Managers
Are
No
Good
William
Sharpe
was
one
of the
brightest
and most militant
of the Random Walk Cosa Nostra. He would go around asking
money
managers
if
they
really
heat
the
market.
They
would
usu
ally
huff and
say
they
did;
then
Sharpe
would
turn
prosecuting
at
torney
and
grill
them
over
the
details.
Sharpe
subscribed
to the
view
167


## Page 179

FORTUNE
S
FORMULA
that
successful
portfolio
managers
are
like
successful
astrologists—
good at
convincing
the
wealthy
and
gullible
that their
services
are
valuable.
For two years Sharpe was a professor at UC Irvine. He came to
know
Thorp,and theyhada
number
of
friendly
parries
overmarket
efficiency.
At
Irvine,
Sharpe
was
working
on the
theory
that
would
make
him
famous,
the
Capital
Asset
Pricing
Model.
Sharpe
moved
to
Stanford.
In
1975
Thorp
invited
him
back
to
UC
Irvine
to
lecture.
During
the
visit,
Thorp
tried
again
to
win
Sharpe
over
to
his
position.
Thorp
had
just
been
starting
out as a
market-beating(?)
investor
when
Sharpe
taught
at UC
Irvine.
Now
he
had
a
track
record.
Thorp
described
some
of
the
trades
he'd
made
to
Sharpe.
One
was
a
1974
trade
in
an
American
Motors
Corporation
(AMC)
con
vertible bond maturing in
1988.
Issued
at $1,000, the bond had
sunk to $600. That
gave
it a
high
return—it
was
a
convertible
junk
bond.
The bond
could
be
exchanged
for 100
shares
of AMC
stock.The stock
was
then
selling
for $6 a
share.
The bond therefore
sold
for
exactly
the
same
price
as
the
stock
you
could
get
by
convert
ing it.
That
was
insane,
Thorp
realized.
The
bond
paid
5
percent
interest.
The
stock
paid
no
dividends.
Owning
the
bond
gave
all
the
upside
potential
of
owning
the
stock.
Ifthe
stock
went
up,
you
could
always
convert
the
bond
to
the
stock. But
there
was no rush!
The
bond
holder
collected
interest
and
was
insulated
from
the
downside
po
tential
of the
stock.
Someone
patient
enough
to
hold
the bond
until
the
1988
maturity
was
guaranteed
the
$1,000
repayment
of the
original loan.
Thorp bought the
convertible
bond and sold short AMC
stock.
What
could
go
wrong?
The
company
could
go
under.
Thorp
would
make
more
money
if
that
happened.
In
case
of
bankruptcy,
the
com
panywould be liquidatedand the
proceeds
distributed to the bond
holders.
There
probably
wouldn't
be
enough
to
pay
off the
bonds
in
full.
That
means
there
would
be
nothing
left
over
forthe
stockhold
ers.
AMC
stock
would
be
worthless.
Bankruptcy
would
therefore
hurt
the
bondholders,
but
it would
hurt
the
stockholders
a lot more.
168


## Page 180

Arbitrage
This
would
be
good
for
someone
who
owned
the bonds and had
sold
short
the
stock.
The
true worst-case scenario was for the stock to stay exactly
where it was. In that
case.
Thorp
still made a decent return.
The
AMC notes were
paying
8.33
percent. Thorp had borrowed at
8 percent to buy them, earning a net
0.33
percent. But since Thorp
had sold the AMC stock short, he already had the cash and was able
to lend it out at 6 percent. He
was
making
a net
6.33
percent return
even if the stock did nothing.
Because
this
trade
was
a
sure
thing
with
no
risk
of
ruin,
the
Kelly
system
permitted
leverage.
Thorp
added
borrowed
capital
to multi
ply
his
profits.
"Situations
that
simple
and clear are
few
and far
between,"
Thorp
explained,
"but we
made
a
large
part of our
living
off scenarios just like that."
Sharpe
was
unconvinced.
There arc
anomalies
challenging
every
scientific
theory ever
propounded.
It is a
tough
call
knowing
which
to take
seriously
and
which
to shrugoff.
Efficient
market
theorists
claim
that
the
market
can
act
as
if
it
were more rational than many of its
participants.
One
mechanism
of that is
arbitrageurs-
such
as
Thorp—who
stepin to
make
a
profit
whenever prices start to get out of line.
The
efficient
market
people
generally
suppose
that it is such
a cinch to
exploit
arbitrage
opportunities
that
prices
never get
significantly
out of
line
for
long.
Thorp's
experience
differed.
He
had
learned
that
arbitrageurs
were
often
constrained
by trading
costs,
the
supply
of
mispriccd
securities,
the
Kelly
formula,
and
other
factors. It took
weeks,
months, and more for mispricings to
diminish, even with Thorp trying to profit from them at the very
mathematical
maximum
rate.
Sharpe
offered
a
counterargument.
Divide
the
world
into
"active"
investors
and
"passive"
investors,
Sharpe
said.
A
passive
investor
is
defined
as
anyone
sensible
enough
to
realize
you
can't beat the mar
ket. The
passive
investor
puts
all
his
money
into a market
portfolio
of everystock in
existence
(roughly,
an "index
fund").
169


## Page 181

FORTUNE
S
FORMULA
An active investor is anyone who suffers from the delusion that
he
can
beat the
market.
The
active
investor
putshis
money
into any
thing
except
a market portfolio.
By
Sharpe's
terminology,
an
active
investor need not trade "ac
tively" A
retired
teacher who has two shares
of
AT&T in the
bottom
of her
dresser
drawer
counts
as
an
active
investor.
She
is
operating
on the assumption that AT&T is a better stock to own than a total
market
index
fund.
Active
investors
include
anyone
who tries to
pick "good"stocks and shun "bad" ones, or who hires someone else
to do that byputting
money
in an
actively
managed
mutual
fund
or
investment
partnership.
Who
does
better,
Sharpe
asked:
the
active
investors
or the
pas
sive
investors?
Collectively,
the
world's
investors
own
ioo
percent
of
all
the
world's
stock.
(Nothing
is
owned
by
extraterrestrials!)
That
means that the
average
return of all the
world's
investors—before
you
factor
in
management
expenses,
brokerage
fees,
and
taxes—has
to be identical to the
average
return of the stock market as a
whole.
It
can't
be
otherwise.
Even
more
clearly
the
average
returnof just the
passive
investors
is equal to the
average
stock marketreturn. That's
because
these in
vestors
keep
their
money
in
index
funds
or
portfolios
that
match
the
return
of
the
whole
market.
Subtract
the return of the
passive
investors
from
the
total.
This
leaves
the
return
of the
active
investors.
Since
the
passive
investors
have
exactly
the same return as the
whole,
it
follows
that the
active
investors,
as a
group,
must
also
have
the
same
average
return as the
whole
market.
This
leads
to a
surprising
conclusion.
Collectively
ac
tive
investors
must
do no
better
or
worse
(before
fees
and
taxes)
than the passive investors.
Some
active
investors
do
better
than
others,
as we all know.
Every
active
investor
hopes
to
do
better
than
the
others.
One
thing's
for
sure.
Everyone
can't
do
"better
than
average."
Active
investing
is
therefore
a
zero-sum
game.
The
only
way
for
one
active
investor
to do better than
average
isforanother
active
in
vestor
to do
worse
than
average.
You
can't
squirm
out of
this
con-
170


## Page 182

Arbitrage
elusion
by
imagining
that the
active
investors'
profits
come at the
expense of those
wimpy
passive
investors
who settle for
average
re
turn. The
average
return of the
passive
investors
is
exactly
the same
as that of the active investors, for the reason just outlined.
Now factor in
expenses.
The
passive
investors have little or no
brokerage
fees,
management
fees,
or capital gains taxes (they rarely
have to sell). The expenses of the active traders
vary.
We're using
that term for
everyone
from
day traders and hedgefund partners to
people who buy and hold a few shares
of
stock. For the most part,
active
investors
will
be
paying
a percent or two in
fees
and more in
commissions
and
taxes.
(Hedge fund
investors
pay much more
in
fees
when the fund does
well.)
This is something like 2 percent
of
capital,
per
year,
and must be deducted
from
the return.
Two percent is no trifle. In the twentieth century, the average
stock market return
was
something like 5 percent more than the
risk-free rate. Yet an active investor has to earn about two percen
tage points more than
average
just to
keep
up with the
passive
in
vestors.
Do some active investors do that?
Absolutely.
They're the smart
or
lucky
few
who
fall
at the upper end of the
spectrum
of
returns.
The
majority
of
active
investors
do not
achieve
that
break-even
point.
Most
people
who think they can beat the market do
worse
than the market. This is an irrefutable conclusion, Sharpe said, and
it is not
based
on
fancy
economic
theorizing.
It
follows
from
the
laws
of
arithmetic.
171


## Page 183

FORTUNES
FORMULA
Enemies
List
In
THE
EARLY
1970s, Thorp got a lead that actor
Paul
Newman
might
be
interested
in
investing.
Newman
had just done
The
Sting.
(The plot concernsa con artist goingby the name of
Kelly
who
uses
a
delayed
wire
service
scam
to
dupe
a
gangster
into
placing
a ru
inously
largebet.) Thorp had a beer with Newman on the
Twenti
eth Century
Fox
lot.
Newman
asked
how much Thorp could make
at
blackjack
if he did it
full-time.
Thorp
answered
$300,000 a
year.
"Why aren't youout there doing
it?"
Newman
asked.
"Would you do it?"
Thorp
asked.
Thorp
estimated
that
Newman
made
about $6
million
that
year.
Thorp
was
making
about the
same.
Newman
decided
not to
invest
with
Princeton-Newport.
He ex
pressed
reservations
about the
way
the firm made trades to mini
mize
taxes.
Newman
explained
that he
was
a
highly
visible
liberal
activist.
Fie was
number
19 on
President
Richard
Nixon's
"enemies
list."
Newman
suspected
the government
gave
his tax returns extra
scrutiny.
He did not want to do
anything
with
his
taxes
that
might
give
the slightest
cause
for
suspicion.
Indeed,
not
all
of the
thinking
at
Princeton-Newport
had to do
with
making
money.
Some
had
to do with
keeping
it. The tax
impli
cations
of
trades
were
carefully
considered.
"I've estimated for
myself
that if I had to pay no
taxes,
state or
federal,
I'd
have
about
thirty-two
times
as
much
wealth
as I
actually
do,"
Thorp told mc
recently.
This statement
shows
how the power
of
compounding
applies
to
expenses
as
well
as
profits.
172


## Page 184

Arbitrage
Take
Shannon's
pipe
dream
of
turning
a
dollar
into
$2,048.
You
buy
a
stock
for
Si.
It
doubles
every
year
for
eleven
years
(100
per
cent
annual
return!)
and
then
you
sell
it
for
$2,048.
That
triggers
capital
gains
tax
on
the
$2,047
profit.
At
a 20
percent
tax
rate,
you'd
owe
the
government
S409.
This
leaves
you
$1,639.
That isthe
same
as getting a 96 percent return,
tax-free,
for
eleven
years.
The tax
knocks
only
4
percentage
points
off
the
pretax
compound
return
rate.
Suppose instead that you run the same dollar into $2,048
through
a lotof
trading.
You
realize
profit
each
year,
so
you
have
to
pay
capital
taxes
each
year.
The
first
year,
you
go
from
$1
to
$2
and
owetaxon the
$1
profit.
For
simplicity,
pretend that the short-term
tax
rate is
also
20
percent
(it's
generally
higher).
Then
you
pay
the
government 20 cents and end the first year with
$1.80
rather than
$2.00.
This
means
that
you
are
not
doubling
your
money
but
increasing
it
by
a
factor
of
1.8—after
taxes.
At the
end
of
eleven
years
you
will
have
not 2" but
1.8".
That comesto about
$683.
That's lessthan half
what the buy-and-hold investor is left with after
taxes.
In the late
1970s,
Jay
Regan
came
up with a
clever
idea.
At that
time, a treasury bond
was
still a
piece
of
fancy
paper.
Attached to the
bond
certificate
were
perforated
coupons.
Every
six
months,
when
an interest
payment
was
due,the holder
would
detach
a
coupon
and
redeem
it
for
the
interest
payment.
After
all
the
coupons
were
de
tached
and the bond
reached
its
maturity
date, the bond
certificate
itself
would
be submittedfor return of the
principal.
Regan's
idea
was
to buynew treasurybonds,
immediately
detach
the
coupons,
and
sell
the
pieces
of paper
separately.
People
or com
panies
that
expected
to needa lumpsumdownthe road
could
buy
a
"stripped,"
zero-coupon
bond
maturing
at the time they
needed
the
money.
It
would
be
cheaper
than
a
whole
bond
because
they
wouldn't be
paying
for
income
they didn't need in the
meantime.
Other
people might want the current income but not care about the
future lump-sum
payment.
They would buy the
coupons.
173


## Page 185

FORTUNE
S
FORMULA
An
even
bigger
selling
point
of
Regan's
idea
was
a
loophole
in
the
tax
law.
Most
of the
pieces
of
paper
from
a
dismembered
bond
would sell for a small
fraction
of
their
face value.
This
was as it
should
be.
A
zero-coupon
$10,000
bond
that
matures
in thirty
years
is
not
worth
anywhere
near
$10,000
now.
Since
there
are
no
interest
payments,
the
buyer
can
profit
only
by
capital
gains.
That
is
possible
only
if
the
buyer
pays
much
less
than
Sio.OOO
for
the
bond
now.
Fair
enough.
Buy
a
SiO,000
bond,
strip
off the
coupons,
and
resell
the
zero-coupon
bond
for,
say,
Si.ooo.
This,
it
was
theo
rized,
ought
to
give
you
the
right
to
claim
a
S9,ooo
capital
loss
on
your
current
year's
taxes.
At
any
rate,
nothing
in the
tax
code
said
how
taxpayers
were
supposed
to
figure
the cost
basis
of the
various
parts
of the
bond.
The
law
said
nothing
because
no one in Con
gress
had
thought
of
stripping
treasury
bonds
at
the
time
the
laws
were
written.
Regan
took
the
idea
to
Michael
Milken.
Milken
thought
it
was
great.
A
wealthy
investor
with
a
million
dollars'
worth
of
capital
gains
had
only
to
buy
Si.i
million
worth
of
new
bonds,
strip
the
coupons,
and
sell
the
stripped
bonds
for
$100,000.
Presto
chango,
the
capital
gains
disappear.
Despite
the
nominal
tax
loss,
the
seller
was
not
really
out
anything.
The $100,000
plus
the
coupons
were
still
worth
approximately
the
$1.1
million
paid.
It
could
even
be ar
gued
(a
few
shades
less
convincingly)
that the
government
wasn't
out
anything.
The
taxes
on the
rest
of
the
bond
would
be
paid,
later
rather
than
sooner.
Milken set up a company called Dorchester
Government
Securi
ties to market the idea to clients. Dorchester was based in Chicago
and
seems
to
have
been
little
more
than
an
address—One
First
National
Plaza,
Suite
2785.
In
1981
Dorchester changed its name
to
Belvedere
Securities.
Regan
and Thorp
were
made
partners of
Dorchester/Belvedere.
The other partners
included
Michael
and
Lowell
Milken
and
Saul
Steinberg's
Reliance
Group
Floldings.
Steinberg
was
oneof
Milken's
most
successful
junk
bond
raiders.
"Creative" tax shelters rarely last
long.
After a few tax seasons,
the
Treasury
Department
complained
it
was
hemorrhaging
rev-
174


## Page 186

Arbitrage
enues
to a
loophole
thatno
one
in
Congress
had
ever
intended.
The
1982
Tax
Equity
and
Fiscal
Responsibility
Act
closed
the
loophole
by
requiring
investors
to
account
for
the
value
of
the
coupons
in
claiming
losses.
At
the
same
time,
the
new
law
confirmed
the
right
to
sell
stripped
treasuries
(they
are
still
being
sold)
and
replaced
pa
per
bond
certificates
and
coupons
with
electronic
bookkeeping.
Widows
and
Orphans
Another
governmental
decision
openeda newopportu
nity for
Princeton-Newport.
The
U.S.
government
decided
that
AT&T was a monopoly after
all.
In
1981
the telecommunications
giant
was
broken up into eight
pieces.
Each
AT&T shareholder
received
shares
of the
seven
"Baby
Bells"
(regional
telephone
com
panies)
and
of
the
"new"
AT&T.
It
was
possible
for
investors
to
get
a
head
start on the
breakup
and
buy
shares
of the
Baby
Bells
and
"new"
AT&T
before
they
were
officially
issued.
Thorp's
computer
alerted him to a
weird
disparity.
The
shares
of old
AT&T
were
slightly
cheaperthan the
equivalent
amounts
of the new
companies.
There
were
Wall
Street
analysts
who
spent
careers
analyzing
AT&T,
and theypaidno attention to
this.
The
price
differential
was
so
small
that
costs
would
eat up
any
profit . . .
unless
someone
bought an awful lot
of
the stock.
Princeton-Newport's
capital
was
thenaboutS60
million.
Judging
the
deal
to be as
risk-free
as
these
things
get,
Thorp
borrowed
mas
sively
to
buy
5
million
shares
of old
AT&T
for
Princeton-Newport
and soldshort a
corresponding
quantity
of the eight
new
companies.
175


## Page 187

FORTUNE
S
FORMULA
The 5
million
shares
costabouta thirdof a
billion
dollars.
That
was
a
leverage
ratio
of
about
6 on the
hedge
fund's
total
capital.
The
trade
was
the
largest
ever
made
in the
history
of the
New
York
Stock
Exchange.
Thorp
paid
$800,000 in
interest
on the bor
rowed
money.
He
still
cleared
a
profit
of
S1.6
million
on the
dissolu
tion of the
former
employer
of
Claude
Shannon
and
John
Kelly.
In
April
1982
a
new
investment
called
S&P
futures
began
trading.
S&P
futures
allow
people
to
place
bets
on the
stock
market
itself,
or
more
exactly
on the
Standard
and
Poor's
index
of 500
large
Ameri
can
companies.
A futures contract is an "option" that isn't optional. In both
types
of
contracts,
two
parties
agree
toa
future
transaction
at a
price
they
set
now.
With
an
option,
one
party—the
option
holder—has
the
right
to
back
outof
the
deal.
The
option
holder
does
back
outun
less
he can
make
a profit by
exercising
the option.
With
a
futures
contract,
neither
side can back out.
The
holder
of
a
futures
contract
gets
all
the
profits
or
losses
that
would
accrue
by
buyingthe
securities
outright.
What's the
difference
between
buying
S&P
futures
and
investing
in a
plain
old
S&P
500
index
mutual
fund?
The
answer
is
that
you
put up a lot
less
money
with
futures.
An
S&P
futures
contract
is a
cheap
ticket
on a
wheel
of
fortune
that
has
big
prizes
and
big
penal
ties.
Anyone
who
knows
which
way
the
S&P
index
is
heading
can
make
a huge profit.
Thorp did not
know
what the
market
was
going
to
do.
He did
see a new
way
to turn a
profit.
The two parties to an
S&P
futures
contract are
theoretically
agreeing
to the
sale
of a
portfolio
of
all
the
S&P
500
stocks.
No one
actually
buys
the 500
different
stocks
to
deliver.
Instead,
the
parties
figure
who
would
owe
whom
and settle up in
cash.
They settle not just on the
transaction
date but at the end of
trading
every
day
throughout
the term of the
contract.
This is nec
essary
because
of the big
losses
possible.
Daily
settling
ensures
that
no one gets too far
behind,
minimizing
the
chance
of a big
default.
176


## Page 188

Arbitrage
What's
an
S&P
futures
contract
worth?
Thorp
suspected
that
people
would
be
playing
hunches.
Brokerages
had
staffs
of
highly
paid
analysts
who
gucsstimated
where
the
S&P
was
going
to
be
inso
many
months.
Thorp
believed
this
advice
was
virtually
useless.
When
people
invest
based
on
useless
advice,
there
may
be
an
oppor
tunity
to profit.
Thorp
used
software
to
determine
a
fair
price
for
S&P
futures.
He had to model the random walkof all 500 S&P stocks. Princeton-
Newport's
minicomputers
had
a
huge
speed
and
storage
advantage
over
what
was
available
to
most
other
traders.
The
computer
model
told
Thorp
that
the
S&P
futures
were,
like
many
exciting
new
things,
overvalued.
That
implied
that
Princeton-Newport
could
make
money
by
selling
S&P
futures.
But
hedging
the
trade
would
mean
buying
all
500
S&P
stocks,
racking
up a lot of
trading
costs.
Thorp did
further
calculations
and
concluded
that
buying
se
lected
sets
of
S&P
stocks
would
provide
sufficient
protection.
As
Thorp
computed
a
high
probability
of
success,
Princeton-Newport
committed
S25
million
of
its
capital
to the
S&P
futures,
doing
as
many
as 700 trades a
day.
There
were
days
when
the
fund's
trades
accounted for more than 1 percent of the total
volume
of the New
York
Stock
Exchange.
The
gravy
train
lasted
about
four
months.
The
profit
came
to
S6
million.
Then the
market
got the
message.
The
prices
for
S&P
contracts
dropped,
and other
traders
started
using
computers.
The
price
anomalies
vanished.
In
1981,
the yearof the
AT&T
deal,
Princeton-Newport
achieved
a
return
of
22.63
percent
net
of
fees. For 1982, with the S&P futures
trade,
it
was
21.80
percent.
As
fiscal
1982
ended.
Thorp and
Regan
could
boast that a
dollar
invested
at the outset had
grown
to
$6.61
in
thirteen
years.
By
that time, Thorp and
Regan
had turned a conviction that the
market
can
be
beaten
into
one
of
the
most
successful
investment
partnerships
of
all
time.
It
was
rare
enough
to
achieve
greater-than-
market return over thirteen
consecutive
years.
Skeptical
academics
177


## Page 189

FORTUNE
S
FORMULA
and
some
traders
tended
to
judge
such
exceptional
performance
as
a
Faustian
bargain.
Successful
arbitrageurs,
it
was
held,
were
risk-
takers.
Sooner or
later,
they lose
big.
Everything
about
Princeton-Newport
refuted
that
view.
The
fund
had
never
had
a
down
year,
or
even
a
down
quarter.
With
his
talk of the
Kelly
formula
to
manage
risk.
Thorp
gave
everyappear
anceof being"the
first
sure
winner
in
history."
The
partnership
was
a
marriage
of
opposites.
Regan
lived
a
con
tinent
away
on a
baronial
225-acre
New
Jersey
ranch
where
he
raised
horses.
In a
1986
profile
of the
partners
in
Forbes,
it is
Regan
who
supplies
the
sound
bites.
"Taking
candy
from
a
baby,"
said
Re
gan
ofone
trade.
"You
back
the
truck
up to the
store
and
start
load
ing it."
Regan
was
"near
the
rumors,
information
and
opportunities
that
arc
always
rattling
through
the
Wall
Street
network,"
Thorp
ex
plained.
"There's
a
string
of
rumors
coming
down
the
pipeline.
The
further
you
arc
down
the
information
chain,
the
less
valuable
the in
formation
is."
Thorp
was
introspective,
approaching
the
challenges
of
his
work
as a scientist. Fie measured his words like he measured everything
else.
Thorp
was
careful
to
characterize
his
fund's
performance
as
"getting
rich
slow,"
as if
more
confident
words
might
jinx
things.
Not until 1982 did he quit his
"day
job" teaching at UC Irvine.
Thorp
was
slow
to
display
his
now-considerable
wealth.
In the
office,
he
dressed
like
a
California
professor
on his day
off,
in mod
shirts and
sandals.
When the Thorps
finally
decided it
was
time to
buy
a big
house,
they
chose
a
hillside
ten-bathroom
home,
saidto be
the
largest
in
Newport
Beach,
with
panoramic
views
from
Catalina
to
the
Santa
Ana
Mountains.
It
had
a
fallout
shelter
with
16-inch-
thick
concrete
walls
and
steel
doors.
Ever
mindful
of
the
odds,
Thorp
computed
that it
could
withstand
a
one-megaton
hydrogen
bomb blast as close as a mile
away.
Neither Thorp nor
Regan
could
have
imagined
how soon it
would
all
end,
or
how.
178


## Page 190

PART
FOUR
St.
Petersburg
Wager


## Page 191

Daniel
Bernoulli
Daniel
Bernoulli
came
from
an
insanely
competitive
family
of
eighteenth-century
geniuses.
It
was
Daniel's
uncle
Jakob
who
had
discovered
the
law
of
large
numbers.
Jakob
tutored
his
brother
Johann
in
math.
Johann
was
as
smart
as
Jakob
was;
he
was
also
a
braggart.
The
Bernoulli
brothers
acquired
the
unfortunate
habit
of
working
on
the
same
problems
competitively.
They
brutally
attacked
each
other in
print.
Johann
grew into an embittered man who took out his
frustra
tions
on
his
son
Daniel
(1700-1782).
Daniel
was
both
a
mathe
matician
and
a
physicist.
He
published
a
famous
analysis
of
the
casinogame of faro and
discovered
the
"Bernoulli
effect" later used
in
the
design
of
aircraft
wings.
Johann
took
little
visible
joy
in
his
son's
triumphs.
When
father
and
son
were
jointly
awarded
a
French
Academy
of
Sciences
prize in
1734,
Johann threw Daniel out of the
house.
Johann
grumbled
that he
alone
should
have
won the
award.
In
1738
Daniel
published
an
important
book
called
Hydraulica.
The
following
year,
his
father
published
nearly
the
same
book
under
his
own
name,
with
the
false
dateof
1732.
This
ruse
allowed
Johann
to
claim
that
his
son's
book
was
a
plagiarism.
It must have been with some relief that Daniel left his father for
far-distant
St.
Petersburg.
There,
working
for
the
Westernizing
Russian
court,
Daniel
wrote
an
article
that
was to be
influential
for
the
reception
of
Claude
Shannon
and
John
Kelly's
ideas
among
twentieth-century
economists.
The article concerned a
fictitious
iSi


## Page 192

fortune's
formula
wager
devised
by
still
another
gifted
Bernoulli,
Nicolas,
a
doctor
of
law
at
the
University
of
Basel.
Nicolas
was
Daniel's
cousin.
The
wa
ger
involves
a
game
of
doubling
that
may
recall
Kelly's
quiz-show
inspiration.
The
S64,ooo
Question.
As
Daniel
described
it
in
1738,
Peter
tosses
a coin and
continues
to do so until it should land
"heads"
when
it
comes
to the
ground.
He
agrees
to
give
Paul
one
ducat
if
he
gets
"heads"
on
the
very
first
throw,
two
ducats
if
he
gets
it
on
the
second,
four
if
on
the
third,
eight
if
on
the
fourth,
and so on, so that with
each
additional
throw
the number of
ducats
he
must
pay
is
doubled.
Suppose
we
seek
to
determine
the value
of
Paul's expectation.
How
much
can
Paul
expect
to
win,
on
the
average?
To
find
the
mathematical
expectation
ofa
random
event,
you
multiply
its
prob
ability
by
its
value.
There's
a
'A
chance
of
heads
on
the
first
throw,
and
heads
wins
Paul
I
ducat
(worth
about
$40
today).
Multiplying
'A
times
I
ducat
gives
an
expected
value
of
'A
ducat.
That
is
just
for
the
case
in
which
the
first
toss
is
heads.
There
are
many
other
ways
to
win.
Should
the
first
throw
come
up
tails,
Peter
tosses
again.
If
the
second
throw
is
heads,
Paul
wins
2
ducats.
The
chance
of
winning
2
ducats
is
'A,
since
that
requires
that
the
first
throw
be
tails
('/i
chance)
and
that
the
second
throw
be
heads
('/i
chance).
A
'A
shot
at2
ducats
is
worth
'A
ducat.
Likewise,
there's
a
'/s
chance
of
winning
4
ducats,
which
isworth
'A
ducat
itself.
There's a '/<
chance
of 8
ducats,
a
lA\
chance
of
16 ducats
...
All of these
distinct
scenarios each have an expecta
tion of
'A
ducat.
Paul's
total
expected
winnings
should
therefore
be
the sum
of
an infinite series of
'A-ducat
terms. His expected win
nings
are
infinite.
Will
you
get
infinitely
rich
by
playing
this
game?
No.
If
you
don't
believe
it, try
flipping
a
coin.
Sec
how
much
you
would
have
won.
The
infinite
expectation
is
a
big
problem
for
anyone
who
wants
to use math to decide what to do in the realworld. It implies that no
amount
of
money
is
too
much
to
pay
for
the
privilege
of
playing
this
game.
Were
a
casino
to
charge
a
million
dollars
to
play
this
game,
ra-
182


## Page 193

St.
Petersburg
Wager
tional
customers
should
jump
at the
chance,
it
would
seem.
Same
if
the
casino
charged
a
trillion
dollars.
You
might
prefer
to
think
of
the
wager
as
an
initial
public
offer
ing
ofa
growth
stock.
People
evaluating
a
new
company's
prospects
must
conclude
that
there
are
many
scenarios
with
varying
degrees
of
probability
and
profitability.
Somehow
they
mentally
tally
up
the
outcomes
to
arrive
at
a
reasonable
price
to
pay
for
the
stock.
Bernoulli's
example
suggests
that in
some
situations
conventional
reasoning
could
find
a
stock
worth
buying
at
any
price,
no
matter
how
high.
Both Nicolas and Daniel Bernoulli knew this was absurd. Daniel
wrote,
Although the standard calculationshows that the value of
Paul's
expectation
is
infinitely
great,
it
has
. . . to be
admitted
that
any
fairly
reasonable
man
would
sell
his
chance,
with
great
pleasure,
for
twenty
ducats.
The
accepted
method
of
calculation
does,
in
deed,
value
Paul's
prospects
at
infinity
although
no
one
would
be
willing
to
purchase
it at a
moderately
high
price.
Daniel
published
these
words
in
Latin.
The
wager
has
come
to
be
known
as
the
"St.
Petersburg
wager"
or
"St.
Petersburg
paradox."
It
has
provoked
sporadic
interest
ever
since.
A
mention
in
John
Maynard
Keynes's
1921
Treatise
on
Probability
made
it part of the
mental
furniture
of
nearly
every
twentieth-century
economist.
Bernoulli's
wager
makes
an
appearance
in von Neumann and Mor-
genstern's
Theory
of
Games
and
Economic
Behavior
and
in
papers
by
Ken
neth
Arrow,
Milton
Friedman,
and Paul
Samuelson.
The
paradox
can
be
resolved
easily
by
noting
that
Peter
would
have
to
possess
infinite
wealth
to
make
good
on
the
game's
potential
payouts. No
one
has
infinite
wealth.
Therefore
most
of
the
terms
of
the
infinite
series
are
irrelevant.
A
minuscule
chance
of
winning
a
quadrillion
dollars
isnot
worth
what
you
might
compute.
It's
worth
practically
nothing
because
no one
has
a
quadrillion
dollars
to
award.
Suppose
a
casino
offered
this
wager
with
winnings
capped
at a
billion
dollars.
How
much
would
the
wager
be worth
then?
A lot
183


## Page 194

fortune's
formula
less!
Assume
prizes
start
with
a
dollar.
Normally,
the
prize
for
heads
on
the
31st
toss
would
be
$1,073,741,824.
The
most
reasonable
course
for
the
casino
would
be
to
halt
the
game
at 30
tosses
and
award
the
billion
dollars
to
anyone
who
has
gotten
30
tails.
The ex
pected
value
of
this
truncated
game
is
a
measly
$15-93-
That's a lot
more
reasonable.
The
wager
is not
worth
infinity,
just
a
few
dollars.
This
explanation
of
the
puzzle
is
as
good
as
any
hardheaded realist could ask
for.
Yet
philosophers,
mathemati
cians—even
economists—have
rarely
accepted
this
solution.
Most
take
the
position
that
we
can
pretend
that
Peter
possesses
infinite
wealth.
Isn't it
still
ridiculous
to
say
that
Paul
should
be
willing
to
pay
any
amount
to
play
the
game?
Daniel
Bernoulli
thought
so.
He
proposed
a
different
solution
that
was
highly
influential
for
future
economic
thought.
Bernoulli
drew a
distinction
between
money
and the
value
people
place
on
money
To
a
billionaire,
$1,000
is
pocket
change.
To
a
starving
beg
gar,
$1,000
may
be
a
fortune.
The
value
ofa
financial
gain
(or
loss)
depends
on
the
wealth
of
the
person
it
affects.
You're
probably
saying
to
yourself
that
you
already
knew
that.
Well
okay,
Bernoulli's
real
contribution
was
to
coin
a
word.
The
word
has
been
translated
into
English
as
"utility."
It
describes
this
subjective
value
people
place
on
money.
Bernoulli
claimed
that
peo
ple
instinctively
act
to
achieve
the
greatest
possible
utility—not
nec
essarily
the
greatest
number
of
dollars
or
ducats.
"The
value
of an
item must not be
based
on its
price,"
Bernoulli
wrote,
"but rather on
the
utility
it
yields.
The
price
of
the
item
is
dependent
only
on
the
thing
itself
and
is
the
same
for
everyone;
the
utility,
however,
is
de
pendent
on
the
particular
circumstances
of
the
person
making
the
estimate."
How much less is a dollar worth to a rich person than a poor
one?
The
only
honest
answer
is,
"It
depends."
As
an
example,
Bernoulli
sketched
the case of a rich man who is imprisoned and
needs
exactly
2,000
ducats
more
than
he
has
in
order
to
buy
his
free
dom.
This
man
might
place
a
greater
valuation
on
those
needed
2,000
ducats
thana
poorer
man
with
no
such
pressing
need.
This isa
contrived
predicament.
Most
of the
time,
a
rich
person
184


## Page 195

St.
Petersburg
Wager
would
value
a
2,000-ducat
gain
less
than
a
poorer
person
would.
Bernoulli
offered
a
rule
of
thumb.
"In
the
absence
of the
unusual,"
he
wrote,
"the
utility
resulting
from
any
small
increase
in
wealth
will
be
inversely
proportionate
to
the
quantity
of
goods
previously
pos
sessed."
In
other
words,
your
friend
who
is
twice
as
rich
as
you
would
be
only
half
as
delighted
to
win
a
Sioo
bet
as
you
would
be.
Picking
up
the
dinner
bill
hurts
him
only
half
as
much.
You
can
make
a chartof
utility
vs.
wealth.
If
people's
valuation
of
moneywere in direct proportion to their
wealth,
the chart would be
a straight line. With
Bernoulli's
rule of thumb, the line curves. This
reflects
the
fact
that
it
takes
a
large
dollar
gain
to
make
the
same
dif
ference
to
a
rich
person
as
a
smaller
dollar
gain
would
to
a
poor
per
son.
The
shape
of
this
curve
(and
Bernoulli's
rule
about
the
value
of
a
monetary
gain
being
inversely
proportional
to
wealth
already
pos
sessed)
describes
a
logarithmic
function.
Bernoulli's
rule
of
thumb
is
therefore
called
logarithmic
utility.
Bernoulli
used
utility
to
resolve
the
St.
Petersburg
paradox.
As
sume
that
Paul
values
gains
in
inverse
proportion
to
his
wealth.
That
means
that
the
value
Paul
places
ona
2-ducat
win
is
not
quite
twice
Logarithmic
Utility
Zero
wealth
is
infinitely
bad
A $1,000gain
makes a big
difference
to
someone who's poor
SI.OOO
Y
A
billionaire
barely
notices
an exlra $1,000
wealth
185


## Page 196

fortune's
formula
that
ofa
i-ducat
gain.
Your
second
ducat,
like
your
second
million,
is
never
quite
as sweet.
This means that the terms in the infinite series need to be ad
justed
downward
to
account
for
the
diminishing
returns
of
large
winnings.
Though
the
series
is
still
infinite,
it
becomes
one
of
those
well-mannered
infinite
series
that
converges.
You
can
addup
'/a
+
'A
+
'/a
+
V16
. . .
and
never
quite
reach
i, no
matter
that the
series
is
endless.
When
Bernoulli's
series
of
expectations
is
adjusted
this
way,
it too
converges
to a
finite
and
modest
sum.
Economic
thinkers
were
infatuated
with
logarithmic
utility for
the
next
couple
of
centuries.
British
economist
William
Stanley
Jevons
(1835-1882)
maintained
that
logarithmic
utility
applied
to
consumer
goods
as
well
as
wealth:
"As
the
quantity
of
any
commod
ity,
for
instance,
plain
food,
which
a
man
has
to
consume,
increases,
so
the
utility
or
benefit
derived
from
the
last
portion
used
decreases
in
degree."
You
might
say
this
explains
how
all-you-can-eat
restau
rants
stay
in
business.
In
1954
Leonard
Savage
called
the
logarithmic
curve
a
"prototype
for
Everyman's
utility
function"—a
reasonable
approximation
to
how
most
people
value
money,
most
of
the
time,
over
the
range
of
dollar
values
they
normally
encounter.
Not
everyone
agreed.
By
Savage's
time,
logarithmic
utility
had
taken
on a
fusty,
old-fashioned
cast.
One
blow
to the
concept
was
the
realization
that
logarithmic
utility
is
not an
entirely
satisfy
ing
resolution
to
the
St.
Petersburg
paradox.
In
the
1930s,
Vienna
mathematician
Karl
Menger
pointed
outthatit
is
easy
to
come
back
with
revised
versions
of the
St.
Petersburg
wager
where
Bernoulli's
solution
fails.
All
you
have
to
do
is
to
sweeten
the
payoffs.
Instead
of
offering
1,
2,4,
8
ducats
on
successive
throws,
offer
something
like
2,
4,
16,
256
ducats
. . .
You
can
arrange
to
have
the
prizes
escalate
so
fast
that the
expected
utility
is
again
infinite.
Menger's
most
devilish
counterexample
was
to
have
the
wager's
prizes
notin
dollars
or
ducats
but
utiles.
A
utile
is
a
hypothetical
unit
of
utility.
You
would
win
I,
2,
4,8
...
utiles,
depending
on
how
many
tosses
it
takes.
The
value
of the
wager,
now in
expected
utility,
is
infinite.
A
rational
person
would
supposedly
give
up
anything
he's
186


## Page 197

St.
Petersburg
Wager
got
to
play
this
game—which
is
still
absurd
because
he's
likely
to
win
the
utile
equivalent
of
chump
change.
What
should
we
make
of
all
this?
Perhaps
not
much.
Paul
Samuel
son
believed
that
the
supercharged
versions
of
the
St.
Petersburg
paradox
do not
"hold
any
terrors
forthe
economist."
The nubof the
issue
is
that
Bernoulli's
utility
function
is
psychologically
unrealistic
at
the
extremes
of
wealth.
A
better
resolution
invokes
a
"bliss
level."
This
is
a
supposed
ceiling
on
utility.
Figure
how
much
money
you
would
need
to
satisfy
every
need
or
desire
that
can
possibly
be
satisfied
with
mere
mate
rial
things.
That
amount
of
money,
and
the
corresponding
utility,
is
the
bliss
level.
An
upper
limit
to
utility
works
much
like
an
upper
limit
to
the
dollars
a
casino
is
able
to
pay
out.
It
truncates
the
infinite
series
at a
reasonable
and
finite
value.
A
logarithmic
utility
function
has
no
bliss
level.
The
curve
in the
chart
appears
to
flatten
out
toward
the
upper
right.
It
never
ceases
rising,
however.
This
means,
for
instance,
that
someone
with
loga
rithmic
utility
would
be
equally
delighted
by
any
gain
that
increased
total
wealth
by
a
factor
of
ten.
Increasing
your
net
worth
from
$10,000
to Sioo.ooo
would
be
just
as
welcome
as
going
from
Sioo.ooo
to
$i
million,
or
from
Si
million
to $10
million.
This
may
or
may
not
sound
plausible.
There
isa
point
where
this
power-of-ten
business
becomes
hard
to
swallow,
though.
Is
there
any
advantage
to
having
$10
billion
instead
ofa
just
Si
billion?
Not
if
you're
just
concerned
with
"living
well."
Is
there
then
any
further
glory
in
possessing
$10
trillion
over
$1
trillion?
Notif
you're
just
in
terested
in
being
the
richest
person
on
earth.
Logarithmic
utility
is
not a
good
model
of
poverty,
cither.
It
im
plies
that
losing
90
percent
of
your
last
million
is
just
as
painful
as
losing
90 percentof yourlast
dime.
That's
absurd.
187


## Page 198

fortune's
formula
lie
In
1936
economist
John
Burr
Williams
published
an
article
in tl
Quarterly
Journal
of
Economics
titled
"Speculation
and
the
Carryover."
The
article
was
about
cotton
speculators,
people
who
buy
excess
cotton
ata
cheap
price
in
hopes
of
selling
ita
year
or
more
later
at a
profit.
Speculators
"bet"
that
the
next
year's
crop
will
be
poor,
caus
ing
prices
to
rise.
Williams
notes
the
strong
element
of
chance
in
this
activity.
No
one
can
predict
the
weather,
for
instance.
Fie
ob
serves
that the
successful
speculator
must
have
an
edge.
He must
know
something
that the
market
does
not.
Ina
"Note
on
Probability"
at theendof the
article,
Williams
says
that
"ifa
speculator
is
in
the
habit
of
risking
his
capital
plus
profits
(or
losses)
in
each
successive
trade,
he
will
choose
the
geometric
rather than the
arithmetic
mean
of
all
the
prices
...
as the repre
sentative
price
for
the
distribution
of
possible
prices"
in
his
cal
culations. Williams does not elaborate on this
somewhat
cryptic
statement.
It has much to do with both Bernoulli's and
Kelly's
ideas.
Williams
was
a
prominent
economist,
known
for
the
(now-quaint)
idea
that
stocks
can
be
valued
by
their
dividends.
Despite
Williams's
reputation,
this
statement
did
not
get
much
attention
and
was
quickly
forgotten.
Nature's
Admonition
to
Avoid
the
Dice
THE
JANUARY
1954
ISSUE
ofEconomctrica
carried
the first
English
translation of
Bernoulli's
1738
article mentioning the St.
Petersburg
wager.
Few
Western
economists
read
the
original,
so
the
full
con-
188


## Page 199

St.
Petersburg
Wager
tent of
the
article
was
not
widely
known.
The
translation
showed
that
Bernoulli's
achievement
had
long
been
distorted
and
under
rated.
The
article
was
not
really
about
the
St.
Petersburg
wager
or
util
ity.
Both
were
mentioned
only
as
asides.
Bernoulli's
thesis
was
that
risky
ventures
should
be
evaluated
by
the
geometric
mean
of
out
comes.
You
may remember from school that there are two kinds
of
"av
erages."
The
arithmetic
average
(or
mean)
is
the
plain-vanilla
kind.
It's
what
you
get
when
you
add
up
a
list
of
values
and
divide
by
the
number
of
values
in
the
list.
It's
what
batting
averages
are,
and
what
an
Excel
spreadsheet
calculates
when
you
enter
the
formula
=AVERAGE
( ).
The
geometric
mean
is
the
one
that
most
people
forget
after
high
school.
It
is
calculated
by
multiplying
a
list
of
n
values
together,
then
taking
the
nth
rootof the
product.
Not
many
people
enjoy
taking
«th
roots
if
they
can
help
it,
so
the
geometric
mean
is
left
mostly
to
statisticians.
Of
course,
nowadays
no one
computes
either
kind
of
average
by
hand.
There isan
Excel
formula
for
computing
the
geometric
mean,
=GEOMEAN
( ).
The
point
of
any
average
is
to
simplify
life.
It
is
easier
to
remem
ber
that
Manny
Ramirez
has
a
batting
average
of
.349
than
to
memo
rize
every
fact
about
his
entire
career.
A
batting
average
may
be
more
informative
about
a
player's
abilities
thana
mountain
of
raw
data.
In
baseball
and
much
else,
the
ordinary,
arithmetic
mean
works
well
enough.
Why
should
we
bother
with
a
geometric
mean?
Bernoulli
starts
with
gambling.
A
"fair"
wager
is
one
where
the
expectation,
computed
as
an
arithmetic
mean
of
equally
likely
out
comes,
is
zero.
Here's
an
example
of a
so-called
fair
wager.
You
bet
your
entire
net
worth
on
the
flip
of a
coin.
You
play
against
your
neighbor,
who
has
the
same
net
worth.
It's
double
or
nothing.
Win
ner
gets
the
loser's
house,
car,
savings,
everything.
Right
now
you
have
Sioo.ooo,
say.
After
the
coin
toss,
you
will
either
have
S200.000
or
So,
each
an
equally
likely
outcome.
The
arithmetic
mean
is
($200,000
+
$0)
fi,
or
$100,000.
If
you
adopt
$100,000
as
the
fair
and
proper
value
of
this
wager,
then
it
might
189


## Page 200

fortune's
formula
seem
you
should
be
indifferent
to
taking
this
wager
or
not.
You've
got
Sioo.OOO
now,
and
you
expect
the
same
amount
after
the
coin
toss.
Same
difference.
People
don't
reason
this
way.
Both
you
and
your
neighbor
would
be
nuts
to
agree
to
this
wager.
You
have
far
more
to
lose
by
forfeit
ing
everything
you
have
than
to
gain
by
doubling
your
net
worth.
Look
at
the
geometric
mean.
You
compute
it
by
multiplying
the
two
equally
possible
outcomes
together—$200,000
times
$0—and
taking
the
square
root.
Since
zero
times
anything
is
zero,
the
geo
metric
mean
is
zero.
Accept
that
as
the
true
value
ofthe
wager,
and
you'll
prefer
to
stick
with
your
$100,000
net
worth.
The
geometric
mean
is
almost
always
less
than
the
arithmetic
mean.
(The
exception
is
when
all
the
averaged
values
are
identical.
Then the
two
kinds
of
mean
are
the
same.)
This
means
that the
geometric
mean
is
a
more
conservative
way
of
valuing
risk)'
proposi
tions.
Bernoulli
believed
that this
conservatism
better
reflects
peo
ple's
distaste
for
risk.
Because
the
geometric
mean
is
always
less
than
the
arithmetic
mean
ina
risky
venture,
"fair"
wagers
are
in
fact
unfavorable.
This,
says
Bernoulli,
is
"Nature's
admonition
to
avoid
the
dice
altogether."
(Bernoulli
does
not
allow
for
any
enjoyment
people
may
get
from
gambling.)
In
Bernoulli's
view,
a
wager
can
make
sense
when
the
odds
are
slanted in one's
favor.
It can also makesense when the wageringpar
ties differ in
wealth.
Bernoulli
thus
solved
one of
Wall
Street's old
est
puzzles.
It
is
said
that
every
time
stock
is
traded,
the
buyer
thinks
he's
getting
the
better
of
the
deal,
and
so
does
the
seller.
The
im
plied
point
is
that
they
can't
both
be
right.
Bernoulli
challenges
that
idea.
"It
may
be
reasonable
for
some
individuals
to invest in a doubtful enterprise and yet be unreason
able
for
others
to do
so."
Though
he
does
not
mention
the
stock
market,
Bernoulli
discusses
a
"Petersburg
merchant"
whomust ship
goods
from
overseas.
The
merchant
is
taking
a
gamble
because
the
ship
may
sink.
One
option
is
to
take
out
insurance
on
the
ship.
But
insurance
is
always
an
unfavorable
wager,
as
measured
by
the
arith-
190


## Page 201

St.
Petersburg
Wager
metic
mean.
The
insurance
company
is
making
a
profit
off
the
pre
miums.
Bernoulli
showed
that
a
relatively
poor
merchant
may
improve
his
geometric
mean
by
buying
insurance
(even
when
that
insur
ance is "overpriced") while at the same time a much wealthier in
surance
company
is
also
improving
its
geometric
mean
by
selling
that
insurance.
Bernoulli
maintained
that
reasonable
people
are
always
maxi
mizing
the
geometric
mean
of
outcomes,
even
though
they
don't
know
it:
"Since
all
of
our
propositions
harmonize
perfectly
with
ex
perience
it
would
be
wrong
to
neglect
them
as
abstractions
resting
upon precarious
hypotheses."
There
is
a
deep
connection
between
Bernoulli's
dictum
and
John
Kelly's
1956
publication.
It
turns
out
that
Kelly's
prescription
can
be
restated
as
this
simple
rule:
When
faced
with
a
choice
of
wagers
or
invest
ments,
choose
the
one
with
the
highest
geometric
mean
of
outcomes.
This
rule,
of
broader
application
than
the
edge/odds
Kelly
formula
for
bet
size,
is
the
Kelly
criterion.
When
the
possible
outcomes
are
not
all
equally
likely,
you
need
to
weight
them
according
to
their
probability.
One
way
to
do
that
is
to
maximize
the
expected
logarithm
of
wealth.
Anyone
who
follows
this
rule
is
acting
as
if
he
had
logarithmic
utility.
In
view
of the
chronology,
it is
reasonable
to wonder whether
Kelly
knew
of
the
Bernoulli
article.
There
is
no
evidence
of
it.
Kelly
does
not
cite
Bernoulli,
as
he
almost
certainly
would
have
had
he
known
of
Bernoulli's
discussion.
As
a
communications
scientist,
it is
unlikely
that
Kelly
would
have
read
Econometrica.
Bernoulli's
article
was,
however,
a
direct
influence
on
Henry
Latane.
It was
Latanc,
not
Kelly,
who would introduce these ideas
to
economists.
191


## Page 202

fortune's
formula
*
Henry
Latane
Henry
Latane
had
the
interesting
fortune
to enter the job
market,
armedwitha
Harvard
M.B.A.,
in the grimyearof
1930.
He
claimed to be the last man hired on Wall Street before the Depres
sion.
Latane
worked
as a
financial
analyst
in the
1930s
and
1940s.
He
was
the
type
of
person
whom
Samuelson
thought
should
get
a
real
job,
and
in
a
way
he
took
Samuelson's
advice.
Well
into
middle
age,
Latane
quit
his
Wall
Street
job
and
went
back
to
school
to
earn
a
Ph.D.
He
spent
the
rest
of
his
life
as
an
educator
and
theorist.
In
1951
Latane
began
doctoral
work
on
portfolio
theory
at
the
University
of
North
Carolina.
He
read
the
translated
Bernoulli
arti
cle and
realized
that its
ideas
could
be
applied
to stock
portfolios.
Latane
later met
Leonard
Savage.
He
convinced
Savage
that the
geometric
mean
policy
made
a
lot
of
sense
for
the
long-term
investor.
Latane
presented
this
work
at a
prestigious
Cowles
Foundation
Seminar
at
Yale
on
February
17,
1956.
Among
those
attending
was
Flarry
Markowitz.
Markowitz was the founder of the dominant school of portfolio
theory,
known
as
mean-variance
analysis.
Markowitz
used
statistics
to
show
how
diversification—buying
a number of different
stocks,
and
not
having
too
much
in
any
one—can
cut
risk.
This
idea
isso
widely
accepted
that it is
easy
to
forget
that
sensi
ble
people
ever
thought
otherwise.
In
1942
John
Maynard
Keynes
wrote,
"To
suppose
that
safety-first
consists
in
having
a
small
gamble
in a
large
number
of
different
[companies]
where
I
have
no
infor
mation
to
reach
a
good
judgment,
as
compared
with
a
substantial
192


## Page 203

St.
Petersburg
Wager
stake
in
a
company
where
one's
information
is
adequate,
strikes
me
as a
travesty
of
investment
policy."
Keynes
was
afflicted
with
the
belief
that he
could
pick
stocks
better than other
people
could.
Now
that
Samuelson's
crowd
had
tossed
that
notion
in
the
dustbin
of
medieval
superstition,
Marko-
witz's
findings
had
special
relevance.
You
may
not
be
able
to
beat
the
market,
but
at
least
you
can
minimize
risk,
and
that's
something.
Markowitz
used
statistics
to
show,
for
instance,
that
by
buying
twenty to thirty stocks in different
industries,
an investor can cut
the
overall
portfolio's
risk
by
about
half.
Markowitz
saw
that
even
a
perfectly
efficient
market
cannot
grind awayall differences between stocks. Some stocks are intrinsi
cally
riskier
than
others.
Since
people
don't
like
risk,
the
market
ad
justs
for
that
by
setting
a
lower
price.
This
means
that
the
average
return
on
investment
of
risky
stocks
is
higher.
As
the
name
indicates,
mean-variance
analysis
focuses
on
two
statistics
computed
from
historical
stock
price
data.
The
mean
isthe
average
annual
return.
It
is
a
regular,
arithmetic
average.
The
vari
ance
measures
how
much
this
return
jumps
around
the
mean
from
year to
year.
No equity investment is going to
have
the same return
every
year.
A
stock
may
gain
12
percent
one
year,
lose
22
percent
the
next, gain 6 percent the next. The more volatile the stock's returns,
the higher its
variance.
Variance
is thus a
loose
measure
of
risk.
Forthe
first
time,
Markowitz
concisely
laid
out the trade-offbe
tween
risk
and
return.
His
theory
pointedly
refuses
to
take
sides,
though.
Risk
and
return
are
apples
and
oranges.
Is
higher
return
more
important
than
lower
risk?
That
is
a
matter
of
personal
taste
in
Markowitz's
theory.
Consequently
mean-variance
analysis
does
not
tell
you
which
portfolio
to
buy.
Instead,
it
offers
this
criterion
for
choosing:
One
portfolio
is
better
than
another
one
when
it
offers
higher
mean
re
turn
for
a
given
level
of
volatility—or
a
lower
volatility/or
a
given
level
of
return.
This
rule
lets
you
eliminate
many
possible
portfolios.
If
portfolio
A isbetterthan
portfolio
B
by
the
rule
above,
then
you
can
cross
out
B.
After
you
eliminate
as
many
portfolios
as
possible,
the
ones
that
193


## Page 204

FORTUNE'S
FORMULA
are left are
called
"efficient."
Markowitz
got that term from a men
tor who did
efficiency
studiesfor
industry.
Markowitz
made charts of mean
vs.
variance.
Any stock or port
folio
is a dot in the
chart.
When
you
erase
all
the
dots
rejected
by
the
above
rule,
the
surviving
portfolios
form
an
arc
of
dots
that
Markowitz
called
the
"efficient
frontier."
It
will
range
from
more
conservative
portfolios
with
lower
return
to
riskier
portfolios
with
higher return.
Financial
advisers
responded
to
Markowitz's
model.
They
were
growing
aware
of
this
new
and
threatening
current
in
academic
thought:
the
efficient
market
hypothesis.
Markowitz
demonstrated
that
all
portfolios
are
not
alike
when
you
factor
in
risk.
Therefore,
even in an
efficient
market, there is reason for investors to pay
handsomely
for
financial
advice.
Mean-variance
analysis
quickly
swept
through
the
financial
profession
and
academia
alike,
estab
lishing
itselfas
orthodoxy.
Latane
s
1957
doctoral
dissertation
treats
the
problem
of
choosing
a
stock
portfolio.
This
is
something
that
Bernoulli
did
not
do,
and
that
Kelly
alluded
to
only
vaguely,
in
the
midst
ofalotof
talk
about
horse
races
and
entropy.
With
Savage's
encouragement,
Latane
pub
lished
this workin
1959.
three
years
after
Kelly's
article,
as "Criteria
for
Choice
Among
Risky
Ventures."
It
appeared
in
the
Journal
of
Polit
ical
Economy.
It's
unlikely
that
any
of the
article's
readers
had
heard
of
John
Kelly.
Latane
himself
had
not
heard
of
Kelly
at the
time
of
the
Cowlcs
seminar.
Latane
called
his
approach
to
portfolio
design
the
geometric
mean criterion. He demonstrated that it isa
myopic
strategy.
A "near
sighted"
strategy
sounds
like
a
bad
thing,
but
as
economists
use
it,
it's
good.
It
means
that
you
don't
have
to
have
a
crystal
ball
on
what
the
market
is
going
to do in
the
future
in
order
to
make
good
deci
sions
now.
This is
important
because
the
market
is
always
changing.
The
"myopia"
of the
geometric
mean
(or
Kelly)
criterion
is
all-
important
in
blackjack.
You
decide
how
much
to
bet
now
based
on
194


## Page 205

St.
Petersburg
Wager
the
composition
of
the
deck
now.
The
deck
will
change
in
the
fu
ture,
but
that
doesn't
matter.
Even
if
you
did
know
the
future
history
of the
deck's
composition,
it
wouldn't
bearon what to do
now.
So it
is
with
portfolios.
The
best
you
can
do
right
now
is
to
choose
a
port
folio
with
the
highest
geometric
mean
of
the
probability
distribu
tion of
outcomes,
as
computed
from
current
means,
variances,
and
other
statistics.
The
returns
and
volatility
of
your
investments
will
change
with
time.
When
they
do,
you
should
adjust
your
portfolio
accordingly,
again
with
the
sole
objective
of
attaining
the
highest
geometric
mean.
Also
in
1959,
Flarry
Markowitz
published
his
famous
book
on
Portfo
lio
Selection.
Everyone
in
finance
read
that,
or
said
they
did.
Markowitz
told
me
he
first
became
aware
of
Latane's
work
in the
1955-56
aca
demic
year,
when
James
Tobin
gave
him
a
copy
of
an
early
version
of
Latane's
article.
Markowitz
devoted
a
chapter
of
Portfolio
Selection
to
the
geometric
mean
criterion
(possibly
the
most
ignored
chapter
in
the
book)
and
cited
Latane's
work
in
the
bibliography.
Markowitz
was
virtually
the
only
big-name
economist
to see
much
merit
in the
geometric
mean
criterion.
He
recognized
that
mean-variance
analysis
is a
static,
single-period
theory
In
effect,
it
assumes
that
you
plan to buy
some
stocks
nowand
sell
them at the
end of a
given
time
frame.
Markowitz
theory
tries
to
balance
risk
and return for that
single
period.
Most
people
do not
invest
this
way.
They
buy
stocks
and bonds
and
hang
on to
them
until
they
have
a
strong
reason
to
sell.
Market
bets
ride,
by
default.
This
makes
a
difference
because
there
are
gam
bles
that
look
favorable
asa
one-shot,
yetare
ruinous
when
repeated
over
and
over.
Any
type
of
extreme
"overbetting"
on a
favorable
wa
ger would fit that
description.
The geometric mean criterion can also
resolve
the
Hamlet-like
indecision
of
mean-variance
analysis.
It
singles
out one
portfolio
as
"best."
Markowitz
noted that the
geometric
mean
can be estimated
from
the
standard
(arithmetic)
mean
and
variance.
The
geometric
mean is approximately the arithmetic mean minus
one-half
the
195


## Page 206

FORTUNE'S
FORMULA
variance.
This
estimate
may
be
made
more
precise
by
incorporating
further
statistical
measures.
One
additional
name
mustbe
added
as
codiscoverer/midwife
of the
Kelly
or
geometric
mean
criterion.
In i960
statistician
Leo
Breiman
published
"Investment
Policies
for
Expanding
Businesses
Optimal
ina
Long-Run
Sense."
This
appeared
ina
publication
as
unlikely
as
the
Bell
System
Technical
Journal,
namely
the
Naval
Research
Logistics
Quar
terly.
Breiman
was
the
first
to
show
that
maximizing
the
geometric
mean
minimizes
the time to
achieve
a particular wealth
goal.
Who
wants to be a
millionaire?
Breiman showed that a gambler investor
will
reach
that (or
any
other)
wealth
goal
faster
using
the
geometric
mean
criterion
than
by
using
any
fundamentally
different
way
of
managing
money.
Because
of this
complex
lineage,
the
Kelly
criterion
has
gonebya
welter
of
names.
Not
surprisingly,
Henry
Latane
never
used
"Kelly
criterion." He
favored
"geometric
mean
principle."
He
occasion
ally
abbreviated
that to
the
catchier
"G
policy"
or
even,
simply
to
"G."
Breiman
used
"capital
growth
criterion,"
and the
innocuous-
sounding
"capital
growth
theory"
is
also
heard.
Markowitz
used
MEL,
for
"maximize
expected
logarithm"
of
wealth.
In one
article,
Thorp
called
it the
"Kelly[-Brciman-Bernoulli-Latane
or
capital
growth]
criterion."
This
is
not
counting
the
yet-more-numerous
discussions
of
logarithmic
utility.
This
confusion
of
names
had
made
it
relatively
difficult
forthe
uninitiated
to
follow
the ideain the eco
nomic
literature.
The
person
most
shortchanged
by
this
nomenclature
is
probably
Daniel
Bernoulli.
He had
218
years'
priority on
Kelly.
The unique
and
unprecedented
part
of
Kelly's
article
is
the
connection
between
inside
information
and
capital
growth.
This is a
connection
that
could
not
have
been
made
before
Shannon
rendered
information
measurable.
Bernoulli
considers
a
world
where
all
the
cards
are
on
the
table,
so to
speak,
and
all
the
probabilities
arc
public
knowledge.
There is no hidden information.
Kelly
treats a darker, more ambigu-
196


## Page 207

St.
Petersburg
Wager
ous world where some people know the
probabilities
better than
others and attempt to profit from that
knowledge
over time. It is
this
feature
particularly
that
has
much
to
say
about the
financial
markets.
The
Trouble
with
Markowitz
TELLING
INVESTORS
to maximizethe geometric mean may cause
a
double
take.
The
geometric
mean
of
return
is
none
other
than
the
"compound
return
on
investment"
that is
Wall
Street's
usual
score-
card.
Everyone
has
been
talking
in that
prose
all
along.
Latane's
University
of North
Carolina
colleague
Richard
W
McEnally
observed
that "the
idea
that
we
should
pick
the
invest
ment
which
will
maximize
the rate of growth of a
portfolio
may
sound
...
like much advice from
economists—laudable,
but
difficult
or
impossible
to
implement
in
practice
because
of the
knowledge
of
the
distant
future it would
require."
A
few
examples
will
show
how
the
geometric
mean
principle
works.
Simple
case:
You've
got just two
choices
for your
money,
a
savings
account
paying
3
percent
interest,
and another
savings
ac
count
paying4
percent.
Both
accounts
are
guaranteed
by
the FDIC.
Because
there's no
risk,
the arithmetic and geometric mean returns
are the same for each
account.
Both
Kelly
and
Markowitz
say to put
your money in the 4 percent
account.
The
choice
is not so pat
when
there's
an element of
chance.
A
hot
technology
stock
might
have
a
higher
arithmetic
mean
return
197


## Page 208

FORTUNES
FORMULA
thana
boring
blue
chip,
but it is
also
likely
to
have
a
higher
volatility,
which
could
result
in a
lower
geometric
mean.
Are
you
better off
buyingthe
technology
stockor not?
This is the sort of
question
that the
Kelly
criterion
can
potentially
answer.
I
say
"potentially"
because
no one
really
knows
the
probabil
ities
underlying
stock
investments.
That
doesn't
prevent
analysts
from
cooking
up
target
figures
and
mathematical
models.
A
mathematical
model
attempts
to
reduce
an
imperfectly
known
real-world
situation
to a
game
of
chance.
Imagine,
then,
that
you
are
thinking
of
investing
in
three
penny
stocks.
You do a
lot
of
research
and
devise
a
mathematical
model
of
the
stocks'
returnsafter a
year.
In
principle,
you
could
builda
wheel
of
fortune
with the
same
probability
distribution
as the
stock.
Di
vide
the
rim
of the
wheel
into
however
many
spaces
you
need.
Mark
the
spaces
with
numbers
telling
how
much
a
dollar
invested
in the
stock
could
be
worth
after
a
year.
If
your
model's
any
good,
playing
the
wheel
of
fortune
is
about
the
same
as
investing
in the
stock.
Let's
say
you
build
a
wheel
of
fortune
for
each
of
three
penny
stocks and they look like this:
Kelly
vs.
Markowitz
Criterion
"Arithmetic
mean.
Geometric
mean
is $1.41.
"Arithmetic
mean.
Geometric mean is $0.00.
"Arithmetic
mean.
Geometric
mean
is $1.22.
These
wheels
are
simpler
than
anyone's
rational
ideaof a
stock's
prospects.
But you get the
idea.
By
adding
enough
spaces
on the
wheel,
you
could
represent
any
precise
idea
you
have
about the
stock's returns and their
probabilities.
198


## Page 209

St.
Petersburg
Wager
Suppose
you
had
to put
all
your
money
on justone
wheel.
Which
is
best?
It's
tough
to
tell.
That's
why
it's
useful
to
compute
"average"
re
turns.
As
sometimes
happens,
the
arithmetic
mean
return,being
bigger,
gets
top
billing,
while
the
geometric
mean
is
buried
in the
fine
print.
The third wheel hasthe
highest
arithmetic
mean.
The first wheel
has the highest geometric
mean.
Assuming
these are the only three
choices
and you
have
to
pick
one, the
Kelly
criterion would
have
you
put your money on the first
wheel.
The
worst
wheel,
by the
Kelly
philosophy,
is the
second.
That's
because it has a zero as one of its outcomes. With each spin, you
risk
losing
everything.
Any
long-term
"investor"
who
keeps
letting
money
ride on the
second
wheel
must
eventually
go
bust.
The sec
ond wheel's geometric mean is
zero.
What does
mean-variance
analysis
say?
To answer that, you have
to
compute
the
variance
of the
wheels'
returns.
I'll spare
you
the
trouble—the variance of the wheels increases from left to right. So
does the arithmetic mean return.
Consequently.
Markowitz
the
ory
refuses
to
decide
among
these
three
wheels.
All
are
legitimate
choices.
A risk-tolerant investor looking for the highest return
might
choose
the third
wheel.
A
conservative
investor
willing
to
sacrifice
return for
security
might
choose
the
first.
The
middle
wheel
is
good,
too,
for
people
in the
middle.
The last bit of
advice
is
particularly
hard to
swallow.
Most
would
agree
thatthe
middle
wheel
is
the
riskiest
because
it
alone
poses
the
danger
of
total
loss.
Yet
the
middle
wheel
has
a
lower
variance
than
the third
because
its outcomesare
less
dispersed.
This is one exam
pleof
how
variance
isnot a
perfect
measure
of
risk.
One point
where
the
Markowitz
and
Kelly
approaches
concuris
the value of
diversification.
A racetrackgambler who
"diversifies"
by
bettingon
every
horse
achieves
a
higher
geometric
mean
than
some
one
who
bets
everything
on a
single
horse
(and
risks
losing
it
all).
The
same
goes
for
someone
who
diversifies
by
buying
many
stocks.
There are two
ways
for a
speculator
to put the
law
of
large
numbers
to
work.
John
Kelly
mentioned
both in
his
article.
In an
unintended
199


## Page 210

FORTUNE
S
FORMULA
take
on
twentieth-century
gender
issues,
he
described
a
gambler
whose wife permits him to place a Si bet each
week.
He is not al
lowed
to reinvestany past
weeks'
winnings.
This gamblershould
forget
about the
Kelly
criterion.
Lie's
better
off
choosing
the
gamble
with the
highest
arithmetic
mean.
The rea
son is that the
henpecked
gambler's
winnings
do not
compound;
they simply accumulate.
This
gambler
does
best by
choosing
the third
wheel
above,
with
the
highest
arithmetic
mean
(Si.75).
After
a
year
of
wagering,
the
law
of
large
numbers
implies
that the
gambler's
actual
winnings
per
week
will
be
proportionately
close
to the
expectation.
The
gambler
will
have
about
52
times
Si.75
or
S91
at
year's
end
(representing
a
profit
of
about
S39
when
you
subtract
the
total
of
$52
he
wagered).
Had the
dollar-a-weck
gambler
chosen
the first
wheel,
he would
have
about
S78
(a
S26
profit),
and
with
the
second,
he
would
likely
have
around
S87
(S35
profit).
The
Kelly
criterion
is
meaningful
only
when
gambling
profits
are
reinvested.
Take
a
gambler
who
starts
with
a
single
dollar
and rein
vests
his
winnings
once
a
week.
(He
does
not
add
any
more
money,
nor takeany out.)
Should
this
gambler
bet on the first
wheel,
he can
expect to
increase
his wealth by a factor of
1.41
each
week.
After
52
weeks,
his
fortune
would
be
something
like
$i.4iS2 =
$67,108,864
The
Kelly
bettor
would
have
run a
single
dollar
into
millions.
Compare
this to the other
two
wheels.
A
compounding
bettor
who
bets on the
second
wheel
can
expect
aftera yearto
have
So52 =
So
Zip!
This
gambler
is
almost
certain
togeta
zero
ina
year's
worth
of
betting.
Once that
happens,
he's
broke.
The
estimate
for
the
third
wheel
is
$i.2252
=--
S37877
200


## Page 211

St.
Petersburg
Wager
None of these
figures
are
"guaranteed."
The law of larger num
bers doesn't work that
way.
A
few
more or
less
lucky
spins, and the
results
could
be
much
different.
That
said,
it is
close
to
certain
that
the first wheel will yield
vastly
more than the third, and anyone so
foolish
as to
make
parlaying
bets on the second
will
be broke.
Standard mean-variance
analysis
does not treat the compound
ing of
investments.
It is,you might
say,
a theory for
Kelly's
dollar-a-
wcck
gambler.
But as the
wealth
to be
amassed
by compounding is
so
fantastically
greater than can be
achieved
otherwise, a
practical
theoryof
investment
must
largely
be a theoryof
reinvestment.
When you try to
apply
Markowitz
theory to
compounding,
the
results can be absurd.
One
of
Ed
Thorp's
theoretical
contributions
to the
Kelly
criterion literature is a 1969 paper in
which
he demon
strated the partial
incompatibility
of
mean-variance
analysis
and the
policy
of
maximizing
the
geometric
mean.
Thorp
closes
his article
by declaring that "the
Kelly
criterion should
replace
the
Markowitz
criterionas the
guide
to
portfolio
selection."
Perhaps
no
economist
of the time
would
have
dared such a
heresy.
It seems
unlikely
a major
economic
journal would
have
pub
lished such
talk.
Thorp's article appeared in the
Review
of
the
Interna
tional
Statistical
Institute.
Probably
few economists saw it. In any event,
few economists had heard of John
Kelly.
That
was about to change.
Shannon's
Demon
I n a
way,
Claude
Shannon
was
the
efficient
market
mob's
worst
nightmare.
He
was
a smart
guy
making
money
hand over
fist
in the
201


## Page 212

FORTUNES
FORMULA
market.
He had turned his
formidable
genius
to the problem of ar
bitrage.
In the
mid-1960s,
Shannon
began
holding
regular
meetings
at
MIT
on the subject of
scientific
investing.
These were attended
byan
eclectic
assortment of
people,
including
Paul
Samuelson.
Shannon
gave
a
couple
of
talks
on
investing
at MIT,
circa
1966
and
1971.
By
then the broad MIT community had heard stories of
Shannon's stock market acumen. So many people wanted to
attend
one talk that it had to be
moved
to one of MIT's
biggest
halls.
Shannon's
main
subject
was
an
incredible
scheme
for
making
money
off the
fluctuations
in
stocks.
You
can
make
money
off
stocks
when they go up (buy
low,
sell
high).
You
can
make
money when
theygo
down
(sell
short).
You
just
have
to
know
which
way
prices
are
going to
move.
That,
suggested
Bachelier,
Kendall,
and
Fama,
is im
possible.
Shannon
described
a
way
to
make
money
off a random
walk.
He
asked
the
audience
to
consider
a
stock
whose
price
jitters up and
down
randomly,
with no
overall
upward
or downward trend. Put
half your capital into the stock and half into a
"cash"
account. Each
day,
the
price
of the
stock
changes.
At noon each
day,
you
"rebal
ance"
the
portfolio.
That
means
you
figure
out
what
the
whole
port
folio
(stock plus
cash
account)
is
presently
worth, then shift
assets
from
stock
to
cash
account
or
vice
versa
inorderto
recover
theorig
inal
50-50
proportions of stock and cash.
To make this
clear:
Imagine
youstart with $1,000, S500 in stock
and
$500
in
cash.
Suppose
the
stock
halves
in
price
the
first
day.
(It's
a
really
volatile
stock.)
This
gives
you a
S750
portfolio with $250 in
stock and $500 in cash. That is now lopsided in favor
of
cash. You
rebalance
by
withdrawing
S125
from
the
cash
account to buy
stock.
This
leaves
you with a
newly
balanced
mix
of
S375
in stock and
S375 cash.
Now
repeat.
The next
day,
let's
say
the stock
doubles
in
price.
The
S375
in stock
jumps
to
S750.
With the
$375
in the
cash
account,
you
have
Si,125.
This time you
sell
some
stock,
ending up with
S562.50
each
in
stock
and
cash.
Look
at
what
Shannon's
scheme
has
achieved
so far.
After
a
dra-
202


## Page 213

St.
Petersburg
Wager
matic
plunge,
the
stock's
price is backto where it
began.
A buy-and-
hold investor would have no profit at
all.
Shannon's investor has
made
$125.
This scheme defies most investors' instincts. Most people are
happy to
leave
their
money
in a stock that
goes
up.
Should the stock
keepgoing up, they might put more of their
free
cash into the
stock.
In Shannon's system, when a stock goes up, you sell some of it.
You
also keep pumping
money
into a stock that goes
down—"throwing
good moneyafter
bad."
Look
at the
results.
The lowerlineof the chart
shows
the price of
an
imaginary
stock that starts at Si and either
doubles
or
halves
in
price each time unit with equal
probability.
This is a geometric ran
dom walk, a popular model of stock price movements. The basic
trend here is neither up nor down. The lower line therefore repre
sents the wealth of a buy-and-hold investor who has put all her
money in the stock
(assuming
no
dividends).
Shannon's
Demon
203


## Page 214

FORTUNE
S
FORMULA
The
chart's upper line shows the valueof a
50-50
stock and cash
portfolio that is
rebalanced
each time unit. This line trends
upward.
The dollar
scale
on this chart is
logarithmic,
so the straight trend
line
actually
means
exponentially
growing
wealth.
The
rebalanced
portfolio
is also less
volatile
than the stock.
The
scale
of the jitters is
relatively
less
for the
rebalanced
portfolio
than
for the
stock
itself.
Shannon's
rebalanccr
is not
only
achieving
a su
perior return, but a superior
risk-adjusted
return.
How does Shannon's stock system
work?
Does
it work?
Shannon's
system
bears a telling
similarity
to a great puzzle of
physics.
In his
1871
book
Theory
of
Heat,
British
physicist
James
Clerk
Maxwell
semiscriouslydescribed a perpetual motion machine. The
machine could be as simple as a container of air divided into two
chambersbya partition. There is a tiny trapdoor in the partition. To
operate
the
machine,
you
need,
as
Maxwell
put it, a
"being
whose
fa
cilities
are so
sharpened
that he can
follow
every
molecule
in its
course."
"Maxwell's
demon,"
as
this
being
was
called,
uses
his
superpower
vision
and
reflexes
to sort air
molecules
by
their
speed.
When a
fast
molecule
approaches
the trapdoor
from
the
right,
the demon opens
the trapdoor and lets the
molecule
pass
into the left side. When a
slow
molecule
approaches
from
the
right,
the demonshuts the trap
door to keep it in the right
side.
After much sorting, the demon
will
have
most of the fast mole
cules
on the left side,and the slow
molecules
on the right
side.
This
is significant because temperature is the measure
of
how fast mole
cules
are
moving,
on the
average.
The demon hascreated one cham
ber of hot
gas
and
another
of
cold
gas,
all
without
expending
any
real
energy.
(Oh, the
demon
has
to
keep
opening
and shutting the
door.
Butif the dooris
very
light
and
very
rigid,
the
energy
require
ment can be as
small
asyou
like.)
A steam engine generates energy from a temperature difference.
By
hooking
up a steam
engine
to his hot and
cold
gas,
the demon
204


## Page 215

St.
Petersburg
Wager
can
therefore
produce
usable
energy
out of the
random
motions
of
molecules.
Few
physicists
imagined
that
such
a
device
was
possible.
It
was
too
well
established
that
you
cannot
conjure
up
energy
outof
thin
air.
Nor can
you
reduce
the
disorder
(entropy)
of the
universe,
which
the
demon
is
also
doing.
The
puzzle
was
deciding
why
it
was
impossible.
There is of
course
no
such
thing
as a
demon
who
can see
indi
vidual
molecules.
You
can
imagine
a
nano-scale
valve
or robot that
docs
what
the
demon
was
supposed
to
do.
Many
twentieth-century
physicists
and
scientifically
minded
philosophers
did
just
that
in
try
ingto
resolve
the
puzzle.
They
mostly
got
sidetracked
on
nuts-and-
bolts
issues
of how a tiny
mechanism
could
detect
molecules
and
open
or
close
an
atomic-scaled
door.
Because
quantum
theory
was
new
and
exciting,
most
of their
thinking
invoked
the
famous
principle
that
you
can't
observe
anything
without
changing
it.
In
order
to
see
the
molecules,
the
demon
must
shoot
photons
(parti
cles
of
light)
at
them.
The
photons
scatter
the
molecules,
making
his
observations
unreliable.
The
uncertainty
principle
defeats
the
demon—or
so it
was
argued.
Actually,
quantum
theory
is
largely
a
red
herring
here.
Physicists
Leo
Szilard,
Leon
Brillouin,
and
Denis
Gabor
attempted
to
resolve
the
problem
in terms
of
what we would now call
information.
Szi
lard,
writing
in
1929.
described
something
very
close
to the
bit,
anticipating
Shannon.
A
full
solution
was
impossible
without
the
insights
of
Shannon's
theory
It
was
supplied
in
1982
by
IBM
scien
tist
Charles
Bennett.
It is
helpful
to
reimagine
Maxwell's
situationso that the demon
has
ESP,
or a
"private
wire,"
telling
him
when
to open and shut the
trapdoor.
(He
does
not
have
to
dirty
his
hands
with
quantum
physics.)
The
simplified
demon
simply
receives
a stream of bits on
his
pager.
When
he
receives
a
"1"
he
opens
the
trapdoor;
when
he
gets
a "o" he
closes
it.
All
this
information
is
magically
correct.
The
more bits
received,
the more moleculesthe demon can sort,
and
the
more
energy
he
can
produce.
This
much
recalls
Kelly's
gam-
205


## Page 216

FORTUNES
FORMULA
bier,
who
converts
a
stream
of bits into
capital
growth.
Now
ask
yourself:
Is
Kelly's
gambler
getting
"something
for
nothing"?
Well,
yes,
if
you
look
at
his
bankroll
and
nothing
else.
No,
if
you
look
at
the
big
picture.
It
is
other
people's
money
he's
winning.
Much
the
same
applies
to
Maxwell's
demon.
Focus
just on the air
molecules,
and the demon's sorting
decreases
entropy and creates
energy
from
nothing.
Look
at
the
big
picture
and
you
will
discover
that the demon is only
redistributing
these
quantities.
Charles
Bennett
argued
that the
demon
is
necessarily
increasing
the
entropy
of
his
own
brain.
In
Maxwell's
time,
no
one
thought
about the
demon
having
a
brain.
The
very
word
"demon"
empha
sized that it
was
fiction.
Shannon's
theory presented information as
an
integral
part of the
physical
world.
Any
demon—whether
made
of
flesh
and
blood,
microchips,
or
nanovalves—needs
a
physical
"brain"
to
operate.
The
demon
does
not
need
much
of
a brain.
He
is
little
more
than
a
remote-control
garage
door
opener.
An
incoming
stream
of bits
tells him what to do and he does it. But at the very
least,
the de
mon's
brain
must
be
capable
of
existing
in one of
two
states.
There
must be one state
where
he
opens
the
trapdoor,
and another
where
he
closes
it. The demon
needs
(at
least)
one bit of
memory.
In
1961
Rolf
Landauer,
another IBM scientist, showed that eras
ing
computer
memory
always
increases
entropy.
You
can
get
the
flavor
of
his
demonstration
from this: Suppose you've got an MP3
file
of a
garage
band's
unrcleased
song.
It's
the
only
copy
in the
world.
If
you
erase
that
file,
it
will
never
be
possible
to
recover
ex
actly
that
particular
performance.
To
erase
isto
destroy
a
small
part
of
history.
Erasing
increases
uncertainty
about
the
past
state
of the
world.
Uncertainty
is entropy.
In his
mathematical
analysis.
Landauer
showed
that erasing
digi
tal
memory
must
increase
entropy
as
measured
by
physicists.
Notice
that
Maxwell's
demon will have to do a
lot
of
erasing.
Every
time a
new
bit
comes
in on
his
private
wire,
he must
"erase"
the oldbit,with
a
consequent
increase
in
entropy.
Charles
Bennett
used
Landauer's
result
to
argue
that the
entropy
increase
in the
demon's
brain
must
be at
least
as
great
asthe
entropy
decrease
in the
chamber
of
air.
206


## Page 217

St.
Petersburg
Wager
The
bottom
line
is
that
the
demon
can't
make
anet
energy
profit
after
all.
It
will
take
at
least
as
much
energy
to runhis
brain
ashecan
produce
by
sorting.
Maxwell's
demon
is
only
redistributing
entropy
and
energy.
In
1974
Paul
Samuelson
wrote
that a high-PQjradcr
"is
in
effect
possessed
ofa
'Maxwell's
Demon'
who
tells
him
how
to
make
capi
tal
gains
from
his
effective
peek
into
tomorrow's
financial
page
reports."
Like
Maxwell's
demon.
Shannon's
stock
system
turns ran
domness
into
profit.
Shannon's
"demon"
partitions
his
wealth
into
two
assets.
As the
asset
allocation
crosses
the 50
percent
line
from
either
direction,
the
demon
makes
a
trade,
securing
an
atom-sized
profit
or
making
an
atom-sized
purchase—and
it
all
adds
up in the
long run.
The
"trick"
behind
this is
simple.
The
arithmetic
mean
return is
always
higher than the
geometric
mean.
Therefore,
a
volatile
stock
with
zero
geometric
mean
return
(as
assumed
here)
must
have
a
pos
itive
arithmetic
mean
return.
Who can
make
money
off an
arithmetic
mean?
One
answer:
Kelly's
dollar-a-wcek
gambler.
One
week
he
buys
Si
worth
of
penny
stock.
If
he's
lucky
the
stock
doubles.
He
sells,
locking
in
a
dollar
profit.
(It
promptly
goes
into
his
wife's
hat
fund.)
The
next
week
he
gets
a
brand-new
dollar
and
buys
more
penny
stock.
This
time,
he's
unlucky.
The stock
loses
halfits
value.
He
sells,
havinglost 50 cents.
Mr.
Dollar-a-Wcck
has
gained
a
dollar
and lost 50 cents in this
typical
scenario.
He
has
averaged
a
25
percent
weekly
profit
while
the stock's price hasgone
nowhere.
The
problem with
Mr.
Dollar-a-Week is that he doesn't think
big.
Because
he
bets
the
same
amount
each
week,
his
expectation
of
profit remains the same.
Someone
serious
about
making
money
should
follow
the
(reg
ular)
Kelly
gambler,
who
always
maximizes
the
geometric
mean.
When the
Kelly
gambler
is
allowed
to split his
bankroll
betweenthe
cash
account
and the
random-walk
stock
in
any
proportion,
he
will
207


## Page 218

FORTUNES
FORMULA
choose a
50-50
split, for this has the highest geometric mean.
Shannon'sschemeis a
special
case
of
Kelly
gambling.
Kelly's
gambler
does
not
coin
money.
He
only
redistributes
it.
Here
the
parallel
breaks
down.
Maxwell's
demon
will
disappoint
anyone
looking
for
an
environmentally
friendly
energy
source.
The
redistributive
nature of
Kelly
gambling
rarely
bothers
people.
Race
tracks and stock markets are
full
of
people
who arc only too glad to
redistribute
money
into their own
pockets.
There
was
a
question-and-answer
period
after
Shannon's
talk.
The
very
first
question
posed
to
Shannon
was,
did
he
use
this
system
for
his
own
investments?
"Naw,"
said Shannon. "The commissionswould
kill
you."
Shannon's stock scheme
harvests
volatility,
if
you
could find a
stock that
doubles
or
halves
every
day,
you'd
be in
business.
As de
scribed
above. Si can be run
into
a million in
about
240
trades.
The
commissions would be thousands of dollars. So what?
You'd
end up
with a
million
for
every
dollar
invested
. . .
No
stock
is
anywhere
near
that
volatile.
With
realistic
volatility,
gains
would
come
much
slower
and
would
be
less
than
commissions.
There are other
problems.
The Shannon
system
postulates a
stock
whose
geometric
mean
return
is
zero.
It
plays
off a
common
frustration with
stocks,
which
all
too often seem to
"go
nowhere."
Efficient
market
theorists
say
no
stock
has
zero mean return. Who
would
buy
such
a
stock?
In the
realistic
case
of a
stock
that
tends
to
drift
upward,
the
optimal
allocation
of
assets
between
stock
and
cash
will
differ.
When the stockhasa highenough mean return, the
Kelly-optimal
trader
will
commit
all
his
assets
to the
stock.
The re
balancing is then moot.
Shannon's
system
is an
example
of what is now
known
as a
constant-proportion
rebalanced
portfolio.
It is an important idea
that
has
been
studied
by
such
economists
as
Mark
Rubinstein
and
Eugene
Fama
(who
were
apparently
unaware
of
Shannon's
un
published
work).
Rubinstein
demonstrated
that
given
certain
as
sumptions,
the
optimal
portfolio
is
always
a
constant-proportion
208


## Page 219

St.
Petersburg
Wager
rebalanced
portfolio.
This
is
one
reason
why
it
makes
sense
for
ordi
nary
investors
to
periodically
rebalance
their
holdings
in
stocks,
bonds,
and
cash.
You
get
a
slightly
higher
risk-adjusted
return
than
you
would
otherwise.
Commissions
and
capital
gains
taxes
cut
into
this
benefit,
though.
In recent years, Stanford information theorist Thomas Cover
has
built
ingeniously
on
Shannon's
idea
of
the
constant-proportion
rebalanced
portfolio.
Cover
believes
that
new
algorithms
can
render
the
concept
profitable,
even
after
trading
costs.
Shannon's
main
point in his
talk,
however,
may
have
been to refute the then-
common
belief
that the
random
walk
of
stock
prices
is an
absolute
barrier
to
making
greater-than-markct
returns.
If
this
particular
arbitrage
scheme
was
not
practical,
who
was
to
say
that
another
couldn't
succeed?
The
Feud
The
feud
between
the
Hatfields
and
McCoys
started over a
pig.
The
feud
over
the
Kelly
criterion
started
with
afootnote.
In
1959
Henry
Latane
was
a
middle-aged
nobody
justout of
grad
school.
He
permitted himselfto name-drop in a footnote.
As
pointed
outto
me
by
Professor
L.
J.
Savage
(in
correspondence)
not
only
isthe
maximization
ofG
(the
geometric
mean)
the
rule
for
maximum expected utility in connection with Bernoulli's function
but (in so
far
as
certain
approximations
are
permissible)
this
same
rule
is
approximately
valid
for
all
utility
functions.
209


## Page 220

FORTUNE'S
FORMULA
The
word
of
authorities is not supposed to matter in science.
The
reality
is
that
famous
names
sell
theories
as
well
as
athletic
shoes.
The
famous
name
gets
the
idea
timely
attention,
anyway,
and
Leonard
Savage's
opinion
counted.
"Bernoulli's
function"
refers
to a
logarithmic
utility
function.
As
reportedby
Latane,
Savage
said
that the
geometric
mean
criterionis
best
for
people
who
have
a
logarithmic
valuation
of
money,
and
it's
"approximately
valid"
for
everyone
else.
Since
you
arc
going
to end
up
richer
using
the
geometric
mean
criterion
than
with
any
other
system,
it
doesn't
matter
what
your
utility
function
is.
So
Savage
ap
peared
to
say.
There
the
matter
rested
for
ten
years.
"Our
analysis
enables
us
to
dispel
a
fallacy,"
wrote
Paul
Samuelson
in
1969.
that
has
been
borrowed
into
portfolio
theory
from
information
theory
of the
Shannon
type.
Associated
with
independent
dis
coveries
by
J.
B.
Williams,
John
Kelly,
and
H.
A.
Latane
is the
notion that if one is
investing
for
many
periods,
the proper be
havior
is to
maximize
the
geometric
mean
of return rather than
the arithmetic
mean.
I
believe
this to be incorrect. . . [T]he im
plicit
premise
is
faulty
to
begin
with
. .
."
In a footnote of his own,
Samuelson
challenged
the "somewhat
mystifying"
statement
that
Latane
credited
to
Savage:
"Professor
Savage
has
informed
me
recently
that
his
1969
position
differs
from
the
view
attributed
to
him
in 1959."
This
discussion
appears
toward
the end of
Samuelson's
"Lifetime
Portfolio
Selection
by
Dynamic
Stochastic
Programming."
This
widely
cited
article
must
have
been
read
by
vastly
more
people
than
those who read
Williams's,
Kelly's,
and
Latane's
papers put
together.
Samuelson
wrote that the line of
reasoning
in his article
"provides
an
effective
counter
example"
to the
Kelly
criterion,
"if
indeed
a
counter
example
is
needed
to
refute
a
gratuitous
assertion."
That
snarky
note started the
catfight.
Is the
Kelly
formula
the
210


## Page 221

St.
Petersburg
Wager
scientific
key
to
riches—or
is
it
an
urban
legend
in
need
of de
bunking?
The
two
sides
of the
debate
were
unequally
matched.
Samuel
son's stature was unparalleled. He was a fierce debater, famous for
feuds
bigger
than
the
one
over
"information
theory
of
the
Shannon
type."
Arguing
alongside
Samuelson
were
people
in his MIT
circle,
most
notably
Robert C.
Merton.
The
opposition
of these thinkers
to the
Kelly
criterion
deserved
to
be
taken
seriously
and
was—by
academia
and by
Wall
Street
professionals.
Claude
Shannon
was
not
party
to
the
debate.
By
1969
the
infor
mal
MIT
meetings
on
finance
had
ended
and
Shannon
no
longer
saw
Samuelson
regularly.
It
appears
that
Shannon
remained
un
aware of Samuelson's 1969 comments until
1985.
when Thomas
Cover happened to mention them. Shannon was shocked. He said
he
and
Samuelson
were
friends,
and
they
agreed
on
many
points.
He
did not
recall
Samuelson
disputing
Kelly's
idea.
The
pro-geometric
mean
side
of the
controversy
included
econ
omists
Latane
and
Nils
Hakansson
and
a
handful
of
mathemati
cians,
statisticians,
and
information
theorists.
Economists
do
not
generally
pay
much
attention
to
non-economists.
One
major
eco
nomic
name,
Mark
Rubinstein,
wrote
a UC
Berkeley
working
paper
grandly
titled
"The
Strong
Case
for
the
Generalized
Logarithmic
Utility
Model
as
the
Premier
Model
of
Financial
Markets"
(1975).
But
Rubinstein
later
recanted
this
position.
Except
for
Harry
Markowitz,
none of the
pro-Kelly
people
had
remotely
the
influ
ence
of
Samuelson.
Samuelson's
favored
word
for
describing
the
Kelly
criterion
was
"fallacy."
From
that,
you
might
think
he
had
spotted
a
subtle
though
fatal
error in the
reasoning.
Not
exactly.
In a
1971
article,
Samuelson
conceded
as
valid
this
Theorem.
Acting
to
maximize
the
geometric
mean
at
every
step
will,
if the
period
is
"sufficiently
long,"
"almost
certainly"
result
211


## Page 222

FORTUNES
FORMULA
in
higher
terminal
wealth
and
terminal
utility
than
from
any
other decision rule. . . . From this indisputable fact it is appar
ently
tempting
to
believe
in
the
truth
of
the
following
false
corollary:
False
Corollary.
If
maximizing
the
geometric
mean
almost
certainly
leads
to a better
outcome,
then the
expected
value
utility of its
outcomes
exceeds
that of
any
other
rule
[in the long
run].
I
have
a
hunch
many
readers'
eyes
are
glazing
over.
Try
this:
The
"false
corollary"
is
in
the
spirit
of the
bumper
sticker
WHOEVER
DIES
WITH
THE
MOST TOTS
WINS.
It is the
credo
that
be
cause
you
endup
richer
with
the
Kelly
criterion
than
with
any
other
money
management
system,
the
Kelly
system
is
the
rational
course
for
anyone
who
wants
to be
rich.
Samuelson
correctly
sensed
that the error of the
false
corollary
(maybe
the
bumper
sticker,
too)
is
far
from
obvious
to
most
average
folks.
In
particular,
people
who
manage
money
for
a
living
arc
likely
to be
mystified
at
why
anyone
would
even
question
the
merit
of
achieving
the
highest
compound
return.
As
B.
F.
Hunt
wrote
more
recently
(2000) of
Samuelson's
position,
"The
Kelly
view,
that
maximizing
investment
growth
of
value
is a
self-evident
superior
strategy,
probably
resonates
more
with
the
investment
sector."
Add to that the fact that the
Kelly
system
avoids
ruin,
and it
might
seem
to the
wide
world
that
with
a
simple
formula,
one
achieves
financial
nirvana.
This
conclusion
Samuelson
disputed. His
subtle
point
is
that
Kelly's
gambler
is
making
trade-offs
in order to
achieve
that pot of
gold
at the end of the
rainbow.
Not
everyone
would choose to make those trade-offs if they truly understood
them.
The
Kelly
criterion
is
greedy.
It
perpetually
takes
risks
in order to
achieve
ever-higher
peaks
of
wealth.
This
results
in that
sexy
fea
ture,
maximum
rate of return. But
capital
growth isn't
everything.
To
performance
car
nuts,
O-to-60
acceleration
time
may
be the
only
number
that
matters.
If
that
were
the
only
criterion
for
prefer
ring
onecarto
another,
we'd
all
be
driving
Lamborghinis.
In the
real
212


## Page 223

St.
Petersburg
Wager
world,
other
things
matter.
Most
people
grow
up
and
buy
sensible
Toyotas.
The
Kelly
system
may
also
be
too
conservative
for
some
people.
It
makes
a
shibboleth
of
long-term
performance
and
zero
risk
of
ruin.
These
go
together.
The
Kelly
gambler
shuns
the
tiniest
risk
of
losing
every
thing,
for
unlikely
contingencies
must
come
to
pass
in
the
long
run.
The
Kelly
criterion
has,
in
Nils
Hakansson's
words,
an
"automati
cally
built in . . .
air-tight
survival
motive."
That
attractive
feature
too
comes
at a
cost.
In the short
term,
the
Kelly
system
settles
for
a
lower
return
than
would
be
possible
by
re
laxing
this
requirement.
A
true
gambler
who
lives
in
the
moment—
who
cares
nothing
about
risk
or
the
long
term—might
well
choose
to
maximize
simple
(arithmetic)
expectation.
This
gambler
can
ex
pect
to
achieve
a
higher-than-Kelly
return,
albeit
with
risk,
on a
sin
gle spin of fortune's
wheel.
Another
automotive
analogy
(due
to
money
manager
Jarrod
Wilcox)
is
in
the
way
we
deny
the
risks
of
driving
a
car.
You
might
say
that
driving
is
a
favorable
"wager."
You
bet
your
very
life
that
you
won't
get
killed
in
a
traffic
accident
in
order
to
get
where
you
want
to go with more comfort and convenience than with
other
means
of
transportation.
The
death
toll
on
American
streets
and
highways
corresponds
to
one
fatal
auto
accident
per
6,000
years
of
driving.
A
Kelly-like
philosophy
would
find
that
unacceptable.
You
would
have
to
forgo
the
benefits
of
driving
because
driving
is
in
compatible
with
living
forever.
Hardly
anyone
thinks
this
way.
As
Keynes
said,
in
the
long
run
we
arc
all
dead.
We
are
willing
to
take
risks
that are
unlikely
to hurt
us
in our
lifetime.
In
short,
the
Kelly
criterion
may
risk
money
you
need
for
gains
you
may
find
superfluous;
it
may
sacrifice
welcome
gains
for
a
degree
of
security
you
find
unnecessary.
It
is
not
a
good
fit
with
people's
feelings
about
the
extremes
of
gain
and
loss.
The
promises
of the
Kelly
criterion
recall
those
tales
of
mischie
vous
genies
granting
wishes
that
never
turn out as
planned.
Before
you
wish
for
maximum
long-term
return
and
zero
risk
of
ruin,
Samuelson
is
saying,
you
had
better
make
sure
that
is
exactly
what
you
want—because
you
may
get it.
213


## Page 224

FORTUNE'S
formula
*
Pinball
Machine
In
the
1970s,
Samuelson
and
Merton
filled
dozens
of
journal
pages
with
equations
showing
what
they
found
to
be
wrongheaded
about
the
policy
of
maximizing
the
geometric
mean.
Their
rigor
and
erudition went over the
heads
of
many
of the
portfolio
managers,
financial
analysts,
and
investors
they
feared
would
be
suckered
by
the
Kelly
"fallacy."
The
gist
of
Samuelson
and
Merton's
argument
is
not
hard
to
un
derstand.
I
will
attempt
to
present
it
here
with
a
picture:
Kelly
Criterion
as
Pinball
Machine
SIOO
$324 $1,620 $8,100
214


## Page 225

St.
Petersburg
Wager
This
shows
the
Kelly
criterion
as a
pinball
machine.
The
dollar
amounts
here
pertain
to a
highly
favorable
wager
in
which
you
bet
on
the
toss
of a
fair
coin.
Heads,
you
get
six
times
your
wager
back.
Tails,
you
lose.
The
bettor's
edge
is
a
whopping
200
percent.
(For
every
dollar
you
bet,
you
stand
a
50
percent
shotat
getting
S6.
That
is
worth
$3.
The
average
gain
is
S2
on
Si
staked,
or 200
percent
of
the
original
wager.)
The
payoff
odds
of
this
wager
are 5 to
1.
That
means
that
the
Kelly
wager,
edge/odds,
is
Vj,
or40
percent
of
your
bankroll.
What
happens
once
you
start
betting?
The
diagram
shows
every
possible
scenario,
up
through
the
first
four
tosses.
You
start
at
the
top
with
a
Sioo
bankroll.
You
plunk
down
40
percent
of
that—the
Kelly
wager—and
toss
the
coin.
Two
diagonal
lines
lead
downward
from
the
Sioo.
They
show
the
two
possible
outcomes
of
the
first
toss.
Either
you
lose
your
S40
wager
(and
are
left
with
S60)
or
you
win,
getting
back
six
times
as
much
(with
the
S60
not
wagered,
this
gives
you
S300
total).
On the next
toss,
you
must
adjust
your
wager
so that it
remains
40
percent
of
the
current
bankroll. Each
of
the two
outcomes
of
the
first
toss
leads
to
two
others.
Notice
that
paths
diverge
and
con
verge.
There
are
two
different
ways
of
arriving
at Si80 on the
second
toss.
The
ever-expanding
web
of
possibilities
is
like
that
interpreta
tion of
quantum
theory
where
every
chance
event
splits
the
world
into
parallel
universes.
By
the
fourth
toss,
there
are
16
distinct
par
allel
universes,
corresponding
to
every
possible
sequence
of
heads
and
tails.
The
diagram
shows
this
as
a
pachinko
machine.
Each
ball
represents
a
possible
outcome
of
one
of
the
16
possible
zigzag
courses from top to bottom.
The pockets at the bottom show the terminal wealth after four
tosses.
The
rightmost
ball
represents
the
luckiest
case
where
you
win
all
four
tosses.
That
leaves
you
with
S8,iOO.
That
is
good
luck.
In
general
you
expect
to geta
mixture
of
heads
and
tails.
The
dotted
zigzag
line
represents
a
case
in
which
you
get
a
tail, a head, a tail, and a tail.
This
ball is
about
to fall
into
a slot
with
215


## Page 226

fortune's
formula
three others, for there are four distinct histories that lead to this
outcome,
worth
S64.80.
There
are
also
four
parallel
universes
that got
three
heads
and
one
tail.
That
produces
a
wealth
of
Si,620.
There
are
six
different
ways
of
having
two
heads
and
two
tails.
This is
"average
luck"
and is the
most
common
outcome.
It runs
Sioo
into
S324
in just four
wagers.
The
worst
outcome
is to lose all four tosses.
That
leads to a de
pleted
bankroll
of justSi
2.96.
Most
people
find
something
unsettling
about
these
outcomes.
There is
such
a
huge
difference
between
best-
and
worst-case
sce
narios.
In 5 of the
16
outcomes,
you
end up with
less
than what you
started
with. This is after four incredibly
favorable
wagers.
In 1of the
16
outcomes,
you
have
a
lot
less
than
what
you
started
with.
The
Kelly
guarantee
of
avoiding
ruin
is
somewhat
hollow.
Okay,
you
won't
lose
everything.
You
still
stand
a
\U
chance
of
losing
87
percent
of
your
bankroll
in
just
four
unlucky
wagers.
The
Kelly
system
leads
to a
distribution
of
wealth
(among
sce
narios
or
parallel
universes)
like
that of
Manhattan.
There
are
ex
tremes
of
wealth
and
poverty,
and the
middle
class
is
smaller
than
you might think.
Maybe
it's
time
to
review
what
the
genie
promised.
Of the
16
possible
outcomes,
the
geometric
mean
is
$324.
No
other
money
management
system
has
a
higher
geometric
mean
than
the
Kelly
system
does.
That's
good.
Another
good
feature
of
the
Kelly
criterion
is
that
it
maximizes
the
median
wealth.
The
median is the
statistical
measure
you
get
by
making
an
ordered
list
of
values,
from
least
to
most,
and
picking
the
value
in
the
exact
middle
ofthe
list.
Medians
are
popu
lar
with
real
estate
agents,
andare
indispensable
in
places
like
Man
hattan, where there is a wide rangeof
prices.
Here the median
wealth
is
also
S324,
and this is higher than the
median
wealth
with
any
other
essentially
different
system.
What the
Kelly
system
cannot
do
is
engineer
luck.
It is
possible
to
216


## Page 227

St.
Petersburg
Wager
be
unlucky
when
using
the
Kelly
system,
to
end
up
with
less
than
the
median.
When
you
do.
you
may
be
worse
off
than
you
would
have
been with another
system.
The
Greek
letter
epsilon
stands
for
an
arbitrarily
small
quantity
(an
"iota,"
as
nonmathematicians
might
say).
Samuelson
closes
one
article
with
the
comment,
"As
Gertrude
Stein
never
said:
Epsilon
ain't
zero."
In
other
words,
the
Kelly
people
err
by
supposing
that
small
(epsilon)
risks
of
losing
a
lot
of
money
can
be
shrugged
off
as
no
risk
at
all.
Jump
out
ofa
plane
with
a
good
parachute,
and
you
are
almost
certain
to
land
safe
and
sound.
Why
doesn't
everybody
take
up
the
exciting
sport
of
skydiving?
The
answer
is
that
people
have
different
tolerances
for
risk.
A
small
chance
of
catastrophe
may
loom
large—it
ain't
zero.
Fraidy-cat
Alice
may
rationally
refuse
to
skydive
even
though
she
knows
that
the
chance
of
anything
going
wrong is
"practically
zero."
It is that
small
chance
of
catastrophic
luck
that
makes
the
false
corollary
false.
There
are
less
aggressive
money
management
schemes
that
handle
runs
of
bad
luck
better
than
the
Kelly
criterion
does.
Of
course,
they
have
a
lower
average
compound
return.
In order to
keep
the
diagram
to a
reasonable
size,
I
charted
the
results
of
just
four
wagers.
Do
things
get
better
in
the
long
run?
Yes
and
no.
The
median
outcome
grows
exponentially
with
time.
That
is
good.
There
are
many
money
management
systems
that
lead
to ruin or virtual ruin for all
but
the luckiest
scenarios.
There
are
other
systems
that
avoid
ruin
but
achieve
ever-poorer
returns
rela
tive
to
Kelly.
The
virtues
of
the
Kelly
system
over
any
and
all
rivals
become
all
the moreapparentwith
time.
In
another
sense,
things
don't
get
better
in
the
long
run.
As
time
goes
on,
the
disparities
of
wealth
and
poverty
among
scenarios
only
grow
wider.
The
richest
get
richer—the
poorest
get
poorer.
217


## Page 228

fortune's
formula
*
It's
a
Free
Country
Like a
long-simmering
family
dispute,
the
Kelly
criterion
feud often
sidetracked
onto what each side thought the other in
sinuated.
Nils
Hakansson's
1971
article
("Capital
Growth
and the
Mean-Variance
Approach
to
Portfolio
Selection")
recast
Kelly's
and
Latane's ideas within the framework of utility theory and mean-
variance
analysis.
He
was
speaking
the
language
practically
all
econ
omists
spoke.
The article contained a
mistake
in the math. In a responding
article,
Merton
and
Samuelson
jumped
all
over
the
error,
rightly
enough.
Concluded
the
MIT
authors:
"Again
the
geometric
mean
strategy
proves
to be
fallacious."
Except
that
it
wasn't
actually
the
geometric
mean
strategy
they
had
refuted.
It was an
error
in an
article
about
it.
Jimmie
Savage
died
in
1971.
His
death
did
not
end
the
squab
bling
over
what
he
said
or
didn't
say
in
that
footnote.
"Given
the
qualifications,"
wrote
Latane
in
1978,
it
was
"very
difficult
to
refute"
Savage's
original
statement,
no
matter
what
he
might
have
said
to
Samuelson
later.
Samuelson
fired
back
that
Latane
should
"spare
the
dead"
and
"free
[Savage's]
shade
of
all
guilt"—the
guilt
of
having
once
en
dorsed the
geometric
mean criterion.
"It
is
surprising
to
note,"
wrote
Hebrew
University's
Tsvi
Ophir
(1978),
"how
some
erroneous
propositions
may
persist
long
after
they
have
been
thoroughly
disproven.
Such
is
the
case
with
regard
to
the
geometric
mean
rule
for
long-run
portfolio
selection—and
this
218


## Page 229

St.
Petersburg
Wager
despite
the
fact
that no
less
an
authority
than
Paul
Samuelson
had
debunked
it."
"As
far
as
I
know,"
countered
Latane
(1978),
by
then
an
elderly
economist at the
University
of North Carolina,
neither
Samuelson
nor
Merton
nor
indeed
Ophir
has
challenged
the
basic
principle
imbedded
in
the
geometric
mean
principle
for
long-run
portfolio
selection.
If
they
or
he
wishes
to
adopt
a
significantly
different
policy
and
I
follow
the
G
policy,
in
the
long
run
I
become
almost
certain
to
have
more
wealth
than
they.
This
hardly
seems
an
erroneous
or
trivial
proposition.
Did
anyone
actually
believe
the
"false
corollary"?
Well,
no
one
was
going
around
saying
they
thought
the
false
corollary
was
true.
("We
heartily
agree
that
the
corollary
is
false,"
Thorp
wrote
in
a
1971
response
to
Samuelson.)
What
some
of the
pro-Kelly
people
were
saying
is that
utility
can
be
irrelevant.
John
Kelly,
for
instance,
wrote
that
his
racetrack
gambler's
system
"has
nothing
to
do
with
the
value
function
which
he
attached
to
his
money."
"My
position
as to the
usefulness
of G in no
sense
depends
on
utility,"
said
Henry
Latane.
"I
have
never
considered
G a
utility
measure."
"We
are
not
interested
in
utility
theory
in
this
paper,"
wrote
Stanford's
Robert
Bell and
Thomas
Cover. "We wish to em
phasize
the
objective
aspects
of
portfolio
selection."
There
were
two
prongs
to
this
post-utility
argument.
One
was
the
positivist
position
that
utility
is
an
unnecessary
concept
that
ought
to
be
discarded
(the
economists'
phlogiston).
Forget
utility.
Think
of
something
you
can
see
and
touch,
like
dollars,
euros,
yen,
casino
chips,
or
matchsticks.
The
growth
of
dollars,
euros,
etc.,
under
various
money
management
schemes
may
be
compared
ob
jectively,
like
the
growth
of
bacteria
in
petri
dishes.
The
dollars
subjected
to the
Kelly
system
survive
and
grow
faster
than
those
subjected
to
any
other
system.
The
experiment
can
be
repeated
as
many
times
as it
takes
to
convince
the
skeptic.
Then
ask:
Which
sys
tem
would
you prefer foryour
money?
Henry
Latane's
years
on
Wall
Street
gave
him
a
more
pragmatic
219


## Page 230

fortune's
formula
approach
than
many
other
economists.
He
apparently
felt
that out
side
of the
ivory
tower,
no one
cares
about
utility
functions.
Return
on
investment
is
the
portfolio
manager's
scorecard.
Investors
flock
toa
manager,
or
abandon
him
or
her,
because
of
that
number.
Is
that
not itselfa
reason
for
being
interested
in the
system
that
maximizes
compound return?
Latane
pointed
out that"it
is
difficult
to
identify
the
underlying
utilities
and to
tell
exactly
when
the
utilities
are
being
maximized"
in the caseof a mutual fund or
pension
fund.
The fund manager is
cooking
for
an
army.
It's
impractical
to
gauge
eveiyone's
taste
for
salt—or
risk.
Thorp
was
managing
money
not
only
for
wealthy
individuals
but
for
corporate
pensions
and
Harvard
University's
endowment.
For
most of these
investors,
Princeton-Newport
was
just one of
many
investments.
The
investors
could
do
their
own asset
allocation.
It
was
Thorp's
job
to
provide
an
attractive
financial
product.
Un
doubtedly,
investors
judged
the
fund
largely
by
its
risk-adjusted
return.
In
articles
published
in
1972
and
1976,
Harry
Markowitz
made
this
point
most
forcefully.
The
utility
function
of a
long-term
in
vestor
should
be
denominated
in
compound
return,
not
terminal
wealth,
Markowitz
suggested.
Imagine
you're
choosing
between
two
mutual
funds.
As
a
long-term
investor,
you
probably
have
no
clear
idea
of
how
long
you'll
stay
invested
or
what
you'll
do
with
future
gains.
You
would
surely
pick
the
fund
that
you
believe
to
have
the
higher
compound
return
rate.
There
is
not
much
point
in
figuring
that
you'll
have
X
dollars
in
so
many
years
with
one
fund
and
Y
dol
lars with the other. There is even
less
point in
deciding
what
you'd
buy
with
that
money
and
how
much
you
prefer
X
dollars
to Y
dol
lars.
Compound
return
is
the
only
reasonable
criterion
for
prefer
ring
one
long-term
investment
to
another.
"What about the
argument,"
asked
Merton
and
Samuelson
(i974).
"that
expected
average
compound
return
deserves
analysis
because
such
analysis
may
be
relevant
to those
decision
makers
. . .
who
just
happen
to
be
interested
in
average-compound-return?
Af
ter some
reflection,
we think an appropriate reaction would go as
220


## Page 231

St.
Petersburg
Wager
follows:
It's
a
free
country.
Anybody
can
set
up
whatever
criteria
he
wishes.
However,
the
analyst
who
understands
the
implications
of
various
criteria
has
the
useful
duty
to
help
people
clarify
goals
they
will,
on
reflection,
really
want
...
In
our
experience,
once
under
standing of the
issues
is
realized,
few
decision
makers
retain their
interest in averagecompound return."
It's
a
duty
to
talk
people
out
of
caring
about
average
compound
return?
Comments
like
that
mystified
the
pro-Kelly
people
almost
as
much
as
Merton
and
Samuelson's
claim
that
they
succeeded
in
do
ing
so.
Thorp
reported
that
when
he
explained
the
Kelly
criterion
to
investors,
"most
people
I
talk
to
say
'Yeah,
sounds
great
to
me,
I
want
that.'
"
Thorp
was
in a better
position
to cite
"real
world"
results
than
anyone.
His
article
"Portfolio
Choice
and
the
Kelly
Criterion"
lists
the
performance
record
of
"a
private
institutional
investor
thatde
cided
to
commit
all
its
resources
to
convertible
hedging
and
to
use
the
Kelly
criterion
to
allocate
its
assets."
This
investor.
Thorp
now
confirms,
was
his
fund
Convertible
Hedge
Associates.
From
No
vember
1969
through
December
1973,
the
fund's
cumulative
gain
was
102.9
percent,
versus
a
loss
(-0.5
percent)
for the
Dow
Jones
average
in
the
same
period.
"Proponents
of
efficient
market
theory,
please
explain,"
Thorp
wrote.
"We
consider
almost
surely
having
more
wealth
than
if
an
'essentially
different'
strategy
were
followed
as
the
desirable
objective
for
most
institutional
portfolio
managers."
221


## Page 232

fortune's
formula
*
Keeping
Up
with
the
Kellys
AT THE
END
of the cul-de-sac stand two near-identical houses.
Inside are two near-identical
families
with near-identical
incomes.
The
Joneses
are
obsessed
with
material
things.
They
have
a
list
of
ambitious
goals,
like
putting
in
a
new
swimming
pool
by
next
sum
mer,
buying
a
big
SUV
when
their
current
lease
runs
out,
and
send
ing
their
four-year-old
to
Harvard.
The
Joneses
have
figured
out
precisely
what
their
goals
will
cost
and
precisely
when
they
will
need
the
money
They
use
these
goals
to
design
the
best
investment
plan
for
themselves.
Under
this
plan
they
have
the
best
chance
of
having
the
money
they'll
need
when
they
need
it.
Their
neighbors,
the
Kellys,
pay
no
attention
to
financial
goals.
They
invest
to
make
money,
specifically
to
achieve
the
highest
pos
sible
compound
return
on
their
investments.
At
cocktail
parties,
neighbors
know
better
than
to
get
the
Kellys
started
on
compound
return. It's all they care about!
As
time
goes
on
(we
may
have
to
wait
a
very
long
time)
it
is
all
but
certain
that the
Kellys
will
be
richer
than the
Joneses.
As
the
years
pass,
the
wealth
gap
between
the
Kellys
and
the
Joneses
will
grow
wider
and
wider.
The
Joneses
can't
help
feeling
a
twinge
of
envy
as
they
gaze
across
the
picket
fence.
They
do,
after
all,
prefer
having
more
money
than
less.
The
Joneses
have
reason
to be
philosophical
about the
growing
disparity
of
wealth,
however.
"The
Kellys
have
money,"
the
Joneses
tell
themselves;
"we
have
something
more
important."
What
222


## Page 233

St.
Petersburg
Wager
the
Joneses
have
is
utility.
They
have
tailored
their
investments
to
meet the
goals
that
really
matter to
them.
The
Kellys
think
the
Joneses
are
crazy.
Who
can
see
this
"utility"
the
Joneses
talk
about?
Goals
can
be
flexible,
the
Kellys
say.
The
im
portant
thing
is
to
make
as
much
money
as
possible,
as
quickly
as
possible—and
then
to
worry
about
how
you'll
spend
it.
Who
is
acting
more
reasonably:
the
utility-obsessed
Joneses
or
the
compound-return-crazy
Kellys?
The
Joneses
have
a
clear-cut
utility
function
based
on
wealth.
Never
do
they
wonder
whether
money
will
bring
happiness.
They
know
exactly
how
much
happiness
X
dollars
will
bring.
They
opti
mize
their
portfolio
to
match
these
preferences.
That
is
the
hall
markof
rationality
as most
economists
see it.
There
is
no
mystery
why
the
Kellys
end
up
richer.
Their
portfolio
is
optimized
for
capital
growth.
No
other,
more
personal
constraints
are
allowed
to
slow
the
Kellys'
wealth-building.
The
only
thing
that's
perhaps
unexpected
is
the
Joneses'
envy
of
the
Kellys.
Even
by
the
Joneses'
own
standards,
the
Kellys'
greater
wealth
is
preferable
to
their
own.
This is the nubof the
Kelly
criterion
debate.
To
an
economist,
it
is
as
natural
as
breathing
to
assume
that
people
have
mathematically
precise
utility
functions
(of
wealth).
They
assume
this
without
a
moment's
hesitation
because
they
need
a
utility
function
to do
math. Due in no
small
part to
Samuelson,
math iswhat
economics
is
all
about.
The
reality
is that
people's
feelings
about
wealth
are often
fluid,
inconsistent,
and hard to
identify
withany neat
mathematical
func
tion
(including
logarithmic
ones).
Preferences
are
often
generated
on
demand.
You
do
not
know
what
you
want
until
you
go
to a
cer
tain
amount
of
trouble
to
find
out.
This
is
hardly
news
to
the
orga
nizers
of
opinion
polls
and
focus
groups.
People
have
deep-seated
opinions
on
some
issues
only.
With
other
issues,
you
have
to
press
them
to
decide—and
a lot
depends
on
how
exactly
you
phrase
the
question.
About
the
only
rock-solid
preference
most
people
have
about
223


## Page 234

FORTUNE
S
FORMULA
money
is
that
they
want
as
much
ofit
as
possible,
as
fast
as
possible.
Ask an
investor
how much risk he's
comfortable
with, and the an
swer
is
often
along
the
lines,
"Gee,
I
dunno
. . .
How
much
risk
should
I be
comfortable
with?"
This does not mean that the
investor
is a dope. It
means
the in
vestor
has
an
open
mind.
He
is
above
all
interested
in
convincing
himself
that
he
is
taking
a
reasonable
position
on
risk
and
return.
The
suggestion
that
utility
might
not
be
a
concept
of
great
prac
tical value is one that most economists resist.
Hebrew
University's
Tsvi
Ophir
ended
one
article
with
the
telling
riposte
that"a
person
accepting
Latane's
[line
of
reasoning]
has
to
forgo
not
only
expected
utility
but
the
concept
of
utility
itself."
Ophir
evidently
felt
that
was
a little
like
forgoing
sanity
itself.
Behavioral
finance
studies
suggest
that
people
are
motivated
not
only
by
absolute
gains
and
losses
but
by
envy.
We
compare
our in
vestment
returns
to our
neighbors'
and
to
market
indexes.
A
"good"
return is one that
compares
favorably.
Of
all
money
manage
ment
strategies,
only
Kelly's
has
the
virtue
of
being
unbeatable
in
the long run.
There
is a catch. Life is short, arid the stock market is a slow
game.
In
blackjack,
it's
double
or
nothing
every
forty
seconds.
In
the
stock
market,
it
generally
takes
years
to
double
your
money—or
to
lose
practically
everything.
No
buy-and-hold
stock
investor
lives
long
enough
to
have
a
high
degree
of
confidence
that
the
Kelly
sys
tem
will
pull
ahead
of
all
others.
That
is
why
the
Kelly
system
has
more relevance to an
in-and-out
trader than a
typical
small
investor.
Economists
are not
primarily
in the
business
of
studying
gam
bling
systems.
Nor
did
the
exotic
doings
of
arbitrageurs
attract
much attention from the theorists of
Samuelson's
generation. The
main
issue
of
academic
interest on
which
the
Kelly
system
appeared
to
have
something
new
to
say
was
the
asset
allocation
problem
of
the
typical
investor.
How
much
of
your
money
should
you
put in
risky
high-return
stocks,
and
how
much
in
low-risk,
low-return
investments
like
bonds
or savings accounts?
The
Kelly
answer
is
to put
all
of
your
money
in
stocks.
In
fact,
several
authors
have
concluded
that the index fund investor is
224


## Page 235

St.
Petersburg
Wager
justified
in
using
a
modest
degree
of
leverage.
(Though
the
stock
market
is
subject
to
crashes,
and
though
many
an
individual
stock
has become worthless, none
of
the
U.S.
stock indexes has ever
hit
zero.)
Economists'
reaction
to
this
sort of
talk
is:
Get
real.
Buy-and-
hold
stock
investing
is
a
case
where
utility
matters.
Few
investors
are
comfortable
with
an
all-equity
portfolio
(much
less
with
buying
on
margin).
A
not-so-unlikely
market
crash
could
cut
life
savings
dras
tically,
and
even
middle-aged
people
might
never
recover
the
lost
ground.
The
"long
run"
is not as
important
to
stock
investors
asthe
short
and
medium
runs.
The
Kelly
system
may
avoid
utter
ruin,
but
that
is
an
inadequate
guarantee
of
safety.
Though
Years
to
Act
Are
Long
For
pure
STRANGENESS,
the
Kelly
debate
peaked
in
1979.
No
bel
laureate
Samuelson
rephrased
his
objections
to
the
geometric
mean
strategy
with
Dr.
Seuss
simplicity.
He
wrote
a
journal
article
using
words
of one
syllable
only.
"Why
We
Should
Not
Make
Mean
Log
of
Wealth
Big
Though
Years
to
Act
Are
Long"
was
published
in
the
normally
polysyllabic
Journal
of
Banking
and
Finance.
"What
I
think
he
was
trying
to
say,"
Thorp
theorizes,
"is:
'You
people
are
so
dumb,
I'm
going
to
have
to
explain
this
in
words
of
one syllable.' "
Samuelson's
gimmick
prevented
him
from
using
the
words
"geo
metric," "logarithmic," or
"maximize."
He could not mention Ber
noulli,
Kelly,
Shannon,
Latane—or
even Gertrude Stein.
225


## Page 236

FORTUNE
S
FORMULA
Why
then
do
some
still
think
they
should
want
to
make
mean
log
of
wealth
big?
They
nod.
They
feel
'That
way
I
must
end
up
with
more.
Moresure beats
less.'
But theyerr. What they do not
seeis
this:
When
you
lose—and
you
sure
can
lose—with
N
large,
youcan
lose
real
big.
Q_E.
D.
Samuelson
deftly
concludes,
No
need
to
say
more.
I've
made
my
point.
And,
save
for
the
last
word,
have
done so in proseof but one
syllable.
Throughout
the
debate,
each
side
indulged
in
speculation
as
to
what defects of character or intellect caused their opponents to per
sist
in
their
grievous
error.
Samuelson
has
remarked
that
the
people
most
impressed
with
the
Kelly
criterion
tend
to
be
the
people
least
schooled in economics.There is much truth to that. They are largely
information
theorists,
gamblers,
mathematicians,
portfolio
man
agers—not
dummies,
but
neither
are
they
people
with
a
Ph.D-level
acquaintance
with the
economic
literature.
At
least
partly
as
a
result
of
Samuelson
and
Merton's
influence,
the
reputation
of
the
Kelly
criterion
among
economists
today
is
scarcely
better
than
that of
painter
Thomas
Kinkade
among
art
critics.
It
only
appeals
to
those
who justdon't
"get
it."
The other side has done its own
psychoanalyzing.
I've heard a
profusion
of
theories
about
how
and
why
Samuelson
became
so
dead
set
against
the
geometric
mean.
One
was
that the
attention
that
Samuelson's
friend Claude Shannon got with his stock market
lecture
put the
Kelly
criterion
on
Samuelson's
agenda.
(If
Jennifer
Lopez
got
a lotof
attention
announcing
a
solution
to
global
warm
ing,
earth
scientists
would
doubtless
take
zest
in
pointing
out
such
flaws
asthey
honestly
found
in
J.Lo's
scheme.)
Another
explanation
is "not
invented
here."
The
Kelly
criterion
is the work of
informa
tion
theorists
(and
an
eighteenth-century
physicist),
not an
econo
mist, and for that reason economists
reflexively
defended their turf.
John
Maddux,
longtime
editor of
Nature,
proposed
a
facetious
law
that
might
in
some
measure
apply
to
either
side
ofthe
Kelly
dis-
226


## Page 237

St.
Petersburg
Wager
pute:
"Reviewers
who are best
placed
to
understand
an author's
work are the least
likely
to draw attention to its
achievements,
but
are
prolific
sources
of
minor
criticism,
especially
the
identification
of
typos."
All
Gambles
Are
Alike
Where
the
two
sides
AGREE
is that the
Kelly
system
poses
some
challenges
to any
investor
hoping
to
harness
its
maximal
return.
This isanotherpointthat
can
be
made
visually.
Consider
the charton the
next
page
a
snapshot
of the
Kelly
cri
terion.
It isa chartof a
Kelly
bettor's
(trader's)
wealth
for a
sequen
tial
series
of
wagers
on a
single
betting
opportunity.
The
horizontal
scaleis time (or bets), and the
vertical
scale
is
wealth.
I haveleft out
the
units.
You
can
think
of
this
chart
as
being
printed
on
rubber
so
that
you
can
stretch
the
time
and
wealth
axes
as
you
like.
You
might
ask
what
game
or
investment
is
being
charted.
It
doesn't
matter
much.
Kelly
betting
is
a
way
of
making
all
gambles
and
investments
interchangeable.
Given
any
gambling
or
investment
opportunity,
the
Kelly
wager
converts
it into a
capital-growth-
optimal
gamble/investment.
When
the
wager
is too
risky,
the
Kelly
bettor stakes only a fraction of the
bankroll
in order to subdue the
risk.
When
an
investment
or
trade
carries
no
possibility
of a to
tal
loss,
the
Kelly
bettor
may
use
leverage
to
achieve
the
maximal
return.
Assuming
that the
Kelly
bettor is
able
to
wager
as muchas justi
fied
(using
leverage
when
applicable)
but is not permitted to
diver-
227


## Page 238

FORTUNE
S
FORMULA
Snapshot
of
the
Kelly
Criterion
Thechance of losing hart
your wealth is 50 percent
sify
by
placing
simultaneous
bets,
thenthe
wealth
path
will
look
ap
proximately
like
this
chart
in
any
game
of
chance
or
investment.
I
am
speaking
not of the
exact
configuration
of
peaks
and
valleys—
these,
of
course,
are
determined
by
random
events—but
rather the
scale
of
these
jitters
relative
to
the
general
exponential
uptrend.
The
graph
may
remind
you
of a
stock
market
chart.
Actually,
a
Kelly
gambler's
bankroll
is
more
volatile
than
the
Dow
or
S&P
500
histor
ically
have been.
This
jagged
mountain
range
can be a
landscape
of
heartbreak.
Suppose
you
found
yourself
at
the
top
ofthe
peak
to
the
right
ofthe
center of the
chart.
Maybe
that
represents
your
first
million.
In this
particular
scenario,
you
are
just
about
to
lose
most
of it.
The
bankroll
fluctuations
in
Kelly
betting obey a simple rule. In
an infiniteseriesof
serial
Kelly
bets,
the chanceof your bankroll
ever
dipping down to half its
original
sizeis . . .
'A.
This is
exactly
correct for an
idealized
gamein
which
the betting
is
continuous.
It is
close
to
correct
for
the
more
usual
case
of
dis
cretebets
(blackjack,
horse
racing,
etc.).
A
similar
rule
holds
for
any
228


## Page 239

St.
Petersburg
Wager
fraction
i/n.
The
chance
of
ever
dipping
to
'A
your
original
bankroll
is
'A.
The
chance
of
being
reduced
to I
percent
of
your
bankroll
is
i
percent.
The
good
news
is
that
the
chance
of
ever
being
reduced
to
zero
is
zero.
Because
you
never
go
broke,
you
can
always
recover
from
losses.
The bad
news
isthat no matter
how
rich
you
get,
you
run the risk
of
serious
dips.
The
l/n
rule
applies
at
any
stage
in
the
betting.
If
you've
run
up
your
bankroll
to
a
million
dollars,
it's
as
if
you're
start
ing
over
with
a
Si
million
bankroll.
You
run
a
50
percent
chance
of
losing
half
that
million
at
some
point
in
the
future.
This
loss
is
quote-unquote
temporary
Any
way
you
slice
it,
the
Kelly
bettor
investor
spends
a lot of
time
being
less
wealthy
than he
was.
*
A
Tout
in
a
Bad
Suit
Try
typing
"Kelly
formula"
or
"Kelly
criterion" into
Google.
Get-rich-quick
schemes
rank
next
to
sex
as
the
Web's
fa
vorite
topic.
The
Web
has
carried
on its
own
debate,
many
of the
writers
unaware
of
what
the
economists
and
information
theorists
were saying.
"All
serious
gamblers
use
something
close
to the
Kelly
criterion,"
claims
a
certain
John
May,
whose
web
site
describes
him
as "oneof
the most
feared
gamblers
in the
world."
AUK
football
betting
site
says
that
the
system's
inventor,
"a
certain
John
L
Kelly
from
the
USA
(who
apparently
worked
for
AT&T's
Bell
Laboratory),
was
obviously
nobody's
fool."
229


## Page 240

FORTUNE
S
FORMULA
However,
the
gambling
community's
relationship
with
the
Kelly
criterion
is best
described
as
love-hate.
Some
of the
anti-Kelly
diatribes
on the
Web
make
Samuelson
sound
wishy-washy.
"The
next time some tout in a
bad
suit
advises
you
to use a
progressive
betting
scheme,
such
as
. . . the
so-called
'Kelly
criterion,'
"
writes
J. R.
Miller,
publisherof the
Professional
Gambler
Newsletter,
"askto see
his
Master's
Degree
in
mathematics—preferably
in
probabilities."
Miller
says
that "the
Kelly
criterion should be
called
the
'Kevorkian
criterion'
or
the
'Kamikaze
Criterion.'
It's
suicide."
He
refers,
of
course,
to the
heartrending
dips
in
wealth
charac
teristic
of
serial
Kelly
betting.
Miller's
curious
remedy
is to bet the
same
amount
all
the
time,
no
matter
what.
With
flat
bets
on
the
sports
picks
in his
newsletter
(S99
a
month),
Miller
suggests
it
is
possible
to
triple
your
bankroll
ina
year.
Miller
also
reports
that
"ac
cording
to expert
researcher
Dr.
Nigel
E.
Turner,
Ph.D.,
Scientist,
Centre
for
Addiction
and
Mental
Health
...
incremental
betting
[as
in the
Kelly
system]
is one of the
telltale
signs
of
someone
with a
gambling problem."
Dozens
of
web
sites
discuss
the
Kelly
approach
to
investing.
Some
attempt to
make
the
Kelly
criterion
relevant
to
ordinary
stock-picking.
These
sites
often
reduce
Kelly's
math
to
homilies
with
which
noone
would
exactly
disagree
("Invest
where
you've
got
an
edge
and
focus
on the
long
term").
The
Kelly
criterion's
interest
ing
features
(maximum
return
and
zero
risk
of
ruin)
require
preci
sionin
estimating
edges
and
odds.
That
precision
is
hard
to
come
by
in ordinary
investing.
A popular belief among some
Kelly
adherents is that Warren
Buffett
is
a sort of
crypto-Kelly
trader.
Buffett's
philosophy
of in
vesting
in a small number of
companies
wherehe
believes
he has an
edge
and
focusing
on
the
long
term
is
equated
to "bet
your
be
liefs"—whether
or not
Buffett
has
even
heard
of
John
Kelly
This
theory
is
developed
in
fund
manager
Robert
Hagstrom's
book
The
Warren
Buffett
Porfolio.
"We
have
no
evidence
that Buffett
uses
the
Kelly
model
when
allocating
Berkshire's
capital,"
Hagstrom
candidly
writes.
"But
the
Kelly
concept
is
a
rational
process
and,
to
my
mind,
it
neatly
echoes
Buffett's
thinking."
230


## Page 241

St.
Petersburg
Wager
"My
experience
has
been
that
most
cautious
gamblers
or
investors
who
use
Kelly
find
the
frequency
of
substantial
bankroll
reductions
to be
uncomfortably
large,"
Thorp
himself
wrote.
The
gambling
community
has
evolved
ways
to
tame
the
Kelly
system's
fearsome
volatility.
Thorp used similar
approaches
at Princeton-Newport.
The
importance
of this is hard to
overstate.
It
would
be
impossible
to
market
a
hedge
fund
whose
asset
value
was
as
volatile
as
the
bankroll
of the
serial
Kelly
bettor.
There are two
ways
to smooth
the
ride.
One
is to stake a fixed fraction
of
the
Kelly
bet or
position
size.
As
before,
you
determine
which
opportunity
or
portfolio
of oppor
tunities
maximizes
the
geometric
mean.
You
then
stake
less
than the
full
Kelly
bet(s).
A
popular
approach
with
gamblers
is "half
Kelly."
You
consistently
wager
half of the
Kelly
bet.
This is an
appealing
trade-off
because
it cuts
volatility
drastically
while
decreasing
the return by
only
a
quarter.
In a
gamble
or
invest
ment
where
wealth
compounds
io
percent
per
time
unit with
full-
Kelly
betting,
it
compounds
7.5
percent
with
half-Kelly.
The
gut-wrenching
and
teeth-gnashing
is
diminished
much
more.
It can be
shown
that the
full
Kelly
bettor standsa
\\
chance
of
halving
her
bankroll
before
she
doubles
it.The
half-Kelly
bettor
has
only
a
'/•>
chance
of
losing
halfher
money
before
doubling
it.
Ray
Dillinger,
writing
on
the
Web,
has
described
the
Kelly
crite
rion
as
the
"bright
clear
line"
between
"aggressive
investing"
and
"insane
investing."
That
is
a
good
way
of
characterizing
the
just-
short-of-fatal attraction of the
Kelly
system.
A chart of compound
return
vs.
bet
(position)
size
appears
on the next
page.
The
horizon
tal
axis
is marked off in units
called
Kelly
fractions.
The I indicates
the
standard
Kelly
criterion
bet
(which
is itselfa
prescribed
frac
tion of the
speculator's
wealth).
Zero is betting nothing at
all,
and
2 is
twice
the
Kelly
bet. The
curve
of
compound
return
peaks
at
the
Kelly
bet. The top of the
curve
has
a
horizontal
tangent.
You
can bet a little less or a little more without affecting the return
rate
much.
231


## Page 242

FORTUNE
S
FORMULA
Aggressive
vs.
Insane
Risk-Taking
"Half
Kelly"
betting gives
3/4
the
return with
much less
volatility
Kelly
bet gives highest return
At twice the
Kelly
bet,
return
is zero
(gambling)or risk-
free
rate
Serious
overbetting
leads
to negative returns
The
bigger
your
bets,
the
more
your
bankroll
is
going
to
fluctuate
up and
down.
Therefore,
volatility
increases
as
you
move
to the
right
in the
chart.
Bet
sizes
justto the left of the
Kelly
bet, and in
cluding
the
Kelly
bet
itself,
are
aggressive.
Bet
sizes
to
the
right
of
Kelly
are
insane.
They
are
insane
because
they
decrease
compound
return
while
producing
even
more
volatility
than
the
Kelly
system.
When the
fraction
is
twice
as
large
as the
Kelly
bet, the com
pound return rate drops to
zero.
With
even
larger
bets it
becomes
negative.
The trend is downward as the bettor's bankroll fluctuates
wildly.
Because
it is better to be
aggressive
than
insane,
it is
wise
for
even
the
most
aggressive
people
to
adopt
a
Kelly
fraction
of
less
than
i. In
practical
applications,
there
is
always
uncertainty
about
the true
odds
of the
gambles
we
take.
Human
nature
may
further
bias
the
estimation
error
in
the
direction
desired.
Bill
Benter,
who
has
made
many
millions
using
a
fractional
Kelly
232


## Page 243

St.
Petersburg
Wager
approach
to
racetrack
wagering,
says
that it is
easy
for the best
com
puter handicapping
models
to
overestimate
the edge bya factorof 2.
This means that someoneattempting to
place
a
Kelly
bet might un
intentionally be
placing
a
twice-Kelly
bet—which
cuts the return
rate to zero. A fractional
Kelly
bet doesn't
sacrifice
much return. In
caseof error, it is
less
likely
to push the bettor into insane territory.
Most of the people who
successfully
use the
Kelly
criterion in
fact
aim
for a bet or
position
size
less
than the
Kelly
bet—the
amount determinedby the
uncertainties
and any
preference
for
less
volatility.
In a 1997 speech in
Montreal,
Thorp encapsulated his
position in four
sentences:
Those individuals or institutions who are long term com
pounders shouldconsiderthe
possibility
of
using
the
Kelly
crite
rion to
asymptotically
maximize
the expected compound growth
rate
of
their
wealth.
Investors
with
less
tolerance
for
intermedi
ate term risk may prefer to use a lesser fraction. Long term com
pounders
ought
to
avoid
using
a
greater
fraction
("overbetting").
Therefore, to the extent that future probabilities arc uncertain,
long term
compounders
should
further limit their
investment
fraction
enough to prevent a
significant
riskof
overbetting.
To its
critics,
the
Kelly
system
is a
mere
utility
function—one
idiosyncratic
blend of
greed
and
recklessness.
To
people
like
Thorp
and
Benter,
the
Kelly
system
is
more
a
paradigm.
It is a
new
way
of
mapping the
landscape
of riskand return.
Another method of taming the
Kelly
system
is
diversification.
Blackjack
players
sometimes
pool their
bankrolls.
Each
takes a share
of the group
bankroll
and
plays
it
independently.
At the end of the
day they rcpool their
winnings
(or
losses)
and split them.
By
averag
ing
out the
players'
luck,
the
team
wins
more
consistently.
Setbacks
are
fewer.
This effect can be all-important. The best
way
to see how it
works is to pretend youare able to
place
simultaneousbets on hun-
233


## Page 244

FORTUNE
S
FORMULA
dreds of
identically
biased
coins.
Each
coin
has
a
55
percent
chance
of
coming
up
heads
and
pays
even
money.
As
we've
seen,
the
Kelly
wager
for
sequential
bets on a
single
such coin is 10 percent of your bankroll. Simultaneous bets are a
whole new
game.
Now you can
diversify
by splitting your bankroll
evenly
among all the
coins.
This
greatly
reduces
the risk of serious
loss.
The
geometric-mean-maximizing
bettor commits more of the
bankroll
overall,
increasing
the compound return rate.
With a hundred
coins
being
tossed
simultaneously,
the
Kelly
wa
ger is
nearly
1/100of the
bankroll
on
each
coin.
In other
words,
the
Kelly
bettor
stakes
almost
the entire
bankroll—but
not
quite—on
the
"portfolio"
of coin
bets.
He doesn't
stake
everything
because
it's
barely
possible
for
all
hundred coins to come up
tails.
The
diversifi
cation among 100 bets
creates
a smooth curve of exponential
growth in
which
large
upward
or
downward
jags
are
extremely
rare.
Princeton-Newport
was
almost
always
highly
diversified.
Mis-
priced
securities
were in limited
supply.
By
necessity,
the fund's
bankroll was apportioned among many simultaneous "bets."
Diversification
works
well
for team
blackjack
players
because
there
is
no
correlation
whatsoever
between
the
luck
at
one
table
and
the
next.
It
worked
well
for
Princeton-Newport,
too,
because
the
correlations
between
bets
were
generally
low.
The
fund's
hedged
trades
were
designed
to be
insensitive
to
general
market
move
ments.
Thorp
also
designed
ways
to
make
the
trades
"volatility
neu
tral."
Neither a
flatlining
market or a
nervous
one made much
difference
to
returns;
Unfortunately,
the
average
stock
investor
can
diversify
only
so
far.
Shecanand
should
diversify
away
some
risk
by
buying
an index
fund or other
well-balanced
portfolio.
That still
leaves
considerable
risk
of a
general
market
crash.
She
can
diversify'
a bit
more
by
buying
a
global
fund.
Thistoo
has
its
limits.
Inour
global
economy,
virtually
all
stocks
and
stock
markets
arc
correlated
to
varying
degrees.
A
crash in Tokyo will depress stocks in New
York.
For
this
reason,
the
Kelly
approach
to
regular
stock
investing
has
limited
appeal.
Anyone
who
puts
all
her
assets
in
stocks
is
going
to
234


## Page 245

St.
Petersburg
Wager
have
to
accept
large
dips in
wealth.
This
fact
has
weighed
heavily
on
the
critics
of
Kelly
investing.
ForThorp and
his
hedge
fund,
it
was
largely
irrelevant.
An acid test of Princeton-Newport's market neutrality came in the
Black
Mondaycrash of October
19,
1987 The Dow Jones index lost
23 percent of its
value
in a single
day,
the
biggest
single-day
drop
ever.
Princeton-Newport's
S600
million
portfolio
shed only about
S2 million in the crash. Thorp's computer immediately began alert
inghim to
rich
opportunities
in the
panicked
valuations.
Duringthe
free
fall,
there were no
buyers,
making
it
impossible
to
sell.
Thorp
nonetheless made about
S2
million
profit in new trades that day
and the next.
Princeton-Newport
closed
October
1987 just about
even for the month. Most mutual funds were down 20
percent
or
more. Princeton-Newport's return for the year
was
an astonishing
34
percent.
Black
Monday
was
also
a
severe
test of the
efficient
market hy
pothesis.
It
was
difficult
for
many
to see how a
rational
assessment
of the market's
value
could
have
changed
23
percent in a single day
with no major bad newsaside from the crash
itself.
Black
Monday
caused
few
economists
to reject the efficient mar
ket
hypothesis.
Terms like
"rationality"
and
"efficient
market" con
tain
wiggle
room.
It
was
possible
to
argue
that the market
was
acting
rationally.
There had been
several
items
of
discouraging
economic
news
in the
weeks
leading
up to the
crash.
Maybe,
it
was
proposed,
the
crash
was
a
delayed
reaction,
a
game
of
musical
chairs
in
which
each
investor
"rationally"
tried to
sell
a split
second
before
everyone
elsedid. In this
way,
sheer
chaos
may
be
explained
as a side effect of
efficient
markets
. . .
Black
Monday
was
a
much
clearer
counterexample
to the geo
metric
random-walk
model of stock
prices.
The crash was astro
nomically
larger
than
would
have
been
anticipated
under that
popular model.
Mark
Rubinstein
(coinventor
of
portfolio
insurance,
which
played
a major role in the crash) estimated the chanceof the market
235


## Page 246

FORTUNE
S
FORMULA
falling
29 percent (as
S&P
futures
did) in a
single
day
as I in
10160.
That's the number youget bywriting 160 zeros after a
"1."
Accord
ing to Rubinstein,
So improbable is such an event that it would not be anticipated
to occurevenif the stockmarketwereto lastfor 20
billion
years,
the upper end of the currently estimated duration of the uni
verse.
Indeed,
such
an
event
should
not
occur
even
if
the
stock
market were to enjoy a rebirth for 20 billion years in each
of
20 billion big bangs.
Crashes were not exactlya new concept. There had been one in
1929,
though
(as
Rubinstein's
words
suggest)
it
seemed
not to
figure
much in the thinking of many
economists
a half century
later.
One
who had taken notice was
Robert
C. Merton. In the 1970s,
Merton
wrote
that
the
market
could
act
like
a flea as
well
as
an
ant.
Most
of
the
time,
stock
prices
wandered
back
and forth
like
an ant.
Every
now and then,
prices
would
take
a
flealike
jump.
Merton
reasoned
that these
jumps
should
be
accounted
for in
pricing
options.
The
existence of these jumps
implies
that many of the popular
models,
including
the
Black-Scholes
formula,
are not
exactly
right.
The
Kelly
system
is not married to any
specific
modelof how the
market
is
"supposed"
to
behave,
including
the
log-normal
random
walk.
The
prescription
of
maximizing
the
geometric
mean
works
with
flealike
jumps,
or with any
model
that can be
described
pre
cisely.
In contrast,
mean-variance
analysis
is ill suited to handle
flcalike
jumps,
for they cannot be
described
solely
by the two num
bers Markowitz theory uses.
236


## Page 247

St.
Petersburg
Wager
My
Alien
Cousin
In
1988,
OUT
of
the
blue,
Paul
Samuelson
wrote
a
letter
to
Stanford
information
theorist
Thomas
Cover.
Samuelson
had
been
sentone of
Cover's
papers
on
portfolio
theory
for
review
"If
I did use
some
of
your
procedures,"
Samuelson
wrote,
"I
would
not
let
that
. . .
bias
my
portfolio
choice
toward
the
choices
my
alien
cousin
with log
[Wealth]
utility
function
would
make."
He
chides
Kelly,
Latane,
Markowitz,
"and
various
Ph.D's
who
appear
with
Poisson-distribution probabilities most
Junes."
Cover
was
flattered
to
receive
a letter
from
the great
Samuelson
(albeit
one
ripping
his
paper
to
shreds).
Cover
drafted
a
tactful
re
ply.
This
initiated
a
correspondence
that
ran
several
years.
The
more
uninhibited
Samuelson
got
off
the
best
lines.
Calling
the
Kelly
sys
tem a "complete
swindle,"
Samuelson
told Cover that "mathemati
cians
who
ignore
remainders
in
approximation
should
be
halved,
then quartered, then
...
Samuelson
wrote
his
last
letter
to
Cover
in
words
of
one
syllable.
"IfI
like
your
ways
to
guess
at
chance,
I
need
not
(and
will
not)
use
your
'growth'
stuff with
them,"
he
wrote.
"Whygo to and
fro
when
we
have
been
there
once?"
237


## Page 249

Ivan
Boesky
There
was
forever
an air of
mystery
about
who
Ivan
Boesky
was
and what he had
been.
He told
people
that his
Russian
immi
grant
father
had
run a
chain
of
delicatessens
in
Detroit.
Actually
it
was a chain of topless dancing bars
called
the
Brass
Rail.
An uncle
ran
a
deli.
In high
school,
one of
Boesky's
best
friends
was
an Iranian ex
change
student
named
Hushang
Wckili.
After
attending
three
small
and not
very
prestigious
Michigan
colleges
without
graduating
from
any,
Boesky
left for
Iran.
Boesky
would
later
testify
under oath that
he taught
English
as a
second
language
to
Iranians
for the
U.S.
In
formation
Agency.
The
U.S.
Information
Agency
said it had no
record
of
anyone
named
Ivan
Boesky
working
for
them.
After his Iranian
sojourn,
Boesky
returned to the
U.S.
and en
rolled
in a
bottom-rung
law
school,
the
Detroit
College
of
Law.
He
graduated
five
years
later after
dropping
out
twice.
No
law
firm
would
have
him.
Boesky's
father
made
Ivan
a partner in the chainof
stripper
bars.
Boesky's
fortunes turned when he married into a
wealthy
family.
His
wife's
father,
Ben
Silbcrstein,
was a
Detroit
real
estate
devel
oper.
Boesky
heard that
buckets
of
money
were
being
made
on
Wall
Street.
He
decided
that
was
the
life
for
him.
Boesky's
father-in-law
set the couple up in a starter apartment in one of Park
Avenue's
most
exclusive
buildings.
Boesky's
specialty
was
risk
arbitrage.
When company ABC at-
241


## Page 250

fortune's
formula
tempts
to
acquire
XYZ,
it
offers
so
many
shares
of
ABC
stock
for
each
share
of
XYZ—assuming
that the
merger
goes
through.
These
terms are
favorable
to XYZ's shareholders because the acquiring
firm
hopes
they
will
approve
the
merger.
It
follows
that each share of XYZ should be worth
precisely
x
shares of ABC under the terms of the
merger.
The two
companies'
share
prices
rarely
trade
in
this
ratio,
however,
because
there
is
usu
ally
much
uncertainty
about
whether
a
merger
will
take
place.
It can
be
blocked
not
only
by
shareholders
but
by
the
government
or
by
the second thoughts of
management.
Someone
who
thinks
a
merger
will
go
through
can
buy
XYZ
and
sell short ABC in order to ensure a profit when the merger takes
place.
Robert
C.
Merton
did
this
with
the
1963
Singer-Fridcn
merger.
It
amounts
to
placing
a
"sports
book"
bet on the
merger
happening.
The bet can be
leveraged
forgreater
gain.
It is
called
risk
arbitrage
because
anyone
who
docs
this
risks
los
ing
money
if the
merger
fails
to
happen.
Boesky
got
his
first
real
shot at
arbitrage
at a
firm
called
Kalb
Voorhis.
In a
single
trade he
lost S20.000 of the
company's
money
and
was
fired.
After several
other
misstarts,
Boesky
decided it was time to open
his
own
company.
He
took
out
ads
in
The
Wall
Street
Journal
touting
the
fantastic
profits to be made in
arbitrage.
Private
investment
firms
did not
generally
advertise,
much
less
take
a
hard-sell
approach.
(Thorp and
Regan's
fund
had an
unlisted
phone
number,
and
this
was
typical.)
Despite
his
unimpressive
record,
Boesky
proposed
to
charge
investors
45 percent of
profits
for his
services.
If
Boesky
lost
money,
the
investors
would be re
sponsible
for 95 percent of the
losses.
Those
fees
must
have
shooed
away
any
sensible
investors.
The
Silberstein
family
pumped in
money,
and in
1975
the Ivan
F.
Boesky
Company was off and running.
Boesky
would
order a
croissant
for
breakfast,
pokeit a
few
times,
and
end up eating a
single
flake
of
crust.
One
employee
saw him take a
normal-size
bite
once.
"Ivan,
youlittle
pig!"
Boesky
scolded
himself.
242


## Page 251

PJCO
"P'ggy"
was
Wall
Street's
nickname
for
Boesky.
It
referred
to
his
appetite
for
large
positions,
leverage,
and
risk.
When
Boesky
be
lieved
a
merger
was
highly
likely,
he
used
leverage
to
increase
his
an
ticipated
profits.
How
much
leverage?
"The
maximum
permitted
by
law,"
according
to the
Boesky
Corporation.
The
Federal
Reserve
permitted
2-to-i
leverage
in
"retail"
security
transactions.
Private
lenders,
such
as
Boesky
used,
could
set their
own
limits.
Asked
by
a
Fortune
magazine
reporter
about
rumors
that
Boesky
had
violated
debt
covenants
with
his
lenders,
Boesky
answered,
"Not
at
all."
Confronted
with
a
few
more
facts,
Boesky
qualified
that:
"In
principle,
we're
always
in
compliance
withour
covenants."
In
1984
the
Boesky
Corporation
claimed
9-to-i
leverage.
This
was
apparently
possible
through
a then-new
technique
called
roll
ing.
Rolling
is
like
buying
a
fancy
dress
and
wearing
it to a
party.
then
returning
it the
next
day.
Instead
of a
party
dress,
Boesky
re
portedly would buy and sell the same amount
of
stock simultane
ously.
The
"buyer"
and
"seller"
(both
Boesky)
each
had
five
days
to
hand
overthe
money
or
stock.
Boesky
could
thereby
arrange
to
own
a
block
of
stock
for
five
days
(after
which
it
had
to go
back
to the
"store").
Duringthat
time,
he
could
put up the
stock
as
collateral
for
a
90
percent
bank credit.
Asked
by a reporter whether he
engaged
in
rolling.
Boesky
an
swered,
"You
are insinuating
improprieties,
and the answer is no.
Some
people
don't
like
the
color
of
my
hair,
so theyare
going
to
say
whatever they
like."
Boesky
had no
illusions
about the strong
form
of the
efficient
mar
ket hypothesis. His business plan was to convert inside information
to
capital
growth.
This
procedure
had
a
long
history,
some of it re
spectable.
Stockbrokers
in the
age
of
Adam
Smith
freely
traded tips
and used them to make timely purchases and sales with their own
money.
This
system
was
unfair to anyone not privy to the tips,
though
apparently
not
many
people
thoughtof it in quite that
way.
Prior
to
electronic
communications,
the
unfairness
was
manifest.
It
took
days
for
news
to
reach
rural
England.
243


## Page 252

FORTUNE
S
FORMULA
Instantaneous
communications
changed
things
for
brokers
as
surely
as
they
did
for
bookies.
The
telegraph
and
Edison's
ticker
tape
machine
accelerated
the
flow
of
information.
Still,
no onepre
tended
that
Manhattanites
didn't
have
better
access to financial in
formation
than
people
on the
frontier.
The
watershed,
as
with
so
many
things
relating
to
the
market,
was
the
1929
crash.
Fortunes
were lost in
hours.
Some
people
on
Wall
Street
were
able
to
salvage
their
wealth
by
selling
early
into the
crash.
These
early
sales
by
in
siders
depressed
prices
further.
That
now
seemed
unfair
to
investors
across
the countrywho
learned
of the
crash
late.
Congress
responded
by
setting
up the
Securities
and
Exchange
Commission.
One
goal
of the
agency
was
to
assure
small
investors
that
they
would
not be
exploited
by
insiders
who
received
informa
tion
first.
U.S.
securities
law
draws
a big
(inevitably
arbitrary) line
between
private
and
public
information.
It is
illegal
to profit
from
unrcleased
corporate
information.
This is a
law
with a
thousand
shades
of
gray,
yetit is
vital
to an
economy
that
expects
to
raise
large
amounts of
capital
from
average
citizens.
Like
many
risk-takers,
Boesky
seems
to
have
thrived on riskand
existed in a denial of it. When he had a tip on a merger, he tried to
confirm
it
through
independent
channels.
He
cultivated
a lot of
sources.
When they
agreed,
Boesky
tended to act as if it were a sure
thing,
borrowing
to
increase
his
profit.
In
1982
Boesky
learned
that
Gulf Oil
was
going
to
buy
Cities
Service
at
S63
a
share.
Boesky
bought
S70
million
of
Cities
Service
stock.
That
was
about
equal
to
the net worth of
Boesky's
trading
corporation.
Boesky's
sources
were
right
about
Gulf's
intentions.
Unfortu
nately,
Gulf worried that the
deal
would
raise
antitrust concernsand
backed out of the deal. Cities
Service
stock plunged.
Boesky
was al
most
ruined.
Like
John
Kelly,
Boesky
had to
place
a
precise
value
on
information
streams.
One
of
Boesky's
most
important
tipsters was a young in
vestment banker at Kidder
Peabody
named Martin
Siegel.
Boesky
244


## Page 253

RICO
and
Siegel
struck
a
deal
where
Boesky
would
pay
a
single
lump
sum,
the
amount
to
be
negotiated
annually,
for
all
the
information
Siegel
supplied
over
a
calendar
year.
The
first
year
of
this
arrangement.
Siegel
leaked
to
Boesky
wordof
Bendix's
hostile
takeover
of
Martin
Marietta.
Kidder
Peabody
had
been
helping
Martin
Marietta
defend
itself
against
the
takeover.
Boesky
used
the
timely
scoop
to
make
a
lot
of
money—Siegel
didn't
know
how
much.
He
asked
Boesky
for
a
$150,000
cash
payment.
Boesky
planned
a
drop.
In
January
1983
Siegel
went to the
lobby
of the
Plaza
Hotel.
He
was
approached
by
a
muscular
Iranian
who
said
"Red
light."
"Green
light,"
Siegel
replied.
The
courier
handed
Siegel
a
briefcase.
He
took
it to
his
East
Seventy-second
Street
apartment.
Inside
were
stacks
of hundred-
dollar bills, tied with ribbons that said "Caesar's Palace."
Boesky
justified
the
cloak-and-dagger
by
telling
Siegel
that
he
had
once
been
a
CIA
agent
in
Iran.
The
next
year,
Siegel
asked
for
$250,000
(he
had
passed
word
on
deals
involving
Natomas
and
Getty
Oil).
Again
Boesky
agreed
without
haggling.
Siegel
went
to
the
Plaza,
met
the
same
courier,
and
exchanged
the
code
words.
When he opened the
briefcase
the
bills
were tied with the same
Caesar's
Palace
ribbons.
This
time,
some
of
the
bills
were
singles
rather
than
hundreds.
Siegel
counted
carefully,
and the
money
came
to
$210,000.
Siegel
told
Boesky
the
payment
was
S40.000
short.
He
tactfully
suggested
that
maybe
the
courier
had
skimmed
it.
Boesky
insisted
that
was
impossible.
The
courier
was
a
man
of
impeccable
character
who
would
never
steal
money.
Boesky
did
not
attempt
to
complete
the
syllogism.
Privately,
Siegel
decided
to
factor
some
shrinkage
into the
next
year's
request.
The
next
year
was
different.
Siegel's
conscience
was
bothering
him,
and
he
wanted
out.
He
avoided
calling
Boesky.
When
he
took
a
call,
he
avoided
giving
Boesky
any
confidential
information.
Aftera
while,
Boesky's
calls,
which
had
been
daily,
let
up.
This
left
the
payoff
for
1984.
Earlier
in
the
year,
Siegel
had
245


## Page 254

fortune's
formula
passed
on
lucrative
tips
about
the
Carnation-Nestle
merger.
Siegel
was
not so
conscience-stricken
as
to
forget
that.
In
January
1985
Siegel
asked
Boesky
for
$400,000.
Boesky
said
it
was
too
risky
to
use
the
Plaza
again.
He
directed
Siegel
to
meet
his
courier
at
a
pay
phone
booth
at
Fifty-fifth
Street
and
First
Avenue.
Siegel
would
pretend
to
make
a
call.
The
courier
would
pretend
to
be
another
guy
waiting
to
use
the
phone.
He
would
place
the
briefcase
by
Siegel's
left
leg.
Then
the
courier
would
walk
away.
Siegel
got
there
early
and
ducked
into
a
coffee
shop
to
get
out
of
the
cold.
As
he
drank
his
coffee,
he
spotted
the
courier
out the
win
dow.
He
was
a dark
Middle
Easterner,
carrying
a
briefcase,
loitering
near the pay phone.
Before
he
could
go
make
the
call,
Siegel
saw
another
man.
He
waswatchingthe first man.
Boesky
had
said
nothing
about
two
men.
Siegel
half
seriously
wondered
whether
Boesky
was
plotting
to
kill
him.
Why
pay
some
one
whose
usefulness
is
over?
The man
might
come up behind
Siegel
and
shoot
him
in
the
back
...
Siegel
left
without
making
the
pickup.
The
next
day
at
the
office,
Boesky
called.
He
wanted
to
know
how
it
went.
Siegel
explained
what
happened.
Boesky
said
of
course
there
was
a
second
man;
he
always
senta
second
man
to
check
up on
the
first
(the
one
with
impeccable
character).
Boesky
urged
Siegel
to
agree
to
another
drop.
Siegel
refused,
but
Boesky
kept
pestering
him. After a few weeks it all seemed so ridiculous that
Siegel
con
sented.
The
drop
went
off
as
planned.
Siegel
counted
the
money.
Some
of
it was missing.
He didn't bother to
tell
Boesky.
Siegel
was
not
calling
Boesky.
When
Boesky
did
call,
Siegel
feigned
being
too
busy
to
talk.
"What's
the
matter,
Marty?"
Boesky
asked
during
one of
these
truncated
conversations.
"You never
want
to talk to me. You
never
call
anymore.
I
never
see
you.
Don't
you
love
me
anymore?"
246


## Page 255

RICO
*
Rudolph
Giuliani
"Boesky's
competitors
whisper
darkly
about
his
omniscient
timing," a 1984
Fortune
article ran, "and rumors
abound
that
he looks
for
deals
involving
Kidder
Peabody
and
First
Boston.
Boesky
vehe
mently denies using inside information . . ."
Press
accounts of
Boesky's
misdeeds
commanded
the
attention
of the
new
U.S.
Attorney
for
the
Southern
District
of New
York,
Rudolph
Giuliani.
Giuliani
had
quickly
gained
a
reputation
as
a
crime-fighter
and
particularly
a
foe
of
organized
crime.
Giuliani
himself
came
from
a
connected
family.
One of
his
un
cles
was
a
bookie
and loan shark for the
mob.
His
father,
Harold,
was
an
enforcer
for
the
loan
shark.
Harold
Giuliani
was
a
big,
pug
nacious
man
with
thick
glasses
and
ulcers.
He
came
of
age
in
the
Depression
and
never
had
much
luck
finding
or
keeping
a
job.
On
April
2,
1934,
desperation
drove
Harold
and
an
accomplice
to
hold
up
a
milkman
at
gunpoint.
Harold
spent
a
year
in
Sing
Sing
for
the
crime.
In
1948
Harold's
brother-in-law
Leo
DAvanzo
started
a
restau
rant and bar in the
Flatbush
section
of
Brooklyn.
It
was
a
cover
for
loan
sharking
and
gambling.
The
place
had
a
secret
wire
room
in
back where bookies and numbers
runners
worked. Leo
offered
Harold
the
first
real
steady
paycheck
of
his
life.
With
a
four-year-
old son to support, Harold
accepted.
He
became
the
restaurant's
bartender
and
the
loan
shark
business's
muscle.
Debtors
would
slip
up
to
the
bar
and
hand
Harold
envelopes
of
cash.
They
were
paying
vigorish—compound
interest—of
150
percent
and
up.
When
they
247


## Page 256

FORTUNE'S
formula
failed
to
make
a
weekly
payment,
it
was
Harold's
business
to
find
them.
He
was
known
for
beating
delinquent
borrowers
with
a
base
ball
bat.
But
Harold
did not
want
his
son
growing
up in the
mob.
He
quit
his
job
with
Leo
and
moved
to
Long
Island,
taking
a
job
as
groundskeeper
for
Lynbrook
Public
High
School.
Harold's
son
not
only
grew
up
with
a
lawfully
employed
father
but
gravitated
to a
career
in the
law.
In
college,
"Rudy"
Giuliani
told
one
girlfriend
of
his ambition to
become
the first
Italian
Catholic president of the
United
States.
He
idolized
John
F.
Kennedy
and
his
crime-fighting
attorney
general
Robert
Kennedy.
At
New
York
University,
Giuliani
had a dartboard in his
room
witha
picture
of
Richard
Nixon
on it.
Giuliani
graduated
with
honors
in
1968.
He
began
clerking
for
U.S.
judge
Lloyd
MacMahon,
who
had
prosecuted
Frank
Costello
for tax evasion. Giuliani was
smart
and motivated, and his career
advanced
quickly.
In
January
1981,
Giuliani
was
named
associate
deputy
attorney
general,
the
third
highest
position
in
Ronald
Rea
gan's
Department
of
Justice.
He
had
changed
his
registration
to
Republican
only
a
month
before.
Giuliani
was
thus
working
in
Washington
at the
time
the
Supreme
Court
handed
down
a
decision
that
would
change
his
life.
The
case was the
United
States
v.
Turkette.
and it concerned the orga
nized
crime
law
RICO.
RICO
stands for
Racketeer-Influenced
and
Corrupt
Organiza
tions. The author of RICO, Notre Dame law professor G. Robert
Blakey,
was
a
former
aide
to
Robert
Kennedy.
The
twisted
syntax
of
the
name
was
allegedly
chosen
so that the
acronym
would
recall
the
name
of
Edward
G.
Robinson's
character
(Rico
Bandcllo)
in the
1931
gangster
film
Little
Caesar.
RICO
was
ultimately
a
response
to
Longy
Zwillman's
plan
for
the
mob
to go
legitimate.
Prosecutors
had
found
it
all
but
impossible
to
pursue
corrupt
companies
in
legit
imate lines of
business—even
when those
companies
were funded
by
mob
money
and
used
threats
of
violence
to
gain
market
share.
Passed
by
Congress
in
1970,
RICO
made
legal
the
dubious
tactic
that hadonce been
used
in the tax
case
against
Zwillman.
It
allowed
248


## Page 257

RTCO
prosecutors
to
freeze
the
assets
ofa
"racket"
from
indictment
up
un
til
the
verdict,
effectively
putting
itoutof
business
before
a
trial.
The
scope
of
RICO
broadened
greatly
with
time.
The
tipping
point was the
1981
decision in
United
States
v.
Turkette.
The
defendants
were
charged
with
drug
dealing,
arson,
insurance
fraud,
and
bribery
They
offered
the
defense
that
since
they
did
not
operate
under
cover
of a
legitimate
business,
they
were
not a
"racket."
Therefore,
they
could
not
be
charged
under
RICO.
The
Court
rejected
this
defense.
It
ruled
that
RICO
could
apply
to any
enterprise,
legitimate
or
illegitimate.
This ruling
recognized
a
contradiction
at the heart of the
law.
The
1970
Congress
apparently
thought
it
would
be
clear
who
the
"racketeers"
or
"gangsters"
arc.
The
acronym
itself
suggests
they
were
thinking
of
Italian
Americans.
The
Court
rejected
a
law
sin
gling
out
ethnically
or
culturally
defined
racketeers.
RICO
could
apply
to
any
organization
committing
the
wide
range
of
crimes
listed
in
the
law.
That
ruling
gave
prosecutors
broad
discretion
in
applying
RICO's
draconian
penalties.
Of
those
prosecutors,
none
made
more of this
power
than
Giuliani.
At
about
the
time
of
United
States
v.
Turkette,
Giuliani
read
Man
of
Honor,
the
memoir
of
mafioso
Joe
Bonanno.
Bonanno's
book
gave
a
detailed
description
of
the
inner
workings
of the
mob.
Giuliani
later
wrote
that
"I
dreamed
up
the
tactic"
of
using
RICO
"to
prosecute
the
Mafia
leadership
for
being
itself
a
'corrupt
enterprise.'
"
This
may
seem
a
strange
comment
today,
when
RICO
is
often
understood
to
be
a
law
for
prosecuting
mob
bosses
who
never
them
selves
pull
a
trigger.
But
RICO
was
initially
intended
for
the
rack
ets,
not
for
patently
illegal
activities
like
drug
dealing
and
murder
for
hire.
According
to
biographer
Wayne
Barrett,
"Rudy
decided
that
RICO
would
be his
Excalibur."
In
June
1983
Giuliani
accepted
a
new
job
as
U.S.
Attorney
for
the
Southern
District
of
New
York.
Covering
Manhattan
and
the
Bronx
and
thus
the
nation's
media
capital,
this
district
has
the
high
est
profile
of
any.
At
thirty-nine,
Giuliani
was
the
youngest
ever
to
249


## Page 258

fortune's
formula
hold
that
job.
He
inherited
a
number
of
ongoing
investigations
in
New
York.
One of
them
already
reflected
the
post-U.S.
v.
Turkette
interpretation
of
RICO.
By
a
weird
coincidence,
it
had
to
do
with
the
Fortune
500
company
that
had
grown
from
one
of the
Zwill
man
mob's
rackets.
In
1973
a
stockbroker
named
Leonard
Horwitz
walked
into
Warner Communications' Manhattan
offices
with
$50,000
cash in
a
paper
sack.
Florwitz
wanted
to
get
Warner
to
invest
in
the
public
offering
of
Westchester
Premier
Theatre.
The
yet-unbuilt
theater
was
to
bring
Vegas-style
acts
to
suburban
Tarrytown,
New
York.
The
offering
was
in
trouble.
Horwitz's
big
bag
of
cash
was
an
in
ducement
for
Warner
to
buy
a
block
of
stock.
Horwitz
was
immedi
ately
referred
to
Solomon
Weiss.
In
personal
life,
Weiss
was
a
quiet,
fatherly
man
and
a
meticulously
observant
Jew.
In
professional
life,
he
was
an
expert
at
concealing
cash
flows
on a
company's
books.
Weiss
had done
books
for the
Kinney
parking
lots,
which
had been
involved
in
labor
union
and
government
payoffs
for
years.
Horwitz
and
Weiss
struck
a
deal
where
Warnergot the
cash;
in
return,
Warner
issued
checks
to
buy
stock in the
theater.
Horwitz
was
told that
Warner
always
hada need for
cash.
Why
did
a
big
and
legitimate
corporation
need
cash?
The
answer
may
have
had
to
do
with
blackjack.
Steve
Ross
habitually
vacationed
with
a
group
of
family
and
friends.
When
the
vacation
spot
had
casinos,
Ross
would
often
ask
his
companions
to name
something
they
wanted.
Then
Ross
would
go
to
the
blackjack
tables,
alone.
Hours
later,
he
would
emerge
from
the
casino
with
enough
chips
to
buy the
named
gifts.
Friends
suspected
that
Ross
simply
bought
the
chips.
Ross
was
known
as a man
who
enjoyed
showering
largesse.
There
was
evi
dence that Ross was far from
invincible
at the
blackjack
tables.
Ross had a
credit
line at Caesars Palace, Las
Vegas.
On
June 1-3,
1973,
Ross
lost
$40,000
in
cash
playing
blackjack.
The
timing
and
amount
of that
loss
was
provocative
because
it
was
shortly
after
Horwitz had delivered the
$50,000
in a paper bag.
Ross told
Warner's
internal audit
committee
that
he had a brief-
250


## Page 259

RICO
case
in
his
office
to
store
his
gambling
winnings.
He
said
he
regularly
won
S6o,ooo
to
$90,000
at
blackjack
through
card-counting.
But
when
the
government
asked
Ross
why
he
had
not
reported
any
blackjack
winnings
on
his
income
tax
forms,
Ross
explained
that
"I
felt
at the end of the
year
that I
had
netted
out."
Leonard
Horwitz
cooperated
with
the
government
and
supplied
ev
idence
against
Solomon
Weiss.
The
U.S.
Attorney's
office
charged
Weiss
with
racketeering,
mail
fraud,
and
perjury
under
RICO.
It
was
the
first
time
RICO
had
been
used
against
a
major
corporation.
The
use
of
RICO
was
justified
by
Warner's
prehistory
as
a
"racket"
and
the
fact
that
the
company
was
literally
partnering
with
the
Cosa
Nostra.
It
was
learned
that
Westchester
Premier
Theatre
was
a
joint
venture
of
the Columbo and Gambino crime
families—and
later the
Genovese
family
as
well.
The
name
"Kimmel"
kept
popping
up
in the
Weiss
prosecution.
After
Weiss
was
held
in
contempt
of
court
for
refusing
to
produce
his
diaries,
a
suspicious
fire
broke
out
in
the
attorney's
office
where
the
diaries
had
been
sent
for
safekeeping.
It
was
hard
to
believe
that
the
fire
was
a
coincidence.
Another
coincidence:
Manny
Kimmel
had
another
son,
Charles,
nicknamed
"the
Torch."
Charles
report
edly
got
that
name
because
he
owned
restaurants
in
New
Jersey
that
burned
down.
Weiss
was
convicted.
Throughout
the
case,
the
prosecution
hinted that the
real
culprit
was
Steve
Ross
and that a further indict
ment might be in the works.
There
was
more
trouble
for
Warner.
Now
The
Wall
Street
Journal
ran
a
story
alleging
Warner's
tics
to
organized
crime.
Bizarrely
it in
volved
a
chain
of
"Looney
Tunes"
character-themed
family
restau
rants.
This
was
Caesar
Kimmel's
new
pet
project.
His
original
idea
was
to
entertain
diners
with
robotic
versions
of
Bugs
Bunny,
the
Tas-
manian
Devil,
and
Marvin
the
Martian.
The
robots
were
dropped
as
impractical
after
Warner
had
gone
to
the
expense
of
buying
a
plant
251


## Page 260

fortune's
formula
in
Connecticut
to
manufacture
them.
Neither
Kimmel nor his asso
ciates
had
restaurant
experience.
They
rented
locations
on the
second
floor
of
malls—death to a
sit-down
restaurant.
Kimmel
spent
an
astonishing
$70
million
opening
eleven
restau
rants.
None
of them
remained
in
business
beyond
three
years.
The
scale
of the
cost
overruns
suggested
organized
crime
to
a
Journal
re
porter.
Fie
did
some
digging
and
found
that
Kimmel's
partner
in
the
venture.
New
Jersey
attorney
Robert
Petrallia,
had
been
charged
with
mail
fraud.
In
1984
Caesar
Kimmel
took
early
retirement.
He had
inherited
from
his
father
a
love
of
thoroughbred
racehorses
and
became
a
well-known
breeder
whose
trademark
was
funny or risque
names.
He named one of his horses Flat Fleet Feet so racetrack announcers
would
have
to
struggle
with it.
After
Kimmel's
retirement,
Ross
took another
gamble.
He re
quested
that
Giuliani
issue
a
statement
saying
that
Ross
was
no
longer
a
target
of a
racketeering
investigation.
That
would
help
Warner's stock
value.
Giuliani
made
a
counteroffer,
if
Ross
would
submit
to a
private
interview
by
prosecutors,
and
if
his
answers
raised
no
further
suspicions,
then
Giuliani
would
make
a
statement.
Ross
did the
interview.
In
February
1985,
Giuliani
announced
that
the
investigation
of
Ross
was
closed.
There
was
"insufficient
evidence" to indict
Ross.
That
was not much of a character refer
ence.
It
was
enough
to
clear
Ross's
name,
more
or
less,
and
let
him
geton
with
running
the
company.
252


## Page 261

RICO
*
With
Tommy
Guns
Blazing
Giuliani
was
more
occupied
with the so-called Commis
sion
case.
The
"Commission" was the successor
of
the old
Combina
tion.
It
was
by
then
all
Italian.
Giuliani
used
RICO
to
go
after
eight
of the most
powerful
CosaNostra
families
in the
New
York
area.
From 1983 to 1985, the FBI recorded
conversations
of
Genovese
family
members
taking
place
at
two
mob
hangouts
in
East
Harlem,
the
Social
Club
and
the
Palma
Boy
Social
Club.
The
agency's
pri
mary
target
was
Anthony
("Fat
Tony")
Salerno,
whom
Fortune
maga
zine
rated
the
wealthiest
gangster
in
America.
The
evidence
on
the
FBI
tapes
helped
Giuliani
to
prosecute
Salerno
in
1986.
Salerno
was
given
a
hundred-year
sentence
and
spent
the
rest
of
his
days
behind
prison
walls.
This
and
the other
Commission
prosecutions
greatly
weakened
the
grip
of
organized
crime
in
New
York.
On
one
of
the
FBI
tapes,
Salerno
said,
"We
own
Kinney."
He
was
talking
about
Kinney
parking
lots,
and the
"we"
was
the
Genovese
family.
This
was
not the
conventional
view
of
things.
After
the
1971
spin-off,
Warner
remained
a
majority
shareholder
of
Kinney
Na
tional.
In
1978
this
stake
was
sold.
Then,
in
a
1986
leveraged
buyout,
Kinney
National
was
sold
again
to a
group
of
investors.
Manny
Kimmel
had been a
friend
of
Salerno's.
In late
1986,
Vin
cent
Cafaro,
who
turned
government
witness,
explained
that the
Gcnoveses
controlled
Local 272
of
the
International
Brotherhood
of
Teamsters.
The
parking
lots
paid
a
bribe
of
$2,000
to
S5,ooo
to
253


## Page 262

fortune's
formula
the
local.
In return the
Teamsters
didn't
make
trouble
about the
use
of
nonunion
labor.
This and other
evidence
of union
corruption
led
Giuliani
to
file
a
RICO
suit
against
the
Teamsters
in
July
1988.
He
charged
that
the
union
had
made
"a
devil's
pact
with
La
Cosa
Nostra"
and
described
the RICO suit
as
a
"careful,
surgical
action."
Despite
the
union's
reputation
for
tough
negotiating,
the
prospect
of
having
its
assets
frozen
rattled the union
management.
The
Teamsters
gave
in to
Giuliani's
demands.
The
leadership
was
turned
out,
replaced
in a
government-supervised
union
election
in
1991.
It
seemed,
in short, that RICO
was
an
all-powerful
weapon
against
the
bad
guys.
Criminals
and
their
attorneys,
who
had
been
contemptuous
of
the
glacial
pace
of
justice,
were
humbled
and
brought
to
the
bargaining
table.
RICO
got
results
now,
rather
than
later.
This
of
course
put
great
responsibility
onthe
prosecutor.
In
later
life
as
New
York
mayor—before
9/11
made
Orwcllianisms
common
place—Giuliani
was
quoted:
"Freedom
is
the
willingness
of
every
single
human
being
to
cede
to
lawful
authority
a
great
deal
of
discre
tion about what
you
do and how
you
do
it."
The
quick
results
had
a
political
advantage.
Within
a
few
years
as
U.S.
Attorney,
Giuliani
was
probably
the
nation's
best-known
crime-fighter
since
J.
Edgar
Hoover.
That
was
due
both
to
how
many
important
convictions
he
secured
and
to
his
genius
for
pro
moting
them.
Though
Giuliani
expanded
the
U.S.
Attorney's
office
to
132
assistants,
he
presented
himself
as
the
iconic
figurehead
of
that
office.
His
assistant
Denny
Young
"would
review
press
releases
like
they
were
indictments.
He'd
cross
out
assistants'
names
and
put
Rudy'sin."
One
former
aide
told
New
York
magazine:
"He
wanted
to
achieve
the
Thomas
Dewey
identity,
the
gangbuster,
the
Eliot
Ness
crime
fighter
...
on
the
running
boards
with
Tommy
guns
blazing—it's
Rudy
Rudy,
Rudy...
So
every
time
the
FBI,
whose
people
really
did
the
grunt
work,
brought
in
a
case
with
a
big
bow
on
it,
he
would
in
sist
on
taking
the
lead.
If
anyone
else
held
a
press
conference,
he'd
go
nuts.
Nuts.
This
man
does
not
do
a
duet,
he
only
does
a
solo."
254


## Page 263

RICO
Giuliani
followed
the
rumors
of
Ivan
Boesky's
misdeeds
carefully.
His
security
fraud
head,
Charles
Carberry
began
looking
into
the
claims.
Like
adultery,
insider
trading
is
notasinthat
can
be
commit
ted
alone.
The
prosecutors
began
making
a
diagram
of
the
suspected
insider
traders
and
their
interconnections.
There
were
about
twenty
names.
They
were
struck
by
how
similar
the
social
networks
of the
Wall
Street
people
were
to
the
Commission
case
people.
Each
group
saw
itself
as
an
elite,
apart
from
the
rest
of
society.
They
were
linked
by
bonds
of
friendship,
power,
money,
and
informarion.
They
traded
tips
and
attended
each
other's
weddings,
bar
mitzvahs,
and
funerals.
They
would
rather go to
jail
than
violate
the codeof
silence.
Giuliani's
people came to the
conclusion
that
Michael
Milken
was
the
most
important
person
in
the
diagram.
Milken
was
a
node
in
the
social
network,
and
his
power
was
then
at
its
height.
He
was
involved
in a
plurality
of
the
biggest
leveraged
buyouts.
This
meant
he
had
the
most
information
of
value
to
unscrupulous
traders.
Milken
was
also
deceiving
his
own
clients
by
collecting
stock
that
was
supposedly
a
needed
premium
to
help
sell
bonds,
but
which
ac
tually went into his own accounts.
The
U.S.
Attorney's
office
orchestrated
its
actions
with a number
of
law
enforcement
agencies.
The
chain
of
events
began
on
May
12,
1986,
when
the
Securities
and
Exchange
Commission
charged
trader
Dennis
Levine
with
making
S12.6
million
through
insider
trading.
Levine
worked
in
Drexel
Burnham's
New
York
office.
He
had
little
or
no
contact
with
Milken
in
Beverly
Hills.
Levine's
undo
ing was that he bragged about his inside trades to friends. "There's a
lot of money to be made in
information,"
he said.
Faced
with
the
evidence
against
him,
Levine
decided
to
cooper
ate.
Levine
had
been
passing
inside
tips
to
Boesky
for
5
percent
of
the
profits.
Levine
implicated
Boesky.
In
May
1986,
Boesky
gave
a
famous
commencement
speech
at
Milken's
alma
mater,
the
Berkeley
business
school.
His
message
was,
"Greed
is
all
right."
Within
days
of
the
talk.
Boesky
was
being
sub-
255


## Page 264

fortune's
formula
poenaed
to
supply
virtually
every
piece
of
paper
connected
with
his
business
activities.
By
August,
Boesky
too
began
cooperating
with
the
government.
Boesky
implicated
Martin
Siegel.
Two
days
before
Halloween,
Siegel
received
a
mysterious
phone
call
from someone named
"Bill."
The
caller
asked
if
Siegel
had re
ceived
his
letter.
What
letter?
Siegel
asked.
Bill
said
he
knew
all
about
Siegel's
relationship
with
"the
Russian."
Siegel
told
Bill
never
to
call
again
or he
would
call
the
police.
"I
doubt
that,"
Bill said.
Siegel
drove
to
his
Connecticut
home
and
found
that
he
had
received
a
letter
signed
"Bill"
asking
for
money
The letter
said,
"I
know."
A
few
days
later,
having
also
been
subpoenaed,
Siegel
decided
he
couldn't
live
this
way.
Hesent
his
lawyer
to
Giuliani's
office
to cuta
deal.
Siegel
admitted
guilt
and
agreed
to
cooperate.
He
implicated
Robert
Freeman
of
Goldman
Sachs.
On
February
12,
1987,
Thomas
Patrick
Doonan,
a
seasoned
in
vestigator
for
the
U.S.
Attorney's
office,
arrested
Freeman
in
his
twenty-ninth-floor
office.
Doonan
handcuffed
Freeman
and
pa
raded
him
past
his
incredulous
colleagues.
Thomas
Doonan
had
also
been
"Bill."
The
day
before,
Giuliani
had
approved
the
handcuffing
of
Freeman
without
argument.
He
felt
it
was
important
to
send
the
message
that white-collar
criminals
would
receive
no
special
treatment from
his
office.
Then
the
string
of
indictments
stalled.
Freeman
refused
to
make
a
deal
or
implicate
anyone.
Fie
vowed
to
fight
the
charges.
The
evidence
against
Milken
was
still
sketchy.
Giuliani
did not
want to indict
Milken
until he had a strong
case.
In
October,
the
government
had
a
very
nervous
Ivan
Boesky
wear
a
"wire"
under
his
suit
during
a
meeting
with
Milken
at
the
Beverly
Hills
Hotel.
Boesky
told
the
Feds
he
was
afraid
of
being
found
out
because
Milken
had
friends
in the
casino
business
who might
kill
him. The
256


## Page 265

R7CO
agents
told
Boesky
it
was
okay
to
run
if
Milken
discovered
the
wire.
Boesky
was
supposed
to get
Milken
to
talk
about
a
S5.3
million
payment
Boesky
had made to him for inside information. Men
tioning
that
the
SEC
was
"breathing
down
my
neck,"
Boesky
told
Milken
he
wanted
to
make
sure
that
they
both
had
the
same
story
about
the
check.
"Well,
my
guy
doesn't
remember
anything,"
Milken
said.
"Does
yours?"
Boesky
understood
this
to
mean,
destroy
the
evidence.
Milken
said
nothing
explicitly
incriminating
during
this
meeting.
It
was
as
if
he
suspected
something
was
up.
"You've
got to be
careful,"
Milken
told
Boesky.
"Electronic
sur
veillance
has
gotten
very
sophisticated."
Martin
Siegel
recounted
for the
government
a
March
1985
conver
sation
with
Robert
Freeman about
Storcr
Communications.
Free
man told
Siegel
that a
private
investment
firm
called
Coniston
Partners
was
accumulating
Storer
stock
for
a
takeover
attempt.
Siegel
asked
how
Freeman
knew
this.
"I'm
very
close
to the
people
buyingthe stock for
Coniston,"
Freeman
said.
This
created
a
loose
end
in
the
government's
diagram.
It
implied
that
Freeman
had
another
source(s)
of
inside
information
besides
Siegel.
Giuliani's
people
set
about
determining
who
the
people
buy
ing for
Coniston
were.
They
found
that the
trades
had
been
done
through
a
firm
called
Oakley-Sutton
Management.
The
government
uncovered
another
six-degrees-of-separation
coincidence.
One of
the
partners
in
Oakley-Sutton,
James
Regan,
had
been
Robert
Freeman's
Dartmouth
roommate.
And
James
Regan
and
Edward
Thorp ran a
hedge
fund
called
Princeton-Newport
Partners.
The
U.S.
Attorney's
office
had
already
gathered
some
Princeton-Newport
trading
records
in
connection
with
the
Freeman
investigation.
While
examining
the
records,
they
identified
some
suspicious
trades
by
William
Hale
of
Princeton-
Newport.
It
looked
like
Flale
might
have
made
trades
based
on in-
257


## Page 266

fortune's
formula
side
information.
They
investigated
Hale
further
and
discovered
he
had
been
fired from
Princeton-Newport
Partners.
Charles
Carberry
had
retired.
His
successor
in
security
fraud,
Bruce
Baird,
knew
that a
good
way
to get the
scoop
on an
organiza
tion
is
to
talk
to a
disgruntled
ex-employee.
The
government
sub
poenaed
Hale.
He
refused
to
talk.
A
plea
bargain
deal
was
proposed,
and
he
still
refused.
Finally,
the
government
called
Hale
before
a
grand
jury.
He
showed
up
for
questioning
in
November
1987
He
was
another
Dartmouth
man,
young,
tall,
and
blond.
The
government
granted
him
immunity.
This
prevents
a
witness
from
invoking
the
Fifth
Amendment.
In the
course
of
not-especially-productive
questioning,
Baird
asked
Hale
why
he'd
left
Princeton-Newport
Partners.
"I
didn't
leave," Hale corrected. "I was fired."
"Why?"
"I couldn't stand all the crimes they were committing."
The
Parking
Lot
Hale
said
that
Princeton-Newport
had been sellingse
curities
at a
loss
to
Milken's
operation.
The
sales
were
recorded
on
the
books,
with
every
i
dotted.
But
there
was
a
verbal
understanding
that
these
sales
were
just
for
show.
Princeton-Newport
would
later
buy
the
securities
back
from
Milken
at
close
to
the
same
price,
no
matter
what the market price was.
258


## Page 267

RICO
This
was
called
stock
"parking."
It
was
done
because
the
fund's
hedges
sometimes
created
peculiar
tax
situations.
Ina
typical
trade,
Princeton-Newport
would
buy
one
security
and
simultaneously
sell
short
another.
When
a
fund
sells
stock
short,
it
is
actually
borrowing
the
security,
which
must
be
purchased
later.
Thus
one
security
in
a
trade is
actually
purchased
later than the other. This meant that it
was
possible
to
have
a
short-term
capital
gain
on onesideof the trade
and a
long-term
capital
loss
on the other. The two would not offset
each
other as they
would
if
they
were
both the
same
kind
of
loss
or gain.
The
stock
parking
was
a
pretend
sale
to
convert
a
long-term
loss
toa
short-term
loss.
The
artificial
short-term
loss
offset
the
existing
short-term
gain
so
that
the
fund
would
owe
taxes
on
its
net
profit
only.
As
tax
dodges
go,
this
was
not
especially
villainous.
It
was,
how
ever,
illegal,
as
most
people
understood
the
existing
tax
code.
Hale
knew
this and
was
uncomfortable.
His
supervisor,
Paul
Bcrkman,
had
brushed
aside
Hale's
qualms.
Berkman
said
that the IRS "didn't
have
the
manpower
to
sort
out
these
types
of
trades."
To
play
it
safe,
Berkman
instructed
Hale
to
camouflage
the
trades
by
buying
the
parked
securities
back
at
slightly
different
prices.
It
was
Hale's
job
to
maintain
the
list
of
parking
transactions.
The
list
was
known
as
the
"parking
lot."
For
their
part
in
helping
Princeton-Newport
cut
taxes,
Milken's
people at Drexel Burnham
earned
an
interest
charge
that
was
built
into
the
buyback
price.
As
part of
the
arrangement,
Princeton-Newport
was
expected
to do
trades
through
Drexel
and
buy
its
junk
bonds.
Hale
said
that
Princeton-Newport
had
a
similar
parking
arrangement
with
Merrill
Lynch.
Hale
let it be
known
that he didn't
want
to
participate
in the
parking.
Because
of that, he was
fired.
Hale wasable to identify two peoplein
Milken's
officewho were
directly
involved
in the
Princeton-Newport
stock
parking.
They
were Bruce Newberg and
Lisa
Ann Jones. Jones was Hale's
counter
part,
keeping
track
of
the
parked
trades
for
Drexel.
Newberg
was
259


## Page 268

fortune's
formula
Jones's
superior.
Hale
said
that
Princeton-Newport
routinely
made
audiotapes
of
its
traders'
phone
calls.
This
was
in
order
to
have
a
record in caseof any later
dispute.
It
was
December
17,1987
and
Christmastime
in
Princeton.
Seasonal
decorations
lined the
streets
of the
college
town's
shopping
district.
In the
middle
of
town
was
a new
colonial-style
building.
The
passerby
might
never
know
that
it
was
home
to
one
of
the
world's
most
successful
hedge
funds.
There
was
no
need
for
window-
shoppers
to
know.
Princeton-Newport
had
no
need
for
attention,
least
of
all the kind it was about to get.
Vans
pulled
up
in
front
of the
building.
They
contained
about
fifty
federal
agents
of
the
FBI,
Treasury
Department,
and
Alcohol,
Tobacco
and
Firearms.
They
were
armed
and
wearing
bulletproof
vests.
The
building's
elevator
had
not
been
built
to
handle
a
militia.
Agents
went
up
in
groups.
They
pushed
past
the
glass
doors
of
the
partnership
office.
They
showed
a
warrant.
The
agents
ordered
em
ployees
to
remain
inthe
building
until
they
were
through.
They
went
through
the
filing
cabinets,
packing
documents
into
three
hundred
boxes.
They
were
under
orders
to
look
for
audiotapes
especially.
At
about
9:50
that
evening,
Pacific
time.
Thomas
Doonan
knocked
on the door of
Lisa
Jones's
apartmentin
Sherman
Oaks,
California.
Doonan identified himself as a
federal
agent. Jones let him in. Doo
nan
began
asking
specific
questions
about
1985
trades
in
which
Princeton-Newport
had
sold
securities
to
Drexel
and
bought
them
back
thirty-one
to
thirty-three
days
later.
As
Doonan
had
intended,
Jones
had not yetheardof the
raid
in
New
Jersey.
Sheadmittedpar
ticipating
in the
trades.
"Were
you
parking
for
them?"
Doonan
asked.
"Yes, I was," Jones said.
"Was it for tax purposes?"
260


## Page 269

RICO
"No,
it
wasn't."
Jones
belatedly
realized
she
was
in
trouble.
She
told
Doonan
that she wanted to sec an attorney.
Doonan's
reaction
was
to
sigh
and
say,
"We were hoping you
would
be
willing
to
cooperate
with
us in
this
investigation."
He left
a
subpoena.
Jones
was
afraid
to use her
phone
in
case
it
was
bugged.
She got
in her car and drove to a pay phone to call an attorney.
Welcome
to
the
World
of
Sleaze
When
Ed
Thorp
heard
the
news, his
initial
reaction
was
that
it
was
nonsense.
He had
followed
the stringof
arrests
on
Wall
Street
like
everyone
else.
The
raid
seemed
to be
some
publicity
stunt on
the part of
Giuliani.
Ominously,
Regan
did not
have
much
to
say
to
enlighten
him.
"Everybody
lawyercd
up,"
explained
Thorp.
"Everyone
talked
in
their own
circle;
they
wouldn't
talk
outsidethe
circle,
so getting in
formation
was
very
difficult.
Trying
to run a
partnership
was
very
difficult
under
the
circumstances."
Actions
spoke
louderthan
words.
Some
of the
East
Coast part
ners took about
S15
million out of the fund and replaced it—under
the
names
of
their
wives.
Giuliani
had
hit
pay
dirt in
Princeton.
Hale
had
said
that the
partnership's
audiotapes
were
kept
just
about
six
months.
It
turned
out that
someone
had
saved
some
tapes
from
December
1984-
Stock
parking
would
normally
take
place
at the end of the
tax
year.
261


## Page 270

fortune
s
formula
The tapes
included
plenty
of
evidence
backing
up
Hale's
alle
gations.
They
implicated
Regan
and a Princeton-Newport trader
named Charles
Zarzecki.
They also
incriminated
two of
Milken's
peopleat
Drexel
Burnham,
Bruce
Newberg
and Cary
Maultasch.
Berkman's
comments to Hale
suggest
that he sawthe stock park
ing as tax
roulette.
They
were
gambling
that the tax
savings
were
large
enough
to
justify'
a
small
chance
of being
caught.
Not
all
of
the stock
parking
was
for tax
reasons,
though.
In
1985
Princeton-
Newport had
parked
some
stock
in the toy
company
Mattel.
A
Drexel
trader sold
Mattel
stock
to
Princeton-Newport
with the un
derstanding
that he
would
buy
it
back
with 20 percent
interest.
Concealing
a
Drexel
financial
interest
in
Mattel
suggested
a
conflict
of
interest,
for
Michael
Milken
was
then
helping
Mattel
to
recapi
talize.
Drexel
had
also
been
doing
a
convertible
bond
offering
for
a
Minneapolis
company
called
C.O.M.B.
that bought
discontinued
products
for
practically
nothing
and
sold
them
to the
public
at bar
gain
prices.
Drexel
wanted
Princeton-Newport
to
help
push
down
the price of C.O.M.B. stock.
In one of the
tapes,
Robert
Freeman
mentioned
a
recent
trip to
Atlantic
City
to
Zarzecki.
"It's
not
fun
anymore,"
he
complained.
"I
guess
I've
been
in
this
business
too
long.
I'm
used
to
having
an
edge."
Another
conversation
recorded
a
parking
transaction
between
Zarzecki
and
Newberg.
"You're
a
sleaze
bag,"
said
Newberg.
"You
taught
me,
man,"
said
Zarzecki.
"Hey
listen,
turkey—"
"Welcome
to the world of beinga
sleaze."
262


## Page 271

RICO
*
Ultimatum
At
THE TIME of the raid on
Princeton-Newport,
Giuliani was
planning
his next career
move.
New
York's
Republican
senator
Alfonse
D'Amato
had been
urging
him to run for senator
against
Daniel
Patrick
Moynihan.
"I think I'd be very good" as a senator,
Giuliani told
The
New
York
Times.
"I don't have any question that I
could
do the job in an
innovative
and
creative
way."
A few
weeks
later,
he
backpedalcd:
"I cannot
leave
unless
I'm sure that the right
person
succeeds
me."
Giuliani's
biggest
concern
was
that the
Wall
Street
investigation
would
fall
apart.
Convicting
Michael
Milken
was
to be his
crowning
achievement
as
U.S.
Attorney.
As long as
Giuliani's
successor
fol
lowed
through,
Giuliani
could
pointto the
achievement
for the rest
of
his career, wherever that might lead him.
But not
every
potential
successor
shared
his
zeal
in
prosecuting
Wall
Street
corruption.
As
Giuliani's
mentor,
D'Amato
had
assigned
his own attorney
Mike
Armstrong,
to screen
possible
replacements.
Armstrong's
favored
candidate
was
Otto
Obermaier.
Both
Ober-
maicr and
Armstrong
published
articles
in the
National
Law
Review
blasting
Giuliani's
heavy-handed
tactics
against
securities
firms.
Armstrong
had
reason
to
complain:
he
represented
Lowell
Milken
in the Drexel
investigation.
It appeared that all the attorneys Arm
strong and
D'Amato
thought
suitable
to
replace
Giuliani
repre
sented Drexel peopleor
Drexel
clients.
Milken in fact hosted a fund-raiser for Al D'Amato in Beverly
Hills. Drexel's investment bankers chipped in about
S70.OOO.
263


## Page 272

FORTUNE
S
FORMULA
D'Amato
was
on the
Senate's
securities
subcommittee
considering
reforms in the junk bond
industry.
On February 8, Giuliani announced he would not run for the
Senate
after
all.
"It
would
be
wrong
for
mc to
leave
this
office
now,"
he
said,
"whatever
the
allure
of
another
office
or
opportunity,
be
cause
it
would
adversely
affect
some very
sensitive
matters now in
progress."
After
being
coached
for
two
days
by
Drexcl-supplied
attorneys,
Lisa
Jones
went
before
a
grand
jury
on
January
II,
1988.
She
requested
additional
time
to
prepare.
This
was
granted.
She
returned
two
days
later.
Almost
immediately
she took the Fifth Amendment.
The
government
was
ready
for
that.
They
granted
her
immunity,
forcing
her
testimony.
Jones
denied
that any stock
parking
had
taken
place.
She did not
know
that the
government
had the
discussions
of
parkingon tape. During a
break,
a prosecutorwarned
Jones's
attor
ney
that
his
client
was
risking
perjury
charges.
The
immunity
was
for past
crimes
only—not
for
lying
to this
grand
jury.
Bruce
Baird
asked
James
Regan
to come in to his
office.
He
wanted
to
play
the
tapes
for
Regan.
Baird
hoped
the
taped
evidence
would
be
enough
to get
Regan
to
testify
against
Freeman
and
Milken.
Regan showed up as defiant in dress as in manner. He wore
casual
clothes
and a
cap
with
the
words
SHIT
HAPPENS.
Regan
listened to the tapes with little emotion.
One of the
taped
conversations
had
Regan
and
Newberg
quib
blingover the
Mattel
parking.
"I
carried
plenty
of
positions
for
you,
in
case
you
haven't
been
realizing
it,"
Newberg
said
to
Regan.
"I've
been
charging
you mycost to
carry."
"What I
carry
on
my
books
now
is
your
position,"
Regan
said.
In
other
words,
Drexel
had
parked
stock
for
Princeton-Newport,
and
now
Princeton-Newport
was
returning
the
favor
by
parking
the
Mattel
stock
for
Drexel.
While
this
exchange
may
sound
ciyptic,
it
264


## Page 273

RICO
was more explicit than a prosecutor could normally hope for. It
would impress a
jury.
Regan had little to say and left. To friends, he made it clear that
he was not about to be a turncoat and testify
Freeman
was his
college
roommate,
and
Milken
was
a longtime
business
associate.
There
was no way he could be convicted. The charges were "too
complicated" for a jury to understand.
Thorp got one
call
from
the
prosecution
team.They wanted him
to come and testify in New
York.
"If I do, I'm going to take the
Fifth,"
Thorp
said.
The prosecutor's reply
was,
"Why are we not surprised?"
The
U.S.
Attorney's office took no further direct action against
Thorp. "Mytheory on takingthe Fifth
was,
I didn't know
anything."
Thorp told
me.
"1
had
no
upside
in
going
and
plenty
of
downside.
The downside was that I might so
aggravate
one of the defendants
that they might
falsely
incriminate me, just as a
revenge
matter."
The decision not to testify was"just a prudent calculation."
In midsummer 1988, Giuliani announced that he was filing
RICO
charges
in the
Princeton-Newport
case.
It
was
the
first
time the or
ganized
crime
law
had been
used
against
a
securities
firm.
At one of
his frequent
news
conferences,
Giuliani
maintained
that the use of
RICO
against
Princeton-Newport
was
"not a
novel
approach"
and
was
used "when we
believe
the magnitudeof the crime warrants it."
According to
Paul
Grand, attorney for Princeton-Newport's
Charles Zarzecki, Giuliani had initially presented an ultimatum. He
threatened to
file
racketeering
charges
unless
at least two Princeton-
Newport officials testified for the government in two
other
contin
uing
investigations.
"You'd
have
to
be a
fool,"
Grand
said,
not
to
know
that
he
was
talking about
Michael
Milken and Robert Freeman.
Giuliani later told
The
Wall
Street
Journal
that he had not made any
such
offer.
Defense attorney
Jack
Arscnault also
claimed
that Baird told
265


## Page 274

FORTUNE
S
FORMULA
him the government had no interest in
prosecuting
Princeton-
Newport—it
was
all
about
Drexel
Burnham.
"If you cooperate,
fine,"
Baird
supposedly
said.
"If
you
don't, we are
going
to
roll
right
over you to get where we want to
go."
This comment too appeared
in
The
Wall
Street
Journal
along
with
Baird's
denial
of
having
said it.
Since RICO had never been used
against
a
security
firm,
it
was
unclear
exactly
how it would
work.
Did the government
have
the
right to freeze the
assets
of
people
accused
of crimes
only,
or of the
unindicted partners and
investors
as
well?
This raised the specter of
the government seizingthe
assets
of the Harvard endowment fund,
or
Weyerhaeuscr's
pension
Rind.
Regan's
attorney,
Theodore
Wells,
called
the
use
of RICO
"frightening."
"It
seems
clear
that
Mr.
Regan
is being used as a pawn in a
chess
game being
played
on a much
larger board."
In order to
invoke
RICO it is
necessary
to
prove
that an ongoing
pattern of
criminal
conduct
existed.
The
government's
best evi
dence,
the
tapes,
was
limited
to
December
1984.
It
might
have
been
a
reasonable
guess
that the stock
parking
had been
going
on for
some time, but suppositions are not evidence.
Giuliani's
office
explored
charges
of tax
fraud,
mail
fraud,
and
wire
fraud.
It
discovered
that
Princeton-Newport
had
inadvertently
reported some income twice on its
1985
and 1986 tax returns. The
overstatement
was
nearly
S4
million.
The stock parking at issue
had
created
a S13
million
understatement
of
income.
The
account
ing error did not
lessen
the
seriousness
of the
charges,
but it made
Princeton-Newport's tax
people
look
like
the gang that couldn't
shoot
straight.
The
fund
subsequently
applied
for
(and got) a re
fund on the overpaid
taxes.
There
was
talk of
Regan
stepping down until his name could be
cleared.
The two partners
failed
to
come
to a
deal.
"My
personal
opinion
is that he was afraid that I'd run off with the firm and he'd
be unable to get it
back,"
Thorp
said. "He didn't know mc. So he
didn't know that that wasan
impossible
act for me."
Meanwhile
Giuliani's
solo
was
in danger of turning into a duet.
266


## Page 275

RICO
The SEC had been
conducting
its
parallel
investigation
of insider
trading.
Much
of the
evidence
against
Levine
and
Boesky
had been
the SEC's
legwork.
In late
July,
the SEC's Gary
Lynch
called
Giu
liani and announced that he
was
ready
to act
against
Milken.
Giuliani threw a fit. He told
Lynch
that if the SEC
filed,
he would
side with the defendantsand support a motion to
dismiss
the
case.
Lynch
was astounded. After Giuliani cooled down, he reversed
himself.
No,
of
course
he
would
never
sabotage
the SEC's
case.
Lynch
agreed
to wait
awhile
longer.
Formal charges would give Drexel the right to see the govern
ment's evidence. Giuliani believed that would decrease the prospect
of getting a
few
of
Milken's
closest
associates
to testify against him.
It would also mean that the SEC and not the
U.S.
Attorney's
office
would command the
spotlight.
Giuliani
was
thinking of running for
mayor
of
New
York.
As a Republican in a very liberal
city,
there
would be
political
mileage
in running as the man who had cleaned
up Wall Street.
On August I, the government played the
Princeton-Newport
tapes for Lisa Jones and her attorney Brian O'Neil.
The
next
day,
O'Neil wrote a letter
saying
that hearing the tapes had refreshed
Jones's
memory.
She did participate in the trades after
all.
and the
tradeswere part of a
scheme
to
avoid
taxes.
She
had
discussed
this
with at least one
Princeton-Newport
employee.
Giuliani
felt
this
was
too
little
too
late.
He
announced
that
the
prosecution
of
Jones for perjury would continue.
Later in August, a grand jury returned
RICO
indictments on
Regan
and four other Princeton-Newport
people:
Jack
Rabinowitz,
Charles
Zarzecki. Paul Berkman, and Steven Smotrich. Also prose
cuted was the former Drexel junk bond trader Bruce Newberg.
While Thorp
was
not
charged
with
anything,
his hedge fund was
mortally
wounded. With RICO
charges
looming,
the fund's in
vestors wanted out. In December
1988.
Thorp
and Regan dissolved
the partnership.
Positions
were
liquidated
and the money returned
to
the
investors.
267


## Page 276

FORTUNES
FORMULA
Thorp
was
aware,
of
course,
that the fund took
aggressive
tax po
sitions. He
says
he knew nothing of the stock
manipulation
and the
parking to subvert credit
requirements.
FIc
blames
the situation on
a
dysfunctional
partnership:
"We didn't
really
connect
well
as peo
ple,"
he said of
himself
and
Regan.
"That
was
probably
the
crack
in
the
edifice.
If we
had,
if I'd
realized
that
actions
were
being taken
that were more
aggressively
bold, closer to the line than I'd dare
contemplate, the whole thing wouldn't
have
happened."
*
Princeton-Newport
Partners,
1969-88
To
many
portfolio
managers
today,
the nineteen-year
record of
Princeton-Newport
Partners is the definitive home run. A
dollar
invested
in the
fund
at the
beginning
of
business
in
1969
would
have
grown to about
S14.78
by the time the fund
ceased
in
1988.
Over nineteen
years,
the compound return rate
averaged
15.1
percent
annually
after
fees.
The
S&P
500
averaged
an
8.8
per
cent annual return over the same
period.
Princeton-Newport's in
vestors beat the market by more than six
percentage
points.
Excess
return is only part of the
story.
A
few
others
achieved
higher
returns over
comparably
long
periods.
George
Soros's
hedge
funds modestly topped Princeton-Newport's returns. Warren Buf
fett's
Berkshire
Hathaway
has
had returns
averaging
more than
25 percent. (Thorp had to
achieve
about a 20 percent return to
leave
15
percent for his
investors.
As a corporation. Berkshire Flath-
away
does
not
charge
fees.)
268


## Page 277

RICO
The
difference
is
that
Buffett's and Soros's
returns
were much
more
volatile.
The
standard
deviation
of
Princeton-Newport's
re
turn was about 4 percent.
That
made the fund much less volatile
than
the
stock
market
itself.
The
S&P
500
shed
over
a
quarter
of
its
value
in
1974,
and
took
a
big
hit
on
1987's
Black
Monday.
A
chart
of
Princeton-Newport's
return
looks
nothing
like
the
jittery
graph
of
the
sequential
Kelly
bettor's
wealth.
Through
diversification,
fractional
Kelly
position
sizes,
and
a
philosophy
of
erring
on the
side
of
caution.
Thorp
achieved
a
smooth
exponential
growth refuting the
conventional
trade-off of riskand return.
Beating
the
Market
Growth
ofSi
invested
in
Princeton-Newport
Partners
S14.78
1968
1969
1970
1971
197?
1973 1974 1975 1976 1977 1978 1979 1980
1981
1982
1983 1984
1985
1986 1987
269


## Page 278

FORTUNE
S
FORMULA
Terminator
In
January
1989,
Giuliani
resigned
from
his
post
of
U.S.
Attor
ney
to
run
for
mayor
of
New
York.
The
first
Princeton-Newport-
related case to come to trial was that
of
Lisa Ann Jones, two
months
later. The main witness
was
William
Hale.
His story was detailed
and
believable.
Until
mid-1985,
he said,
Princeton-Newport
had
been
buying
back
parked
securities
at
the
price
paid,
plus
expenses.
Then
Berkman
instructed Hale to "add or subtract something like
$5
from
the
buy-back
price"
to
make
the
parking
less
evident.
This
meant that there
was
an
ongoing
tab,
money
that
Princeton-
Newport
owed
Drexel
or
vice
versa.
Hale
said
the
"parking
lot"
list
was
distributed
to
Regan,
Berkman,
Zarzecki,
and
Smotrich,
all
of
the
Princeton
office.
Hale
ticked
off a list of
companies
whose
stock
had
been
parked:
Sony
American
Express,
Transco
Energy,
and
Pulte Home
Corporation.
I
[ale
said
that
Regan
"told
mc
it
was
illegal."
Berkman
told
Hale
"not to worry but to
relax."
Lisa
Jones
had left her
family
in
New
Jersey
at the
age
of four
teen.
By
pretending
to be
eighteen,
shegot a jobandan
apartment.
Eventually
this led to the job at
Drexel.
In
closing
arguments,
pros
ecuting
attorney
Mark
Hanson
showed
that
Jones
had
lied
about
her
place
of
birth,
education,
age,
and
marital
status:
"a
long
litany
of
lies
that
has
made
up the
tangled
scheme
of her
life."
It
was
by
then
clear
that
Jones
was
lying
when
she
denied
that
stock
parking
went
on.
Jones
was
found
guilty.
Giuliani's
replacc-
270


## Page 279

RICO
ment,
U.S.
Attorney
Benito
Roman,
said
the
verdict
proves
that the
government
takes
perjury
"very
seriously"
Jones
was
released
on Sioo.ooo
bond
and
underwent
"psychi
atric
counseling
on the
advice
of her
lawyer."
The
Princeton-Newport
defendants
went on
trial
in
June
1989.
The
case
was
extensively
covered,
largely
because
it
was
seen
as a
bellwether
for
the
Milken
case.
The
Wall
Street
Journal,
which
generally
sides
with any
security
industry
defendants
short of
serial
killers,
came
down
hard on
Giuliani's
expansive
use
of
RICO.
In the
Jour
nal's
pages,
the
government's
actions were likened to the "I don't
have
to
show
you
any
stinkin'
badges"
law
of
The
Treasure
of
the
Sierra
Madre
or
The
Terminator
("Arnold
Schwarzenegger
couldn't
play
a
scarier
role").
One
editorialist
gleefully
quoted
from
the
Justice
De
partment's
398-page
RICO
manual,
which
warns
against"
'imagi
native'
prosecutions
under
RICO"
and
its
use
as
a
"bargaining
tool"
for plea
negotiations.
A
former
IRS
commissioner
was
willing
to
testify
on
behalf
of
Princeton-Newport.
This
was
a
subtle
issue
because
Congress
had
recently
changed
the
tax
law
so
that
both
sides
of a
hedged
trade
would
be
treated
as
short-term.
The
judge
ruled
that the
former
IRS
commissioner's
views
would
confuse
the juryand did not
allow
the
commissioner
to
testify.
"I
did
not
commit
a
crime,"
Regan
told
the
jury
"I
did
not
cheat
on my taxes, I'm totally 100 percent innocent."
The
prosecutors
hammered
on
the
petty
subterfuge
of the
trades.
Rather
than
openly
buying
back
the
securities
all
at
once,
at
the
same
price,
Princeton-Newport's
people
broke
up
the
transac
tions
and
varied
the
prices.
They
played
the
tapes
for
the
jury.
"Wel
come
to the
world
of
sleaze"
does
not
sound
like
a
man
proud
of
what he is
doing.
On
July
31,
the
jury
convicted
the
defendants
on
sixty-three
of
the
sixty-four
counts,
including
racketeering.
Regan
was
sentenced
to
six
months
in
prison
and
fined
$325,000.
These
penalties
were
271


## Page 280

fortune's
formula
lighter
than
what
the
prosecution
had
asked
for.
Andrew
Tobias,
writing
in
Time
magazine,
felt
that
"the
judge
seemed
to
be
saying
by
his
sentence
that the
U.S.
Attorneys
had
gone
a bit
wild."
For his
part,
the
judge
said
he
intended
to
give
Regan
a
three-month
sen
tence but doubled it
because
he
believed
Regan
had lied to the
court.
Thorp
put
up
a
new
dartboard
in
his
Newport
Beach
office:
a
photo
of
Rudy
Giuliani.
"When
half
the
leadership
of
your
firm
is
convicted."
Thorp told
Business
Week,
"it doesn'thelp
any."
In March 1989,
Michael
Milken wasindicted under
RICO
on rack
eteering
and
securities
fraud
charges.
A
year
later,
he
admitted
guilt
on
six
felony
charges,
paid
a
S600
million
fine,
and
was
sentenced
to
ten
years
in
prison.
By
that
time,
the
junk
bond
market
had
col
lapsed,
Drexel
Burnham
was
in
bankruptcy,
and the
1980s
were
just
about
over.
In
June
1990
Martin
Siegel
got a meretwo months'sen
tence
because
of his
cooperation.
Boesky
was
released
from
his
prison
term
in
December
1989.
After
serving
two
years
ofa
three-
year
sentence,
he
looked
like
a
slightly
sinister
depiction
of
God
himself,
with
patriarchal
beard
and
shoulder-length
gray
hair.
Regan
and
the
other
Princeton-Newport
defendants
appealed
their
cases.
All
six
convictions
were overturned on
appeal.
None of
the
Princeton-Newport
people
served
prison
time.
All
hadlost their
jobs,
and
Regan
had
paid
far
more
in
legal
fees
(about
$5
million)
than the
imposed,
then
overturned,
fines.
The one
person
who
came
out
relatively
unscathed
was
Thorp.
Yet
his fortunes had been stunted by
contingencies
that his care
ful risk
assessment
had
been
unable
to
forestall.
"The
destruction
of
wealth
was
huge,"
Thorp
observed.
The
partnership
employed
about
eighty
people
on
two
coasts.
They
managed
S272
million.
To
gether
Thorp
and
Regan
were
collecting
about
$16
million
a
year
in
general-partner
fees.
Their
own
investments
in the
fund
were
com
pounding
at an impressive rate.
Even
these
figures
pale
against
what
might
have
been.
"There
was
an
explosion
in the
hedge
fund
world
shortly
after"
Princeton-
272


## Page 281

RICO
Newport's
dissolution,
"as
far
as
money
invested
and
size
of op
portunities,"
Thorp
explained. "We could have, I think, been run
ning
a
five-
or
ten-billion-dollar
hedge
fund
easily
now."
There
is
some
psychological
truth to
logarithmic
utility
No one is so
rich
as
not to
fantasize
about
adding
another zero onto net worth. Had
Regan
only
stepped
down.
Thorp
theorizes
wistfully,
"we'd
be
billionaires."
*
The
Only
Guy
on
Wall
Street
Who's
Not
a
Rat
Expansive
use
of
RICO
makes
strange
bedfellows.
In the
lockup
at
Manhattan's
Metropolitan
Correctional
Center,
"Fat
Tony"
Salerno
ran into
portfolio
manager
John
Muiheren,
head
of
another red-hot
New
Jersey
investment
firm,
Jamie
Securities.
Af
ter
hearing
that
Boesky
had
implicated
him,
Muiheren,
who had
stopped
taking
lithium
for
manic-depressive
illness,
packed
guns
in
his
car
and
went
off
with
the
stated
intent
of
killing
Boesky.
Tipped
off
by
Mulheren's
wife,
sympathetic
local
police
stopped
Muiheren
and
took
him
into
custody.
He
was
charged
with
threatening
a
witness
in a federal case.
Giuliani's
office
offered
to
overlook
that
if
Muiheren
would
admit
to
stock
parking
and
testify
against
oth
ers. Muiheren indignantly refused.
Muiheren
and
Salerno
got
along
well.
Muiheren
had
resumed
taking his medication and had recovered his considerable charm.
Salerno
admired
Mulheren's
refusal
to
testify
against
friends.
273


## Page 282

fortune's
formula
Just
before
Muiheren
was
transferred
to a posh
psychiatric
insti
tution
in
New
Jersey,
Salerno
patted
him
on the
back.
"You're
all
right,"
Salerno
said.
"You're
the
only
guy
on
Wall
Street
who's
not
a
rat."
"But I don't
know
anything,"
Muiheren
insisted.
"I don't
have
anything
bad to
tell
them."
"Oh,
yeah,"
Salerno
said,
rolling
his
eyes.
"Right."
274


## Page 284

*
Martingale
Man
Gambling
ran
in
John
Meriwether's
family.
As
a
boy,
he
learned
blackjack
from
his
grandmother
and
was
permitted
to
place
bets
at
the
racetrack
and
on
sports.
Always
looking
for
an
edge,
John
would
check
the
weather
forecast
for
wind
velocity
at
Wrigley
Field
and
use
that to
decide
how
to beton
Cubs
games.
Born
in
Chicago
in
1947,
Meriwether
was
a
bright,
mathemati
cally
inclined
kid
educated
by
priests.
He attended
Northwestern
University
on a
scholarship
for
golf
caddies.
Meriwether
taught
a
year
of
high
school
math,
then
got
a
business
degree
at the
Univer
sity
of
Chicago.
His
first
job
out
of
business
school
was
trading
government bonds at Salomon Brothers in New
York.
Pre-Milken,
bonds
were
pretty
boring,
and
government
bonds
the
most
boring
of
all.
Meriwether
found
much
to
keep
his
interest.
New
York
City
came
close
to
defaulting
on
its
bonds.
The
bond
market
panicked,
and all government bonds took a hit. Meriwether reasoned that
New
York's financial woes were
irrelevant
to the
credit
of
mu
nicipalities
elsewhere.
He
therefore
bought
government
bonds
at
bargain
prices,
expecting
to
see
them
rebound.
When
they
did,
Meriwether
suddenly
looked
like
a
genius.
In
1977
Meriwether
started
Salomon's
Arbitrage
Group.
This
was
bond
arbitrage,
and
it
became
the
firm's
biggest
profit
maker.
A shy
man,
Meriwether
gained
a share of
fame
in
Michael
Lewis's
1989
memoir.
Liar's
Poker.
It
was
Meriwether
who
bluffed
his
way
out
of a
high-stakes
game
of
liar's
poker with
Salomon
chairman
John
277


## Page 285

fortune's
formula
Gutfreund. In fact
Meriwether's
tastes ran more to horse
racing.
He
boarded racehorses on his 68-acre estate in North Salem, New
York,
and at
Belmont
racetrack.
To
hedge
the bets he
made
ever)'
working
day,
Meriwether
kept
a
set
of
rosary
beads
in
his
briefcase.
Meriwether
left
Salomon
Brothers
during a
scandal-driven
shake-up
in
which
Meriwether
was,
it
appears,
innocent
of
wrong
doing.
He
decided
to
start
a
hedge
fund.
It
was
a
good
time
to
do
that.
Princeton-Newport's
long
run
had
convinced
many
wealthy
investors
of
the
possibility
of
beating
the
market
while
containing
risk
scientifically.
Scores
of
new
hedge
funds
were
started
in the
early
1990s.
Of
all
these
new
funds,
Meri
wether's
Long-Term
Capital
Management
was
to
become
the
best
known.
Ed
Thorp
first
heard
of
Meriwether's
fund
through
a
mutual
friend.
The
friend
knew
some
of the
people
who
were
writing
soft
ware
for the new
fund.
"It's
gonna
be a great
investment,"
Thorp
was told, "and for ten million dollars you can get into it."
Like
most
of the
new
group
of
fund
managers,
Meriwether
promised
better-than-markct
returns
through
science
and
software.
Meriwether
did not
himself
possess
a
first-rate
mathematical
mind.
Instead,
he
recruited
the
top
academic
talent.
No
finance
professor
was
more
respected
than
Robert
C.
Merton.
Merton
had
consulted
for
Salomon
Brothers,
so
Meriwether
already
knew
him.
He
agreed
to come on board. Meriwether's
other
great coup was recruiting
Myron
Scholes.
As
journalist
Roger
Lowenstein
said,
that
was
like
putting
Michael
Jordan
and
Muhammad
Ali
on
the
same
team.
Thorp
decided
not to put
any
of
his
money
in the
fund.
He
was
concerned that Merton and
Scholes,
brilliant as theywere,had little
experience
investing
other
people's
money
It
didn't
help
that
Mer
ton
was
second
only
to
Samuelson
asa
critic
of the
Kelly
criterion.
Thorp
also
had
heard
that
Meriwether
was
a
"martingale
man."
"The
general
chatter
was
thathe
was
a
high
roller,
and
it
wasn't
clear
that the
size
of
his
bets
were
justified,"
Thorp
recalled.
"The
story
was
that
if
he
got
in
the
hole,
if
things
went
against
him,
he'd
bet
more.
If
things
still
went
against
him,
he'd
bet
more."
278


## Page 286

Blowing
Up
Kicking
and
Screaming
Long-Term
Capital
Management
(LTCM)
was
the first
fund
to
raise
a
billion
dollars.
It
did
this
by
projecting
a
30
percent
annual
return
netof
fees—better
than
even
Princeton-Newport
had
done.
LTCM's
partners
charged
25
percent
of
profits
(rather
than
the
usual
20)
plus
I
percent
of
invested
assets
per
year.
The
25
per
cent
fee was a
deal-breaker
for the
trustees
of
the
Rockefeller
Foun
dation,
who
decided
they
did not
have
that
kind
of
money
to
burn.
Other
wealthy
and in
some
cases
glamorous
investors
didn't
seem
to
mind.
Flarvard
University,
which
had had
money
in
Princeton-
Newport,
put some in
LTCM.
LTCM
investors
ranged
from
Mer
rill
Lynch
to the
Kuwaiti
state
pension
fund,
the
Bank
of
China
(the
People's
Republic
of
China)
to
Hollywood
agent
Mike
Ovitz.
LTCM
hit the
ground
running
in
March
1994.
By
the end of the
calendar
year,
its
investors
had
racked
up a 20
percent
return af
ter
fees.
In
1995
the return
was
43
percent
after
fees.
The next
year,
it
was
41
percent.
These were good years for the stock market, too. The S&P 500
sprinted
34
percent
in
1995
andanother20
percent
in
1996.
LTCM
was
9 and
21
pointsaheadof
these
already
rich
returns.
Zillionaires
were
begging
Meriwether
to
take
their
money.
It
didn't do them much
good.
The fund
was
closedto new investment.
Some
people
were
so
desperate
to own a
piece
of
Wall
Street's
hottest property that
gray-market
LTCM shares sold for about
IO
percent
above asset value.
279


## Page 287

FORTUNE'S
FORMULA
In
1997
LTCM
made
a
17
percent
return after
fees.
That is su
perb
by
any
reasonable
standards,
but
1997
was
not
an
especially
reasonable
year.
The
S&P
500 shot up
31
percent.
By
October
1997,
the
fund's
capital
had
mushroomed
from
$1.2
billion to
$7.1
billion. After the lukewarm 1997 showing, Meri
wether
decided
to return the
money
of
some
of his
investors
in the
hope
of
boosting
future
performance.
Fortune
magazine
reported
that
"many
went
kicking
and
screaming,
and
at
least
one
protested
so
angrily
that
LTCM
allowed
him
to
stay
onboard."
By
the end of
December,
the hind's
capital
was
down to
S4.7
billion.
LTCM's
trading
strategics
were
secret.
It is
startling
how
much
money
Meriwether
was
able
to
raise
while
disclosing
almost
nothing
about what he intended to do with it. One thing
was
disclosed.
LTCM
used
a lot of
leverage.
That
was
how
they were
able
to ob
tain
better-than-market
returns from a nearly efficient market.
Adherents of the
efficient
market
hypothesis
generally
allow
that
small
mispricings
can
arise
and
persist
because
they're
too
small
for
anyone
to bother
with.
The
transaction
costs
would
eat up
any
profit.
LTCM's
strategy
was
to
use
leverage
to
multiply
these
small
profit
opportunities
to the point
where
they
were
big
enough
to
matter.
Paul
Samuelson
said he had
doubts
about
LTCM
when
he
first
heard
of it. It
appeared
that the
fund
was
placing
a lotof
faith
in the
random-walk
model.
The
leverage
left little room for any
misfit
of
theory
and
reality.
Myron
Scholes,
however,
threw
himself
into
his
new
role
as
hedge
fund
pitchman.
In
presentations
to
potential
in
vestors, Scholes said they were vacuuming up nickels no one else
could
see.
As he said this he
would
snatch an
imaginary
nickel
out of
the
air.
The coreof
LTCM's
business
was
convergence
trades,
the
long-
and-short
hedged
trades
that
many
other
hedge
funds
ran.
LTCM
favored
government
bonds,
the area
where
Meriwether
had such
success
at Salomon Brothers. One type of trade was known as "on
the run, off the run." A brand-new thirty-year
U.S.
Treasury bond is
said to be "on the
run."
It costs$10,000 and is good for a
full
thirty
years
of
semiannual
interest
payments
and
repayment
of the origi-
280


## Page 288

Blowing
Up
nal $10,000 at the end of that
time.
An older bond, with some of
the
interest
payments
already
made,
is
"offthe
run."
The
market
price
of
an
older
bond
depends
on
a
lot
of
things,
most
important
the
current
interest
rate.
Meriwether
had found that
off-the-run
bonds
were
usually
a
bargain
compared
to
new
bonds.
As
with
cars,
people
pay
an
irrational
premium
for
the
shiny
new
models.
Once
you
drive
a
car
off
the
lot—once
a
bond
becomes
last
year's
model-
it
takes
a hit in
price.
Meriwether's
people
bought
older bonds and sold short brand-
new
bonds.
Then
they
waited
for
the
prices
of the
two
bonds
to
converge.
In time, the new
bonds
would
become
"old"
and
move
closer
in
price
to
the
old
bonds.
When
this
happened,
they
could
re
alize
a
minuscule
profit.
It
took
leverage
to
inflate
this to the
kind
of
sky-high
returns
investors
were
expecting.
In
1996
oneof
LTCM's
investors
spoke
by
phone
with
several
of
the
partners.
The
investor
asked
exactly
how
much
return
they
were
making
on the
dollar.
The
answer
was
67
basis
points.
The
return
was
0.67
percent.
The
LTCM
investor
also
learned
that
the
fund
was
using
lever
age
of
about
thirty
times.
For
every
dollar
of
investor
money,
the
fund
borrowed
S29
more.
This
meant
that
the
fund
achieved
thirty
times
the
profit.
After
paying
offthe
lender,
it
had
thirty
times
the
O.67
percent
profit
on the
original
dollar,
or 20
percent.
Despite
their
value
in
selling
the
fund,
Merton
and
Scholes
played
modest
roles
in
the
day-to-day
decision-making.
The
fund's
investors
surely
understood
that neither great
scholar
sat at a desk
barking
trades into a
phone.
It is
less
clear
whether
investors
believed
that
the
two
famous
economists
had
created
the
hind's
detailed
financial
models
(they
had
not).
One LTCM road-show presentation was held at the insurance
company Conseco in
Indianapolis.
Andrew Chow,a Conseco deriv
atives
trader,
interrupted
Scholes.
"There
aren't
that
many
oppor
tunities,"
Chow
objected.
"You
can't
make
that
kind
of
money
in
Treasury markets."
Scholes
snapped:
"You're
the
reason—because
of
fools
like
you
we
can."
281


## Page 289

fortune's
formula
Traveling
with
Scholes
were
some
Merrill
Lynch
people
who
were
experts
in
raising
investment
funds.
They
advanced
the
expert
opinion
that
Scholes
should
apologize.
Another
LTCM
partner,
Greg
Hawkins,
doubled
up
with
laughter.
Conseco
did
not
invest
in
LTCM.
I've
Got
a
Bad
Feeling
About
This
Thirty
times
leverage
sounds like a lot. On many
of
the
fund's
positions,
the
leverage
was
higher
than
that—effectively
in
finite.
As
much
as
possible,
LTCM
tried
to
operate
like
an
info-
mcrcial
real
estate
guru
who
walks
into a
city
without
a
dollar
in
his
pocket,
buys
real
estate
on
credit,
and
makes
a
positive
cash
flow—all
with "no
money
down."
When you don't
have
to put up
any
money,
you
make
a
return
on
investment
of
infinity.
Or
negative
infinity,
when things go
wrong.
When a trader
buys
on
credit,
the
securities
arc
themselves
col
lateral.
The bank or other lender hasa right to
repossess
the securi
ties
and
sell
them
in
the
event
of
a
serious
loss. Because
securities
can drop in
value
quickly,
this
right
might
not be
enough
to protect
the lender's interests. The trader is therefore normally required to
put up a
down
payment
called
a
"haircut."
It
works
much
like
the
down
payment
on a
house.
When
you
put up 20
percent
of the pur
chase
price
of a
house,
the
bank
can
be
reasonably
confident
that it
will
be
able
to
sell
the
property
for at
least
the
amount
of the
80
percent
mortgage.
The
bank
will
not endup
with
a
loss.
282


## Page 290

Blowing
Up
Haircuts
are
also
required
when
selling
short.
A
short-seller
can,
theoretically,
lose
an
unlimited
amount
of
money.
Collateral
is
required
to
protect
against
that,
too.
Since
all
long-short
hedged
trades
involve
selling
short,
collateral
requirements
are
an
integral
part of the
game,
even
when
leverage
isnot
used.
The
size
of
the
haircut
depends
on
security
law,
the
type
of
secu
rities
being
bought
or
sold,
and
the
trader's
credit
and
negotiating
skills.
Investment
banks
routinely
borrow
99
percent
of the
cost
when
purchasing
treasuries.
This
is
one
hundred
times
leverage,
and
it is not
necessarily
considered
reckless.
It
was
a point of
pride
with
LTCM's
people
that
they
paid
zero
haircuts
on
many
of
their
deals.
This
is
testimony
to the
fund
man
agement's ability to romance creditors.
Zero
haircuts
do
not
change
the
facts
of
life.
LTCM
was
simply
in the
position
ofa
gambler
who
goes
to a
casino
where
the pit
boss
extends
him
unlimited
credit.
You
might take the position that with unlimited credit it's irrele
vant
how
much
money
you've
got in
your
pocket
or
bank
account.
The
more
you
bet,
the
more
you
win.
Therefore
any
wager,
no
mat
ter how
high,
is
justified.
This argument might hold water in the caseof a casinowith lit
erally
unlimited
credit
and
bet
size.
You
wouldn't
even
need
an
edge
in a
casino
likethat.
Martingale
would
work.
In the
real
world,
"unlimited
credit"
is
a
figure
of
speech.
What
thepit
boss
means
is
roughly:
"I
know
this
guy,
and
he's
okay.
Don't
bother
running
a
credit
check.
Let
him
start
gambling
right
away.
Of
course,
check
with
me
if
he
wants
alotof
money
oris
losing
heavily"
The pit
boss
has
no
intention
of
lending
more
money
than
the
casino can readily collect, should it come to that. So it was
with
LTCM's
banks.
A
home
buyer
puts
up
a
down
payment
only
once.
A
hedge
fund's
collateral
requirements
are
constantly
adjusted.
Each
day,
the
value
of the
account
is
recomputed
at
current
prices
("marked
to
market")
and
collateral
figured
from
that.
When
the
value
of
the
account
rises, the
trader
is allowed to
withdraw
collat
eral from the margin account. When the value of the account
falls,
the
bank
demands
that
more
collateral
be put in the
account.
283


## Page 291

fortune's
formula
Should the trader be
unable
to do this, the bank may sell some of
the
account
to
raise
collateral.
LTCM
had
a
sophisticated
system
for
handling
collateral
re
quirements.
When
a
particular
trade
showed
a
profit,
less
collateral
was
required.
This
money
could
be
withdrawn
and
wired
to
meet
the
collateral
requirements
of a
losing
trade.
One
term
for
gambler's
ruin
among
traders
is
blowing
up.
To
blow
up
an
account
is to
lose
everything
in
high-risk
trades
with
borrowed
money
A
stellar
career
can
end
in a
few
miserable
days
or
hours.
Blown-up
traders
are
Wall
Street's
undead.
They
have
failed
at the
most
important
judgment
a
trader
can
make,
namely
how
much
money
to
commit
to a
risky
trade.
LTCM's
people
were
well
aware
that
multiplying
profits
through
leverage
also
multiplies
risk
of
ruin.
They
told
investors
that
they
had risk under control through their
financial
engineering.
LTCM
used
a
sophisticated
form
of the
industry
standard
risk
reporting
system,
VaRor
"Value
at
Risk."
After the
Black
Monday
crash
of
1987,
investment
bank J.
P.
Morgan
became
concerned
with
getting
a
handle
on
risk.
Deriva
tives,
interest
rate
swaps,
and
repurchase
agreements
had
changed
the
financial
landscape
so
much
that it
was
no
longer
a
simple
thing
for
a
bank
executive
(much
less
a
client)
to
understand
what
risks
the
people
in the
firm
were
taking.
Morgan's
management
wanted
an
executive
summary.
It
would
be a numberor
numbers
(just not
too
many
numbers)
that
executives
could
look
at
every
morning.
Looking
at the
numbers
would
reassure
the
execs
that
the
bank
was
not
assuming
too much
risk.
Two
of
Morgan's
analysts.
Til
Guldimann
and
Jacques
Longer-
staey,
devised
Value
at
Risk.
The
concept
is
as
simple
as
it
can
be.
Compute
how
much
a
portfolio
stands
to
lose
within
a
given
rime
frame,
and with what
probability.
A
VaR
report
might
say
that there
is a
i-in-20
chance that a portfolio
will
lose
$1.64
million
or more in
the next dayof
trading.
Want more
numbers?
VaR's
got as many numbers as you want.
284


## Page 292

Blowing
Up
Make
a
spreadsheet.
The
cells
of
the
spreadsheet
arc
the
possible
losses,
for
different
time
periods
or
various
thresholds
of
likelihood.
Throw
in
color
charts,
print
it
out
on
the
good
paper,
and
hand
it to
the
client.
Morgan's
management
liked
the
idea.
Practically
everyone
else
did,
too.
Other
banks
began
hiring
"risk
managers"
to
prepare
daily
VaR
reports.
The
Basel
Committee
on
Banking
Supervision—head
quartered in the city of the
Bernoullis—endorsed
VaR
as a meansof
determining
capital
requirements
for
banks.
VaR
migrated
downstream
to
private
investment
managers.
By
calculating
VaR,
a
money
manager
shows
the
client
that
she
is
seri
ousabout
managing
risk.
She's
got it
all
down
in
numbers,
and
num
bers
are
good,
right?
When
the
investor
scans
the
figures
and
raises
no
fuss,
he
has
implicitly
signed
off on
those
risks.
Should
some
thing
terrible
happen
later
on,
the
money
manager
can
always
pull
out
the
VaR
report,
point
to
cell
D18,
the
5
percent
risk
ofa
37
per
cent
loss.
As
a
ritual
between
portfolio
manager
and
client,
calculat
ing
VaR
is
not
such
a
bad
idea
in
a
litigious
society
where
many
well-off peopledon't know much math.
In
October
1994,
LTCM
sent
its
investors
a
document
compar
ing
projected
returns to
risks.
One reported
factoid:
In order to
make a 25 percent annual return, the fund would have to assume a
1percent
chance
of
losing
20 percentor moreof the
fund's
value
in
a year. A
20-percent-or-more
loss was the
worst
case
considered.
The chapteron
Value
at
Risk
in the
popular
finance
textbook
Paul
Wilmott
Introduces
Quantitative
Finance
begins
with
a
cartoon
of the
author
shrugging.
"I've
gota
bad
feeling
about
this
. .
."
he
says.
Wilmott
isn't
alone.
There are at
least
two
problems
with
VaR.
One is that it
plays
into the
mystique
of
numbers.
The
consumer
of VaR reports is led to
believe
that the numbers are
reliable
be
cause
smart
people
have
gone to a lot of
trouble
to work them
out.
The
numbers
are
only
as
good
as
the
assumptions
underlying
them.
When
the
assumptions
arc
bad,
VaR
is
a
case
of
garbage
in,
garbage out.
285


## Page 293

fortune's
formula
The
other
problem
exists
even
when
the
assumptions
and
num
bers
are
right.
VaR
does
not
tell
you
everything
you
ought
to
know
about
risk.
It
sidesteps
the
two
questions
that
are
central
to
John
Kelly's
analysis:
What
level
of
risk
will
lead
to
the
highest
long-run
return?
What
is
the
chance
of
losing
everything?
(A
VaR
report
could
address
the
second
question.
In
practice
it
rarely
does.
Who
wants
to freakout the client with scare
talk?)
Every
Tuesday
at
LTCM's
Greenwich,
Connecticut,
headquar
ters,
the
fund
management
held
a
meeting
on
risk.
These
meetings
centered
on
printouts
from
a
top
secret
program
called
the
"Risk
Aggregator."
Most
of
the
fund's
employees
never
saw
these
reports,
and
apparently
none
of the
investors
did.
The
Risk
Aggregator
was
capable
of
diverse
what-if
calculations.
"We
spent
time
thinking
about
what
happens
if
there's
a
magnitude
ten
earthquake
in
Tokyo,
what
happens
if
there's
a
35
percent
one-
day
crash
in
the
U.S.
stock
market,"
said
LTCM's
David
Modest.
"We
certainly
spent
hours
and
hours
thinking
about
it."
According
to
Modest,
the
worst-case
outcome the model ever projected
was
a
loss
of
$2.5
billion,
or about half the
fund's
capital.
In the end, peo
ple
shrugged
and
went
back
to
their
trading.
♦
Thieves'
World
After
the
fall
of
communism,
billions in
Western
money
flowed
into
Russia.
With the
money
camedaring and opportunistic
Westerners,
many
of
them
Americans
of
Russian
Jewish
descent.
This
reverse
exodus
included
Ivan
Boesky
and Caesar
Kimmel.
286


## Page 294

Blowing
Up
Boesky
volunteered
his
expertise
in
guiding
Russia
into
a
market
economy.
Kimmel
managed
one
of
Moscow's
new
gambling
casinos.
As
in
America,
Russia's
casinos
had
links
to
organized
crime.
Unlike
in
America,
the
banks
did
too.
Many
of
those
who
started
Russian
banks
were
gangsters
of the
vorovskoi
mir—"thieves'
world,"
also
known
asthe
Russian
Mafiya.
In
July
1998,
the
International
Monetary
Fund
made
a
S17
bil
lion
loan
package
to
Russian
banks.
It
has
been
reported
that
about
S4.5
billion
of this
money
was
quickly
wired
to
mobsters'
offshore
bank
accounts.
The
thug-controlled
banks
had
no
intention
of
repaying
many
of
the
Western
loans.
The
Russian
treasury
was
scarcely
more
credit
worthy.
The
U.S.
Treasury
has
such
a
flawless
credit record that
economists
often
fall
into
the
error
of
identifying
its
bonds
with
the
"risk-free"
investment
of
theory.
No one
made
that
mistake
in
Rus
sia.
Russia's
treasur)'
bonds,
called
GKOs,
were
the
junkiest
of
junlc
bonds,
paying
40
percent
interest
and
up.
About
halfof
Russia's
tax
collections
went to
pay
interest
on
treasur)'
debt.
LTCM's
Greg
Flawkins
devised
an
ingenious
trade that let the
fund
collect
rich
interest
at
GKO
rates
yet
get
paid
in
American
dollars.
Hawkins
had
no
illusions
about
the
Russian
treasury
or the
mob-controlled
Russian
banks.
He
arranged
things
so
that
LTCM
had
no
direct
contact
with
these
dubious
parties.
LTCM
dealt
only
with
Western
banks, which in turn dealt with the Russians.
The
Russian
banks
were kept at a
remove
from
LTCM,
like
viruses
in a
hazmat
chamber.
Hawkins
began
running
this
trade
in
1997
By
August
1998,
the
GKOs
were paying
70
percent
interest.
Then,on
August
17,
Prime
Minister
Sergei
Kiriyenko
announced
that
Russia
was
devaluing
the
ruble and defaultingon the GKOs.
LTCM
instantly
lost
millions.
It
had
reason
to
count
itself
lucky
Others
did
worse.
One
was
a
hedge
fund
accurately
called
High-Risk
Opportuni
ties
Fund
(HRO).
HRO
was
running
many
of
the
same
strategies
LTCM did, including a version of its Russian GKO trade. The
Russian
default came on a
Monday.
HRO was in default of its own
287


## Page 295

FORTUNE
S
FORMULA
obligations
by
Wednesday.
It
was
rumored
(apparently
incorrectly)
that Lehman Brothers had suffered steep lossesin
Russia,
too.
The
real
and
imagined
problems
set off a
medium-size
panic.
The
big
investment
banks
pulled
out of
Russia.
It
was
a
"flight
to
quality."
Everyone
wanted
to
shift
funds
from
riskier
investments
in
developing
economies
to
safer,
more
liquid
investments
in
the
United States and Western Europe.
This
psychological
reaction
was
much
like
the
one
that
had
caused
New
York
City's
near-default
to
depress
municipal
bonds
nationwide. But Meriwether was not profiting this time. LTCM's
overarching
philosophy
was
that
people
pay
too
much
for
safe
and
liquid
investments.
The
Russian
default
temporarily
changed
that.
This hurt not only the
Russian
trades
but
much
of
LTCM's
port
folio.
By
the end of the
week,
LTCM
had
shed
$551
million.
It
des
perately
needed
collateral
to
cover
too
many
simultaneous
losing
trades.
Positions
were
liquidated
at a
loss.
The
fund
tried to
raise
money from Warren Buffettand George
Soros.
Meriwether
spoke
with a trusted
friend,
Vinny
Mattonc,
for
merly
of
Bear
Stearns.
"Where
are
you?"
Mattone
asked.
"We're
down
by
half,"
Meriwether
answered.
"You're
finished,"
Mattone
said.
"Whatare
you
talking
about?
We
still
have
two
billion.
We
have
half—we
have
Soros."
"When
you're
down
by
half,"
Mattonc
explained,
"people
figure
you
can
go
down
all
the
way.
They're
going
to
push
the
market
against
you.
They're
not
going
to
roll
your
trades.
You're
finished."
As Mark Twain wrote,
"A
banker is a fellowwho lends you his um
brella when the sun is shining but wants it back the moment it
rains."
LTCM's creditors stopped lending new money and insisted
that the
fund
put up
cash
(safe
securities)
to protect the
lenders
from
further
exposure.
In late
August,
Meriwether
called
Merrill
Lynch
chairman
Herb
Allison
to
ask
for
S300
to
$500
million
in
288


## Page 296

Blowing
Up
additional
funds.
Allison's
answer
was,
"John,
I'm not
sure
it's in
your
interest
to
raise
the
money
It
might
look
like
you're
having
a
problem."
The
gambler
using
borrowed
money
must
determine
how
much
he can
lose
without
touching
off a
disastrous
chain
of
misfortunes
from
which
recovery
is
impossible.
"When
they
first
started
losing,"
observed
Jarrod
Wilcox,
"obviously
they
had
less
discretionary
wealth
so
they
should
have
pulled
down
their
leverage
multiple.
In
stead,
they
allowed
the
leverage
to
drift
up to
like
sixty
times.
That's
a
horrible
mistake.
No
Las
Vegas
gambler
would
ever
make
that
mistake—no
surviving
one."
As
word
of the
hind's
troubles
spread,
a lot of
people
started
worrying.
The
U.S.
Federal
Reserve
feared
that an
LTCM
collapse
might
imperil
the
whole
market
economy.
The
Western
world's
biggest
investment
banks
were
partners
in
LTCM's
trades.
The
first
outsider
to
view
the
Risk
Aggregator
was
Peter
Fisher
of
the
Federal
Reserve
Bank
of
New
York.
In
an
emergency
Sunday
meeting
on
September
20,
LTCM's
Larry
Hilibrand
handed the
printoutto
Fisher.
As
Fisher
read
it, he
was
appalled.
The document
was
relatively
simple.
It
summarized
all
of
LTCM's
positions,
reporting
the
potential
loss
in a
"one-year
storm"—the
loss
if
rates
or
prices
went
the
wrong
way
by
an amount
equal
to the
average
volatility
experienced
in a
year.
That
was
the
worst- and only-case scenario shown.
One of the
shockers
was
the
fifth
entry It
was
labeled
"USD_Swap
Spread."
This
reported
trades
making
a
"bet"
on the
swap
spread
rate in the
U.S.
dollar.
The
annual
volatility
of
this
spread had been
15
basis
points.
The
hind's
potential
loss,
should
the spread
change
15
basis
points,
was
a
staggering
S240
million.
This
floored
Fisher
because
the
U.S.
swap
spread
had
already
moved
40
basis
pointsin the
first
eightand a halfmonthsof
1998.
This
was
just the
fifth
entry on the
first
page.
There wereabout
twenty-five
entries
per
page,
and
it
was
a
fifteen-page
document.
As Fisherscanned the report, he had another
shock.
LTCM was
simultaneously
making
nearly
the same bets allover the
world.
This
289


## Page 297

FORTUNE'S
FORMULA
was
supposed
to
be
diversification,
but
it
wasn't.
The
default
in
Rus
sia
affected
credit
all
over
the
world.
According
to
another
document
Fisher
was
shown,
the
largest
banks
and
brokerages
that
LTCM
did
business
with—among
them
Merrill
Lynch,
Goldman
Sachs,
Morgan,
and
Salomon
Brothers-
would
lose
something
like
$2.8
billion
if
LTCM
suddenly
failed.
This
figure
was
candy-coated,
too,
Fisher
believed.
All
of
these
firms
were
counting
on
income
streams
from
LTCM
that
would
suddenly
dry
up
if
the
fund
failed.
The
banks
would
rush
to
seize
such
collat
eral as
existed
and
sell
it,
causing
prices
to
plunge.
Fisher
guess-
timated the real loss at $3 to
S5
billion. "I'm not worried about
markets
trading
down,"
he
said.
"I'm
worried
that
they
won't
trade
at
all."
Wednesday,
September
23,
1998,
was
effectively
LTCM's
last
day
of
operation
as
a
free
agent.
The
U.S.
Federal
Reserve
Bank
of
New
York
convened
a
meeting
of
banks
and
investment
firms
that were
counterparties
to
LTCM's
trades.
The
consortium,
as
they
called
it,
agreed
to put a
total
of
$3,625
billion
into
the
fund.
They
were
not
buying
out the
original
investors,
who
continued
to
own
their
much-devalued
investments.
They
were
investing
in the fund until
its
positions
could
be
slowly
and
safely
dismantled.
LTCM had lost S4.4 billion from its peak asset
value—about
90
percent.
The
fund's
partners
alone
had
dropped
about
Si.8
bil
lion.
That
was
roughly
what their
investment
in the
fund
had been
worth earlier in the
year,
and now it had
shriveled
to
S28
million.
It's
said
that
Merton
lost
as
much
as
$100
million
and
that
he
was
especially
mortified
at
having
talked
Harvard
into putting en
dowment
funds
into
LTCM.
Many
of the partners had
substantial
fortunes before LTCM that they
rolled
over into the fund. Larry
Ililibrand
was
said to be in tears at one
meeting.
He had taken out a
personal
loan
of $24
million
from
Credit
Lyonnais
to
increase
his
stake in the
fund.
He
was
using
leverage
to buyhis own fund,
which
was
itself
operating
at
nosebleed
leverage
levels.
Hilibrand's
net
worth went from over something
like
SlOO
million
to $20
million
290


## Page 298

Blowing
Up
in
debt.
Hilibrand
requested
that
the
bailout
cover
his
personal
debts.
The
consortium
said
no.
Warren
Buffett
marveled
at
how
"ten
or
15
guys
with
an
average
IQ_of
maybe
170"
could
get
themselves
"into
a
position
where
they
can lose all their
money."
That
was
much the sentiment of Daniel
Bernoulli, way back in
1738,
when he wrote:
"A
man who risks his
entire
fortune
acts
like
a
simpleton,
however
great
may
be the
possi
ble
gain."
Fat
Tails
and
Frankenstein
The
PRESS
TORE
into LTCM and most especially its newly
minted (1997) Nobel laureates Merton and
Scholes.
"Rocket Sci
ence
Blew
Up on the
Launching
Pad,"
went a
Business
Week
headline.
For
Michael
Lewis
in
The
New
York
Times
Magazine,
the story
was
"Flow
the
Eggheads
Cracked."
Fortune
suggested
that the two No-
belists
had
"swapped
their
laurels
for the
booby
prize
of the
finan
cial
markets,
which
is the
ignominy
of being
largely
wiped
out and
viewed as bumbling
losers."
Journalists
offered three
reasons
for the
downfall:
leverage,
fat
tails, and hubris. None wasan entirely satisfyingexplanation.
LTCM's
web
of
interlocking
trades
was
so
complicated
that its
official
leverage
figures
don't
tell
much.
The fund said it had a lever
age
ratio of
25.6
at the end of
1996.
That
was
less
than the
leverage
ratio of
Morgan
Stanley
(26.5),
Lehman
Brothers
(332), and
Salo
mon
(42.5).
None of the banks
imploded.
They didn't
because
their
portfolioswere
less
volatile
and/or theyhad the
resources
to wait out
291


## Page 299

FORTUNE
S
FORMULA
convergence
trades.
Leverage
is
not
always
bad.
You
cannot
even
say,
asa
general
rule,
that
thirty
times
leverage
is
always
bad.
It
depends.
LTCM
put "fat
tails"
in the
semipopular
lexicon.
The term
comes from the form of a bell-shaped
curve.
If you graph the prob
ability
distribution of
typical
security
price or interest rate move
ments,
you
get a
bell-shaped
curve
approximating
the
normal
distribution of statistics
classes.
On closer inspection, the curve has
"fat
tails."
The leftand
right
ends
of the
curve
(the
rim
of the
bell)
do not hugthe
baseline
so
tightly
as in a true
normal
distribution.
This
simply
means that big
price
or rate
movements—Mcrton's
flealike
jumps—are
much
more
common
than in a true
normal
dis
tribution. A "fat tail" is thus an event that would be fantasticallyrare
if it occurred by the
usual
workings
of
chance,
but
which
is
actually
more
common.
You
go your
whole
life without seeing a mime on a
unicycle,
then one
day
you
stand in linebehind three of them at the
local
Starbucks.
Explanation:
The circus is in town.
Thorp found that LTCM had
based
some of its models on a
mere four
years
of data. In that short period, the spread between
junk bonds and
treasuries
hovered
in the
range
of 3 to 4 percentage
points. The fund
essentially
bet that the spread would not greatly
exceed
this
range.
But as
recently
as 1990, the spread had topped
9
percent.
"People
think that if
things
are
bounded
in a certain
historical
range,
there's
necessity
or
causality
here,"
Thorp
explained.
Of
course, there's not. In 1998, when the spread widened suddenly to
6 percent, "they said this
was
a one-in-a-million-yearevent. A year
or two later, it got
wider,
and two
years
after that, it got wider
yet."
The hubris theory
was
the most
irresistible
of
all.
For a
few
years,
LTCM's
people
were
the
cool
clique
in the
high
school
of
Wall
Street. Fewcould resist takingdelightin the humblingof the stuck-
up.
Asto the natureof the
hubris,
mostof the
reportage
saw
it as the
latest installment in the Frankenstein myth. The computer geeks
who had taken over finance made the fatal mistake of placing too
much faith in their
machines.
Exposed
to the contagion
of
human
unpredictability, the models withered. Roger Lowenstcin's best-
sellingbook
When
Genius
Failed
charged
that Merton and
Scholes
292


## Page 300

Blowing
Up
had
forgotten
the
predatory,
acquisitive,
and
overwhelmingly
protective
instincts
that
govern
real-life
traders.
They
had
for
gotten the
human
factor.
Or
as Nicholas
Dunbar
wrote in
Inventing
Money,
When the
young
Fis[c]her
Black
had
crossed
the
Charles
river
bridge
to
work
with
Scholes,
29
years
earlier,
the
film
2001:
A
Space
Odyssey
was
in
the
movie
theatres.
In that
film,
a
computer,
HAL[,]
runs
amok
and
tries
to
kill
the
hero.
LTCM's
computer
ized
money
machines
had
also
gone
berserk,
and
had
destroyed
their
creators.
Survival
Motive
As
APPEALING
AS
the
Frankenstein
image
may
be,
it is
hard
to
draw
a
practical
moral
from
it.
Portfolio
managers
are no morego
ing
to
abandon
computer
models
than
mobile
phones.
Software
is
just
a
tool
for
implementing
policies
that
humans
have
decided
are
reasonable.
Probably
the
best
single-word
explanation
for
what
went
wrong
at
LTCM
is
overbetting.
Overbetting
(unlike
leverage,
fat
tails,
or
even
a
certain
amount
of
healthy
self-esteem
a.k.a.
hubris)
is
al
ways
bad.
Overbetting
is
a
concept
from
gambling,
not
standard
economic
theory.
Its
role
in
the
LTCM
debacle
was
hard
to
ignore,
with
two
Nobel
laureates
crawling
out of the
wreckage.
Since
1998
the
aca-
293


## Page 301

FORTUNES
FORMULA
demic
world
has
studied
LTCM's
collapse
exhaustively
After
years
of
relative
neglect,
arbitrage
and
hedge
funds
have
become
objects
of
serious
study.
Some
of the
analyses
of
LTCM's
downfall
invoke
formerly
taboo
concepts
like
overbetting
and
the
capital
growth
criterion to address the question of how much risk is "too much."
Among
the
small
group
of
Kelly
economists
and
money
man
agers,
the
rhetoric
is
stronger
yet.
In
several
articles,
portfolio
man
ager
Jarrod
Wilcox
offers
a
sweeping
vision
in
which
overbetting
is
behind
many
of the
world's
financial
ills—not
only
LTCM
but
Enron,
debt-financed
telecommunications
industry
overexpansion,
and
the
1987
failure
of
portfolio
insurance
on
Black
Monday.
In a
2003
issue
of
Wilmott
magazine,
Thorp
linked
the
LTCM
collapse
to
Merton
and
Scholes's
intellectual
critique
of
the
Kelly
system:
"I
could
see
that
they
didn't
understand
how
it
controlled
the
danger
of
extreme
risk
and
the
danger
of
fat-tail
distributions,"
Thorp
said.
"It
came
back
to
haunt
them
in a
grand
way."
Could
Kelly
money
management
have
prevented
the
LTCM
disas
ter? It is
easy
to see the
appeal
of the
Kelly
philosophy.
In a
world
where
return
is
so
highly
valued,
people
will
always
be
tempted
to
venture
out onto the
precipice.
The
Kelly
criterion
tells
exactly
how
far
a
trader
can
go
before
tumbling
into
the
abyss.
Mean-variance
analysis
and VaR do not.
In the
most
direct
human
terms,
LTCM's
problem
was
group-
think.
Under
John
Meriwether,
there
was
an
organizational
culture
in
which
questions
of
risk
were
pressed
only
so
far.
This
appears
to
have
led
to
systematically
rosy
projections.
Too
little of the
fund's
brainpower
went
to
skeptical
probing
of
what
could
have
gone
wrong.
LTCM
goofed
by
greatly
underestimating
the
chance
ofa
panic
in
which
its
trades
would
become
highly
correlated.
The
fund
was
making
hundreds
of
simultaneous
bets.
It
operated
on
the
assump
tion
that
these bets had low
correlation.
The
chance
of
all the bets
going
bad
at
once
was
estimated
to be
fantastically
small.
Then
Rus
sia
defaulted,
and
suddenly
a
lot
was
riding
on
the
same
losing
hand.
294


## Page 302

Blowing
Up
LTCM
had
"a
whole
lot
of
bets
on
Southeast
Asian
debt,
a
whole
lot
of bets on the
spread
between
government
and
junk,"
Thorp
said.
"So
it's not
really
millions
of
small
bets.
It'sa
few
big
bets."
You
might
then
ask
how
LTCM
would
have
been
any
betteroff
with the
Kelly
system.
The
answer
is that the
Kelly
criterion
canbe
more
forgiving
of
human
error than
many
other
systems—including
highly
leveraged
approaches
such
as
LTCM's.
Recall
the
example
of
simultaneous
betson a
large
numberof
coins,
each
with a
55
percent
chance
of
coming
up
heads.
The
Kelly
bettor
stakes
almost
his
whole
bankroll,
splitting the
wagered
money
equally
among
all
the
coins.
He
refuses
to
bet
the
entire
bankroll
because
of
the
remote
chance
that ever)'singlecoin
will
come up
tails.
This
illustrates
the
"paranoid"
conservatism
of
Kelly
betting.
The chance of hundreds of coins
simultaneously
coming up tails is
of
course
astronomically
small.
No
matter—the
ideal
Kelly
gam
bler's
"survival
motive"
precludes
taking
any
chance
of ruin
whatso
ever.
By
not
betting
the entire
bankroll,
the
Kelly
bettor is
taking
out an
"insurance
policy"
guaranteeing
that he
will
be
able
to re
cover
after any
possible
run of bad
luck.
It is
easy
to do better
than
the
Kelly
gambler
in the short
run.
Someone
who
skips
the
"insurance"
and
bets
lOO
percent
of her
bankroll,
spreading
it
among
the
hundreds
of
simultaneous
favor
able
bets,
is
not
likely
to
have
cause
to
regret
it
anytime
soon.
And
why
stop
there?
You
canbe
more
aggressive
by
using
leverage.
Bor
row
twenty-nine
times
your
bankroll,
add
it to
your
own
money,
and
apportion
it
among
all
the
coins.
You
will
make
thirty
times
the
profit, on
average.
The downside is that there is a
chance
of losing
everything,
and a
further
chance
of ending up in debt to
your
lenders.
These
chances
are not quite so
remote.
When
you
use
leverage,
you
have
to get a
certain
number
of
winning
tosses
just to
pay
back
your
lenders.
If
you
don't get them,
you're
broke
or in debt.
Are these
chances
acceptable?
You
can do a
VaR
calculation
to
help
decide.
Pick
a
leverage
and
a
risk
level
that
feels
right,
and
go
for
it.
This is
roughly
what
LTCM
did.
It is not
necessarily
crazy.
We
295


## Page 303

FORTUNE
S
FORMULA
all
take
risks
that are
inconsistent
with
living
forever.
But
this
ap
proach
leaves
little
margin
for
error.
Estimates
about
the
market's
probabilities
are
always
going
to be
just that:
estimates.
It is good
practice
to
have
a senseof how far off
these
estimates
may
be,and how
much
likely
errors
would
affect
the
results.
"Margins
of error" are
themselves
estimates.
Human nature
often
skews
these
estimates
optimistically.
A decade
rarely
passes
without a market event that some re
spected
economist
claims,
with
a
straight
face,
to be a
perfect
storm,
a ten-sigma event, or a catastropheso
fantastically
improbable
that
it
should
not
have
been
expected
to
occur
in
the
entire
history
of
the
universe
from
the big bang
onward.
In a
world
where
financial
models
canbe so
incredibly
wrong,
the
extreme
downside
caution
of
Kelly
betting
is
hardly
out of
place.
For
reasons
mathematical,
psy-
Fat
Tails
and
Leverage
Thewager: Biasedcoins pay even
money and are believed to have a
55%chance of coming up heads
A "fat tail"
event:
only 45%of coins
come up heads
Kelly
bettor
is
left
with
V^-^
Bettor
using
30x
leverage
is
over 90% of bankroll
broke and
owes
an
amount
equal to
twice
the former
bankroll
296


## Page 304

Blowing
Up
etiological,
and
sociological,
it is a good idea to use a money
manage
ment
system
that is
relatively
forgiving
of estimation errors.
Suppose you're betting on a
simultaneous
toss of coins
believed
to
have
a
55
percent chance of coining up
heads,
as depicted on
the
previous
page.
But on this
toss,
only 45 percent of the coins
are
heads.
Call
it a
"fat
tail"
event,
or
a
failure
of
correlation
co
efficients,
or a big dumb
mistake
in
somebody's
computer
model.
What
then?
The
Kelly
bettor cannot be ruined in a single toss. (He is pre
pared to
survive
the
worst-case
scenario,
of
zero
heads.)
In this situ
ation, with many
coins,
the
Kelly
bettor
will
stake just short of his
full
bankroll.
He wins only 45 percent of the
wagers,
doubling the
amount bet on each coin that comes up
heads.
The
Kelly
bettor
therefore
preserves
at least 90 percent of his
bankroll.
If the
preponderance
of
tails
on this
toss
is just bad
luck,
the
Kelly
bettor can
expect
to
recover
lost
ground
on
succeeding
tosses.
If
instead
the
"real"
chances
arc
less
favorable
than
the
estimated
55
percent,
the
would-be
Kelly
bettor
will
actually
be
overbetting.
This will cut into compound return and
increase
volatility.
At any
rate, the
Kelly
bettor
will
have
time to
live
and
learn,
revising
prob
ability
estimates along the
way.
Compare this to
someone
who
uses
thirty-times
leverage.
In
stead of
losing
just 10 percentof the
bankroll,
the
leveraged
bettor
loses
300
percent.
That
means
he
loses
everything
and still
owes
twice
the amount of the
previous
bankroll
to
lenders.
He
probably
can't learn from this
mistake,
either.
Who's going to give him an
other
chance?
The core of John
Kelly's
philosophy
of risk can be stated without
math. It is that even
unlikely
events must come to
pass
eventually.
Therefore,
anyone
who
accepts
small
risks
of
losing
everything
will
lose
everything,
sooneror
later.
The
ultimate
compound
return rate
is
acutely
sensitive
to fat
tails.
The
University
of
British
Columbia's
William
Ziemba
has esti
mated that LTCM's
leverage
was
somewhere
around
twice
the
Kelly
297


## Page 305

FORTUNE
S
FORMULA
level.
If correct, that
would
imply
that the
fund's
true compound
growth rate was
hovering
near
zero.
The
familiar
mean-variance
mapping
isnot a
good
way
of
visual
izing this type of problem, noted the Universityof North Carolina's
Richard
McEnally.
In the
mean-variance
mapping(left), return
rises
as a straight line as
leverage
increases.
Risk
rises,
too, but this dia
gram shows no reason why a vcr)'
aggressive
and risk-tolerant trader
should
not
increase
leverage
to
any
degree
obtainable.
In the
Kelly
Two
Views
of
Risk
and
Return
Mean-Variance
Mapping
Kelly
Mapping
mapping
(right),
the
line
of
return
is a
curve
that
boomerangs
back
to zero and
negative
returns.
It
is
not a
question
of
which
mapping
is
"right."
Both
mappings
are right for different
contexts.
The
highly
leveraged
overbettor is
likely
to do
well
on many bets that are not
parlayed.
It is when
bets
compound
over time that the
Kelly
mapping
becomes
all-
important. A strategy like LTCM's
fails—and
here the fund's name
is
grimly
ironic—in
the long term.
For true
long-term
investors,
the
Kelly
criterionis the
boundary
between
aggressive
and
insane
risk-taking.
Like
most
boundaries,
it
is an
invisible
line.
You
canbe
standing
righton it,and
you
won'tsee
a neat dotted line
painted
on the
ground.
Nothing
dramatic
hap
pens when you
cross
the
line.
Yet
the
situation
on the ground is
298
Overbettor


## Page 306

Blowing
Up
treacherous
because
the
risk-taker,
though heading for doom, is li
able to find thingsgetting better before they get
worse.
"Convergence trades arc a real snake pit," said Thorp, "unless
they
have
a timetable drivingthem,such as an expiration date in the
case of warrants, options and
convertible
bonds."
LTCM was trad
ing thirty-year bonds. It
was
in no position to wait thirty years for
"sure"
profits.
Nor could it
have
reduced
leverage
on these trades,
with their tiny profit
margins,
and remained attractive to investors.
"If
they had not overbct," noted Thorp, "it seems likely that, with a
O.67
percent expectedgain
(annualized)
on a
typical
trade,
leverage
of,
say 5 or 10
would
only
produce
gains
of
3.3
to
6.7
percent—
hardly interesting to the
general
partners or
investors."
Bycompari
son, had
LTCM
skipped
the
fancy
arbitrage
and
simply
bought
thirty-year
Treasury
bonds at
August
1998 rates, it would
have
earned
a
rock-solid
5.54
percent.
Eternal
Luck
THE
LTCM
DISASTER
was
like a
grisly
highway
accident. Arbi
trage funds
scaled
down their
leverage
for a
few
seasons,
then it was
back
to
business
as usual.
One
of
the
victims
of
the
1998
Russian
default
was
another
MIT-trained
trader.
John
Koonmen.
Koonmen
worked in Lehman Brothers'
Tokyo
office,
trading convertible
bonds for Lehman's own account. He lost so much money that
Lehman had to scale back bonuses for the entire Tokyo
department.
Koonmen
was
asked
to
leave
the
firm.
299


## Page 307

FORTUNE
S
FORMULA
He acquired one souvenirof the panic that had done him in. It
was a pool table
formerly
used
in
LTCM's
Tokyo
office.
Koonmen
was
an expert
backgammon
player.
Before
coming to
Tokyo,
he haunted the
illegal,
big-money
backgammon
scene in
New
York.
From the
backgammon
circuit,
Koonmen
knew John
Bender,
a gamblerwho
managed
the AmberArbitrage
Fund.
Amber
Arbitrage had a number of
professional
backgammon and poker
players
as
investors.
Its major investor
was
George
Soros,
through
his Quantum
Fund.
Bender
was
looking
to get into the
Japanese
market.
He hired
Koonmen in 1999.Then, in spring
2000,
Benderhad a stroke. Koon
men
began
tradingmore
aggressively.
This
violated
one of the
rules
of
the
profession:
The
boss's
illness
or
vacation
is not the time to tryout
exciting
new
approaches.
Bender
felt
Koonmen
was
taking
too
much
risk.
By
October,
Bender
had
recuperated
enough
to
close
the fund
and retire to a
game
preserve
in
Costa
Rica.
He and
Koonmen
spent
the next
few
years
squabbling
over
division
of
profits.
Koonmen
meanwhile
went to Amber
Arbitrage's
investors
and
claimed
credit for the
fund's
recent
performance.
He persuaded
manyof them to roll their
money
over into a new fund that Koon
men wasstarting,
Eifuku
Master Trust.
One of the
first
things
Koonmen
had to
explain
to
his
investors
was
how to
pronounce
"Eifuku."
It
was
ay-foo-koo.
Eifuku
means
"eternal
luck."
Soros
invested
in
Eifuku.
Sodid
several
high-net-worth
Kuwaitis
and
UBS,
a
Swiss
bank
still
smarting
from
the
distinction
of
having
been
Long-Term
Capital
Management's
largest
investor.
Like
Meriwether,
Koonmen
believed
that his management was
worth a 25 percent cut of the profits. He also intended to rake in
2 percent
of
the fund's assets each
year,
profitable or not.
Koonmen installed his LTCM pool table in
Eifuku's
offices on
the
eleventh
floor
of the
Kamiyacho
MT
Building.
These
lavish
offices
were
the most
extreme
ostentation
in
Tokyo's
real
estate
market. Koonmen habitually wore
black,
often a black turtlcneck
with black pants. lie drove around
Tokyo
in a metallic blue Aston
Martin
Vantage.
300


## Page 308

Blowing
Up
Eifuku
Master
Trust lost 24 percentof
asset
value
in
2001.
That
misstep
was
forgotten
as
it
posted
a
76
percent
gain
in
2002.
That
wasa terrible yearfor the stock
market.
Eifuku's
investors
must have
counted
themselves
lucky
indeed.
In
the
first
seven
trading
days
of
2003,
Eifuku
lost
98
percent
of
those
investors'
money.
As 2003
began.
Koonmen
had
positions
worth Si.4
billion
backed
by
S155
million
of
asset
value.
That
is
about
nine
times
leverage,
less
than
LTCM
had
used.
Unlike
LTCM.
Koonmen
wasn't
even
try
ing
to
diversify
His
resources
were
committed
to
just
three
major
trades.
He
had
bought
half
a
billion
dollars'
worth
of
Nippon
Tele
phone and
Telegraph
stock and sold short the
same
amount of its
partly
owned
mobile
phone
subsidiary,
NTT
DoCoMo.
A
second
trade
involved
long
and
short
positions
in
four
Japanese
banks,
with
some
short
index
futures
as a
hedge.
Finally.
Koonmen
owned
Si
50
million
worth
of the
video
game
company
Sega.
On
January
6 and
7.
the
fund
lost
15
percent of its
value.
It
dropped
another
15
percent
on
Wednesday
the
eighth.
The
bank
that
had
extended
Koonmen
all
this
leverage
was
Goldman
Sachs.
They
had
the
right
to
liquidate
Koonmcn's
positions
to
satisfy
col
lateral
requirements.
Koonmen
talked
them
into
holding
offa
day.
Koonmen
spent
Thursday
the ninth on the phone with in
vestors.
He
was
trying
to
talk
them into putting more
money
into
his
dying
fund.
No
one
was
interested.
While
this
was
going
on,
the
fund
lost another
16
percentof its
value.
Friday
the
tenth
was
going
into
a
three-day
weekend
in
Japan.
Goldman
Sachs
realized
it
wasn't
such
a good idea to
sell
massive
amounts
of
Sega
and NTT
before
a
long
weekend.
They
held
off
until
Tuesday.
The
fund
shed
12
percent
more
in
Friday's
trading.
On
Tuesday
Goldman
Sachs
started
unloading.
The
market
in
the
securities
Koonman
held
crumbled.
Eifuku
lost
40
percent
of
its
value,
shrinking
to a
mere
3
percent
of
where
it
started
the
year.
By
Wednesday,
that
was
down
to 2
percent.
Koonmen
was
described
as
eerily
emotionless
during
the car-
301


## Page 309

FORTUNE'S
FORMULA
nage.
When
he
came
to
write
the
"Dear
Investor"
letter,
he
assured
his
readers
that he
was
doing
everything
to
"preserve
and
maximize
any
remaining
equity
in
the
fund.
There
is
however
a
strong
possi
bility
that
there
may
not
be
any
equity
left
at
the
end
of
the
liquida
tion."
The
letter
concluded,
John
Koonmen
will
try to
contact
each
investor
individually
by
phone
in
the
next
few
days
to
further
explain
these
unfortunate
events
and
answer
all
direct
questions.
In
particular,
if
any
in
vestors
have
questions
concerning
the
logic
and
analysis
behind
the
positions,
John
would
be
happy
to
answer
these
questions
during
those
calls
. . .
This
letter
has
been
very
hard
to
write.
1
amsurethat it
has
been
equally
difficult
for
you
to
read.
We
will
be
in
contact
soon.
Koonmen closed the fund and went to Africa to photograph
wildlife.
Life's
Rich
Emotional
Experiences
In
HIS
notes,
Claude
Shannon
recognized
that the
motives
of a
hedge
fund
manager
are
not
necessarily
congruent
with
those
of the
fund's
investors.
In
recognition
of
this
fact,
virtually
all
fund
man
agers
have
their
own
wealth
in
their
funds
(they
"eat
their
own
cooking").
There
are
still
incentives
to
assume
risks
that
managers
might
not
take
with
just
their own
money.
It is now
common
to
302


## Page 310

Blowing
Up
Hedge
Fund
Returns
Value of $1
invested
at fund's
outset
Princeton-NewportPartners
^^^T
Long-Term
Capital
Management
^*»—
/
Eifuku
$0.10
n
$0.01
observe
that a
fund
manager
has
a
call
option
on
fund
investors'
wealth.
The
manager
shares
the
upside
but
does
not
directly
share
the
investors'
losses.
Investors
choose
one
fund
over
another
on the
strength
of a
few
basis
points
of
return.
This
creates
the
severest
temptation
for
man
agers
to boost return any
way
possible.
One
way
to do that isto
take
"Russian
roulette"
risks
thatarc
likely
to
pay
off in theshort run,yet
carry
the
possibility
of
disaster.
Human
nature
and
single-period
financial
models
make
it
easy
to blindoneselfto
long-term
risk.
Risk
management
is a
tough
lesson
to
learn
on the
job.
It can
take
years
for
ruinous
overbetting
to
blow
up in a trader's
face.
When that happens,a career
may
be
over.
There is
much
overlap
between
portfolio
managers
and
serious
gamblers.
Whether this is
good
can be
argued
either
way.
William
Ziemba
believes
that it is
mostly
good.
Gambling
provides
the
most
important
object
lesson
of
all:
going
broke.
There isnobetter
way
of
303


## Page 311

FORTUNE'S
FORMULA
demonstrating
the
need
for
money
management
than
seeing
your
own
money
vanish
while
making
positive-expectation
bets.
It
is
im
possible
to
make
the
same
point
so
viscerally
with
mere
stochastic
differential
equations.
As
Fred
Schwed,
Jr.,
author
of
Where
Are
the
Customers'Yachts?,
putit
back
in
1940,
"Like
all
of
life's
rich
emotional
experiences,
the
full
flavor
of
losing
important
money
cannot
be
conveyed by literature."
304


## Page 312

PART
SEVEN
Signal
and
Noise


## Page 313

Shannon's
Portfolio
In
1986
Barron's
ran an
article
ranking
the recent
performance
of
seventy-seven
money
managers.
Claude
Shannon,
though
not
mentioned
in
the
article,
had
done
better
than
all
but
three
of
the
pros.
The
Barron's
money
managers
were
mostly
firms
with
up to
a
hundred
people.
Shannon
worked
with
his
wife
and
a
decrepit
Apple
11
computer.
The
August
11,1986.
Barron's
reported
on the
recent
performance
of
1,026
mutual
funds.
Shannon
achieved
a
higher
return
than
1,025
of
them.
When
Warren
Buffett
bought
Berkshire
Hathaway
in
1965,
it
was trading at
S18
a
share.
By
1995
each
share
was
worth S24.000.
Over thirty
years,
that
represents
a
return
of 27
percent.
From
the
late
1950s
through
1986.
Shannon's
return
on
his
stock
portfolio
was about 28 percent.
Shannon
had
long
thought
of
publishing
something
on
his
investment
methods.
Apparently
his
ideas,
though
profitable
in
practice,
never met his standards of
originality
and
precision.
Shan
non's
memory
was
starting to
fail,
too,
making
it
unlikely
he
would
ever
complete
such
an
article.
In
1986
Philip
Hershbcrg,
an
engineer
turned
investment
adviser,
interviewed
the
Shannons
about
their
investing
methods.
Hershbcrg
intended
to
publish
an
article,
but
this
too
never
appeared.
A draft of
Hcrshberg's
article
(supplied
by
Betty
Shannon),
along
with
Hershberg's
recollections,
307


## Page 314

FORTUNE'S
FORMULA
give
the
most
complete
view
of
how
Shannon
achieved
these
returns.
It
had
nothing
to
do
with
arbitrage.
Shannon
was
a
buy-and-
hold
fundamental
investor.
"In
a
way,
this
is
close
to
some
of
the
work
I
have
done
relat
ing
to
communication
and
extraction
of
signals
from
'noise,'
"
Shannon
told
Hershberg.
He
said
that a smart
investor
should
understand where he has an edge and
invest
only in those op
portunities.
In
the
early
1960s,
Shannon
had
played
around
with
technical
analysis.
He
had
rejected
such
systems:
"I
think
that
the
technicians
who
work
so
much
with
price
charts,
with
'head and
shoulders
for
mations'
and
'plunging
necklines,'
are
working
with
what
I
would
call
a
very
noisy
reproduction
of the important
data."
Shannon
emphasized
"what
we
can
extrapolate
about the
growth
of
earnings
in the
next
few
years
from
our
evaluation
of the
company
management
and
the
future
demand
for
the
company's
products
. . .
Stock
prices
will,
in
the
long
run,
follow
earnings
growth."
He
therefore
paid
little
attention
to
price
momentum
or
volatility.
"The
key
data
is.
in
my
view,
not
how
much
the
stock
price
has
changed
in
the
last
few
days
or
months,
but
how
the
earnings
have
changed
in
the
past
few
years."
Shannon
plotted
company
earnings
on
logarithmic
graph
paper
and
tried
to
draw
a
trend
line
into
the
future.
Of
course,
he also
tried
to
surmise
what
factors
might
cause
the
exponential
trend to
continue
or sput
ter
out.
The Shannons would visit start-up
technology
companies
and
talk
with the
people
running
them.
Where
possible,
they
made
it a
point
to
check
out the
products
of
companies
selling
to the
public.
When
they
were
thinking
of
investing
in
Kentucky
Fried
Chicken,
they
bought
the
chicken
and
served
it to
friends
to
gauge
their
reac
tions.
"If
we
try it and don't
like
it,"
Shannon
said,
"we
simply
won't
consider
an
investment
in
the
firm."
Shannon became a board member of
Teledyne.
He was not just a
distinguished
name
in
the
annual
report
but
was
actively
scouting
308


## Page 315

Signal
and
Noise
potential
acquisitions
for
CEO
Henry
Singleton.
For
instance,
in
1978
Shannon
investigated
Perception
Technology
Corporation
on
behalf
of
Teledyne.
Perception
Technology
was
founded
by
an
MIT
physicist,
Huscyin
Yilmaz.
whose
training
was
largely
in
general
relativity.
During
the
visit
with
Shannon,
Yilmaz
spoke
enthusiasti
cally
about
physics,
asserting
that
there
was
a
"gap
in
Einstein's
equation"
which
Yilmaz
had
filled
with
an extra term.
Yilmaz's
company,
however,
was
involved
in
speech
recognition.
They
had
developed
a
secret
"word
spotter"
that
would
allow
intelligence
agencies
to
automatically
listen
for
key
words
like
"missile"
or
"atomic"
in
tapped
conversations.
Another
product
allowed
a
com
puter
to talk.
Shannon's
pithy
report
warned
Singleton
that
speech
synthesis
"is
a
very
difficult
field.
Bell
Telephone
Laboratories
spent
many
years
and
much
manpower
at
this
with
little
result
...
I
had
a
curious
feeling
that the
corporation
is
somewhat
schizoid
between
corporate
profits
and
general
relativity.
Yilmaz,
Brill
and
Ferber
all
impressed
me
as
scientifically
very
sharp
and
highly
motivated,
but
much
less
interested
in
product
development,
sales
and
ear
nings."
Shannon
concluded:
"I
think
that
an
acquisition
of
PTC
by
Teledyne
would
be
meaningful
only
as
a
long-term
gamble
on
scientific
research.
I
would
not
recommend
such
an
acqui
sition."
Warren
Buffett
himself
said
that
Singleton
had
the
best
operat
ing and capital deployment record in
American
business.
It is at
least
conceivable
that
Shannon's
judgments
played
a
supporting
role
in
that
success.
Shannon
was
among
the
first
investors
to
download
stock
prices.
By
1981
he
was
subscribing
to
an
early
stock
price
service
and
down
loading
price
quotes
into
a
spreadsheet
on
his
Apple
II.
The
spread
sheet computed an
annualized
return.
In a
computer
printout
dated
January
22,
1981.
the
Shannon
portfolio
ran:
309


## Page 316

fortune's
formula
COMPANY
SHARES
PURCHASE
PRICE
I/22/8I
PRICE
VALUE
Baxter
International
10
$42.75
S50.00
Sl.SOO.OO
Crown
Cork
& Seal
SO
$8.00
$31.75
$1.58750
Hewlett-Packard
348
So.
13
$82.00
$28,536.00
International
Flavors
&
Fragrances
70
$26.50
$22.00
$1,540.00
John II. Harland
I
$30.00
S
39.00
$390O
Masco
120
Si.63
$28.88
$3,465.00
MILI
40
$32.00
$28.13
Si.125.OO
Motorola
1086
Si. 13
$65.00
$70,590.00
Schlumberger
22
$44.00
$108.75
$2.39250
Teledyne
2428
S1.00
$194.38
$471,942.50
TOTAL
S582.7i7.50
This
list
may
not
be
complete,
as
elsewhere
Shannon
spoke
of
owning
at
least
one
other
stock
(Datamarine)
at
this
time.
The
portfolio
value
is
a
relatively
modest
S582.717.50.
In
2004
dollars,
that
would
qualify'
Shannon
as
the
Millionaire
Next
Door.
What
is
remarkable
is the compound return.
The
"purchase
price"
appears
to
be
an
average
cost
basis.
Some
of
the
stocks
were
acquired
through
mergers
and/or
purchases
at
vari
ous
prices.
The
average
appreciation
of
the
Shannon
portfolio
at
this
point
was
about
sixty-fold.
Shannon's
portfolio
would
have
appalled
Harry
Markowitz
(or
any
financial
adviser).
By
this
point,
nearly
81
percent
of
the
portfo
lio
was
ina
single
stock,
Teledyne.
The
three
largest
holdings
consti
tuted
98
percent
of
the
portfolio.
"We
have
not,
at
any
time
in
the
past
30
years,
attempted
to
balance
our
portfolio,"
Shannon
told
Hcrshberg.
"I
would
have
liked
to
have
done
so
were
it
not
for
tax
considerations."
At
age
seventy,
Shannon
was
fully
invested
in
stocks.
"I
am
willing
to
borrow
on our
investments
if
necessary,"
Shannon vowed,"rather than sellour stocksand convert to interest-
bearing
instruments."
310


## Page 317

Signal
and
Noise
Shannon
told
Hershbcrg
that
the
wortf-performing
company
he
then
owned
was
Datamarine
International.
He
had
bought
it
in
1971,
and
it
had
averaged
only
13
percent(!)
over
that
period.
He
planned
to
hold
ontoit
as
he
liked
its
acquisition
plans.
Shannon
picked
several
winners
that
had
nothing
to
do
with
dig
ital
technology.
One
was
Masco,
a
company
that
makes
building
supplies.
In
the
early
1980s,
the
Shannons
bought
stock
in
two
companies
that
printed
checks
(John
H.
Harland
and
Deluxe).
The
stocks
were
reasonably
priced,
apparently
because
PCs
had
just
be
come
popular
and
everyone
was
abuzz
about
paperless
transactions.
Betty
doubted
that
paper
checks
would
become
obsolete
quite
so
soon.
Both
companies
had
good
earnings
growth.
From
1981
to
1986,
the
compound
return
was
34
percent
for
Harland
and
40
per
cent
for
Deluxe.
As
to
overall
performance,
Shannon
told
Hershberg,
We've
been
involved
for
about
35
years.
The
first
few
years
served
as
a
kind
of
learning
period—we
did
considerable
trading
and
made
moderate
profits.
In
switching
to
long-term
holdings,
our
overall
growth
rate
has
been
about
28?o
per
year.
Shannon
is
apparently
excluding
the
early
learning
period
from
the
claimed
28
percent
return.
He
did
not
say
how
or if
he
ac
counted
for
stocks
he
no
longer
owned.
That
can
make
a
big
differ
ence
in the
return
of an
actively
managed
portfolio.
However,
the
Shannons
apparently
never
put
too
much
money
into
a
new
stock,
and
they
sold
rarely
after
the
mid-1960s.
Practically
all
of
the
profit
came
from
the
Teledyne/Motorola/Hewlett-Packard
triumvirate.
Shannon
had
bought
Teledyne
for
88
cents
a
share,
adjusted
for
stock
splits.
Twenty-five
years
later,
each
share
was
worth about
S300, a 25 percent annual return. Codex had cost Shannon 50 cents
a share; by 1986 each share had become a share
of
Motorola worth
S40, translating into a 20 percent return rate.
Dividends,
not in
cluded
in
these
returns,
would
nudge
up
the
figures.
311


## Page 318

fortune's
formula
Shannon's
best
long-term
investment
was
Harrison
Labs/
Hewlett-Packard.
This
achieved
a 29 percentreturn overthirty-two
years.
In
his
initial
purchase
of
Harrison
Labs,
Shannon
paid
the
equivalent
of
1.28
cents
for
what
would
become
a
S45
share
of
Hewlett-Packard
by
1986.
That's
over
a
3,500-fold
increase.
The
initial investment had doubled eleven times and then some. Shan
non's
blackboard
projection
had
come
true:
2" = 2048.
Egotistical
Orangutans
It
will
be
plausible
to
many
that
Shannon's
knowledge
and
vision
gave
him
an
edge
in
picking
technology
stocks.
In
the
1950s
and
1960s,
Shannon
stood
on the
cusp
of
history.
He
foresaw
the
digital
revolution
and
bet
his
money
on
it.
The
average
Wall
Street
analyst,
much
less
the
average
investor,
could
not
have
guessed
the
future
so well as
Shannon
did.
It
is
unlikely
that
this
would
or
should
convince
a
diehard
be
liever
in
market
efficiency.
Nearly
all
of
Shannon's
gain
came
from
three
smart
(lucky?)
picks.
Three
data
points
do
not
have
much
sta
tistical
significance.
Scientific
proof
demands
repeatability.
Repeatability
has
been
the
nub
of
the
broad
reappraisal
of
the
efficient
market
hypothesis
(EMM)
in the
academic
literature.
Starting
in
the
1980s,
computers
and
databases
allowed
finance
scholars to winnow historical data for investor biases supposedly
demonstrating
market
inefficiency.
They
found
scores
of
biases
im
pressive
enough
for
a
journal
to
publish
an
article
about
them.
Among
the
"irrational"
effects
discussed
in
the
literature
are
the
312


## Page 319

Signal
and
Noise
P/E
effect
("value
stocks"
with
low
price-to-earnings
ratios
suppos
edly
do
better
than
others),
the
size
effect
(small
companies
have
higher
returns
than
large),
the
January
effect
(stock
markets
post
higher
returns
in
January),
the
Monday
effect
(poor
returns
on
Monday),
and
even
a
weather
effect
(market
returns
correlate
with sunny
days).
Few
of
the
reported
biases
could
pass
the
repeatability
test.
Once
an
"effect"
was
reported,
another
study
would
come
along,
with
more
data
or
more
realistic
assumptions,
showing
that
the
original
effect
was
less
statistically
significant
than
reported,
or
never
existed
at
all,
or
had
vanished
since
the
first
publication,
possibly
because
people
started
trying
to
exploit
it.
"I
have
personally
tried
to
invest
money,
my
client's
money
and
my
own,
in
every
single
anomaly
and
predictive
device
that
academ
ics
have
dreamed
up,"
complained
economist
and
portfolio
manager
Richard
Roll
in
1992.
"And
I
have
yet
to
make
a
nickel
on
any
of
'these
supposed
market
inefficiencies..
.
If
there's
nothing
investors
can
exploit
in
a
sys
tematic
way,
time
in
and
time
out,
then
it's
very
hard
to
say
that
information
is
not
being
properly
incorporated
into
stock
prices."
Most efficient market economists concede that there are anec
dotal
cases
of
egregious
market
inefficiencies.
They
shrug
them
off.
Those
traders
or
hedge
funds
that
seem
to
beat
the
market
are
just
lucky
and
will
eventually
blow
up
like
LTCM
or
Eifuku.
No
one
truly
achieves
excess
risk-adjusted
return.
The
other
side
of
the
debate
has
often
done
a
meager
job
of
an
swering
this
challenge.
Many
papers
barely
address
how
one
might
exploit
the
reported
biases.
How
would
you
make
money
off
the
weather
effect,
for
instance?
If
the
effect
is
genuine,
the
weather
forecast
for
Manhattan
gives
a
small
edge
in
predicting
that
day's
NYSE
performance.
Okay,
you
could
buy
stocks
in
sunny
New
York
and
sell
them
short
in
foggy
London
(if
that's
what
the
forecasts
call
for).
Unlike
a
good
hedge,
there
is
no
logical
necessity
that
stocks
can't
drop
in New York
and
rise in London, whatever the weather.
You
could
lose
out
on
both
ends
of
the
trade.
This
risk
and
the
large
transaction
costs
(the
weather
changes
ever)'
day)
make
this
scheme
an
unlikely
candidate
for
excess
risk-adjusted
return.
313


## Page 320

FORTUNE'S
formula
There
is
little
overlap
between
the
"effects"
reported
in theliter
ature
and
those
in
use
by
successful
arbitrageurs.
Most
ofthe
studies
concern
relatively
simple
stock-picking
or
market-timing
systems,
the stuff
of
investor
fads.
The few investors who
successfully
pursue
fundamental
analysis
over
extended
periods
are
judges
of
people
as
well
as
P/E
ratios.
Warren
Buffett's
excess
return
probably
resides
in
what he reads between the lines of balancesheets. This is unlikely to
be
captured
in
any
model
crunching
"official"
figures
from
data
bases.
In
a
1984
speech,
Buffett
asked
his
listeners
to
imagine
that
all
215
million
Americans
pair
off
and
beta
dollar
on
the
outcome
ofa
coin
toss.
The one who
calls
the
toss
incorrectly
is
eliminated
and
pays
his
dollar
to the one
who
was
correct.
The
next
day,
the
winners
pair
off
and
play
the
same
game
with
each
other,
each
now
betting
$2.
Losers
arc
eliminated
and
that
day's
winners
end
up
with
$4.
The
game
continues
with
a
new
toss
at
doubled
stakes
each
day.
After
twenty
tosses,
215
people
will
be
left
in
the
game.
Each
will
have
over
a
million
dollars.
According
to
Buffett,
some
of
these
people
will
write
books
on
their
methods:
How
I
Turned
a
Dollar
into
a
Million
in
Twenty
Days
Working
Thirty
Seconds
a
Morning.
Some
will
badger
ivory-tower
economists
who
say
it
can't
be
done:
"Ifit
can't
be
done,
why
are
there
215
of
us?"
"Then
some
business
school
professor
will
probably
be rude
enough
to
bring
up
the
fact
that
if
215
million
orangutans
had
en
gaged
in a
similar
exercise,
the
result
would
be
the
same—215
ego
tistical
orangutans
with
20
straight
winning
flips."
What
sortof
evidence
ought
to
convince
us
that
someone
can
pick
stocks
well
enough
to
beat
the
market?
Ever)'
year,
the
Morningstar
ratings
identify
mutual
fund
managers
who
have
done
much
better
than the
market
or their
peers.
A
few
of these
managers
manage
to
stay
near
the
top
of
the
ratings
for
many
years
in
a
row.
Their
funds'
ads
leave
the
distinct
impression
that
these
track
records
have
pre
dictive
power
going
forward
(ignoring
the
fine
print).
But
as
Buf
fctt's
talc
suggests,
there
must
inevitably
be
a
small
group
of
very,
314


## Page 321

Signal
and
Noise
very
lucky
managers
who
achieve
very
long
and
impressive
track
records.
It makes sense to measure track records in decisions
rather
than
years.
The more
profitable
decisions
the
better.
It is
also
more
convincing
(less
orangutan-like)
when
outside
observers
can
under
stand
at
least
some
of
the
logic
behind
the
stock
picks.
Stock-
picking
is
often
subjective.
It
is
based
on
so
many
factors
that
it
is
hard
for
an
investor,
or
anyone
else,
to
understand
what
a
fund
manager
is
doing.
You
are
unlikely
to
convince
a
skeptic
that a
man
ager's
return
is not just luck when no one else can
understand
the
logic
of his stock
picks.
Indicators
Project
One
of
the
best
cases
for
beating
the
stock
market
involves
a
scheme
called
statistical
arbitrage.
To
make
money
in
the
market,
you
have
to
buy
low
and
sell
high.
Why
not
use
a
computer
to
tell
you
which
stocks
are
low
and
which
are
high?
In
concept,
that
is
statisti
cal
arbitrage.
Fundamental
analysts
look
at
scores
of
factors,
many
of
them
numerical,
in
deciding
which
stocks
to
buy.
If
there
is
any
va
lidity
to
this
process,
then
it
ought
to be
possible
to
automate
it.
Ed
Thorp
began
pursuing
this
idea
as
early
as
1979.
It
emerged
as one of the
discoveries
of what became known as the "Indicators
Project" at Princeton-Newport. Jerome
Baesel,
a former UC Irvine
professor
whom
Thorp
had
talked
into
coming
to
Princeton-
Newport
full-time,
was
in
charge
of the
research.
The
fundamental
analyst
usually
buys
stock
to
hold
for
months,
315


## Page 322

fortune's
formula
years,
or
decades.
The
longer
you
hold
a
stock,
the
harder
it
is
to
beat
the
market
by
much.
Say
you
are
convinced
that a
stock
is
selling
for
80
percent
of
its
"real"
value,
a
nice
discount.
If
the
market
comes
around to
your
way
of
thinking
in a
year's
time,
you
will
be
able
to
sell
the
stock
for
a
25
percent
profit
(on top of
any
other
return:
the
25
percentage
points
are
how
much
you
"beat
the
market"
by).
If
instead
the
market
takes
twenty
years
to
realize
that it
has
un
dervaluedthe
stock,
this slow
reappraisal
addsonlyabout
1.1
percent
to
your
annual
return
over
those
twenty
years.
The
long-term
in
vestor who
intends
to beat the market must find stocks that arc se
riously
undervalued
now
and
must
have
a
crystal
ball
on
the
distant
future. Both are formidable requirements.
Thorp
and
Baesel
focused
instead
on
the
short
term.
They
had
the
software
pick
out
the
stocks
that
had
gone
up
or
down
the
most,
percentage-wise,
in
the
previous
two
weeks,
adjusted
for
dividends
and
stock
splits.
These
were
companies
that
had
surprised
the
mar
ket
with
news,
good
or
bad.
They
found
that
the
up
stocks
had
a
strong
tendency
to
fall
back
in
the
near
term,
while
the
down
stocks
tended
to
rise.
This
is
exactly
the
opposite
of
what
"momentum
investors"
bet
on
happening.
It
accords
well
with
the
truism
that
the
market
over
reacts
to
good
news,
bad
news—and
sometimes
to
no
news
at
all.
Then the emotion
fades
and the
pendulum
swings
back.
Thorp
and
Baesel
experimented
with
portfolios
in
which
they
bought
the
"most
down"
stocks
and
sold
short
the
"most
up."
As
long
as
they
bought
enough
stocks,
this
provided
a
decent
hedge
against
general
market
movements.
They
concluded
they
could
make
about
a 20
percent
annual
return.
Ironically,
that
was
the
stumbling
block.
Princeton-Newport
was
already
making
that
and
more
with its other
trades.
(The
years
1980-82
were
an
especially
hot streak, with annual returns of 28, 29, and 30 percent after the
20
percent
fees
had
been
deducted.)
The
returns
of the
most
up,
most
down
portfolios
were
also
more
variable
than
Princeton-
Newport's
other
trades.
3i6


## Page 323

Signal
and
Noise
Brilliant
as
the
concept
was,
Princeton-Newport
had
no
use
for
it.
The
Indicators
Project
was
quietly
tabled.
In
1982
or
1983,
Jerry
Bamberger
independently
got
almost
the
same
idea.
Bamberger
worked
for
Morgan
Stanley
in
New
York.
He
came
up
with
a
most-up,
most-down
system
that
was
apparently
su
perior
to
the
discarded
one
at
Princeton-Newport,
for
its
returns
were
steadier.
Bamberger
began
trading
with
it
for
Morgan
Stanley
in
1983.
The
system
worked,
and
Morgan
Stanley
expanded
it
mas
sively
under
Bamberger's
boss,
Nunzio
Tartaglia.
Tartaglia
got
much
of
the
credit.
Feeling
unappreciated,
Bamberger
quit
his
job.
He
then
came
across
an
ad
offering
to
bankroll
people
who
had
promising
low-risk
trading
strategies.
The
ad
had
been
placed
by
Princeton-Newport
Partners.
Bamberger
met
with
Thorp
in
Newport
Beach
and
explained
his
system
there.
Bamberger's
system
reduced
risk
by
dividing
the
stocks
into
industry
groups.
It
had
counterbalancing
long
and
short
positions
in
each
industry
group.
Thorp
concluded
that it
was
a
real
improvement
and
agreed
to
fund
Bamberger.
They
began
testing
the
system
in
Newport
Beach.
Bamberger
was
a
chain-smoker.
Thorp,
a
competitive
runner
who
measured
his
pulse
daily,
had
a
policy
of
not
hiring
smokers.
They
compromised
by
letting
Bamberger
go
outside
for
cigarettes.
Bamberger
was
also
forbidden
to
go
into
the
computer
room,
whose
gigabyte
hard
drives,
each
the
size
ofa
washing
machine,
were
reputedly
vulnera
ble to
the
tiniest
airborne
mote.
Thorp
noticed
that
Bamberger
brought
in the
same
brown-
bagged
lunch
day
after
day.
"How
often
do
you
have
a
tuna
salad
sandwich
for
lunch?"
he
asked.
"Every
day
for
the
last
six
years,"
Bamberger
answered.
Bamberger's
trading
system
worked
well
in
computer
simulations.
Thorp and
Regan
set up a
new
venture
named
BOSS
Partners,
for
Bamberger
plus
Oakley
Sutton
Securities.
Based
in
New
York,
BOSS
317


## Page 324

fortune's
formula
began
managing
money
for
Princeton-Newport,
S30
to
S60
million.
It
earned
25
to
30
percent
annualized
in
1985.
This
return
eroded
over
the
next
couple
of
years.
By
1987
it
was
down
to
15
percent,
no
longer
competitive
with
Princeton-Newport's
other
opportunities.
The
problem
was
apparently
competition.
Tartaglia
continued
to
expand
Morgan
Stanley's
statistical
arbitrage
operation.
By
1988
Tartaglia's
team
was
buying
and
selling
S900
million
worth
of
stock.
Bamberger
would
often
be
trying
to
buy
the
same
temporarily
bargain-priced
stock
as
Morgan
Stanley,
driving
up
the
price.
This
cut into the profit.
Bamberger,
who
had
made
a
good
deal
of
money,
decided
to
re
tire. BOSS was
closed
down.
Finally,
according
to stories, Morgan
Stanley's
operation
suffered
a
substantial
loss.
The
bank
closed
down its statistical arbitrage business too.
Thorp
continued
to
tinker
with
statistical
arbitrage.
He
replaced
Bamberger's
division
by
industry
groups
with
a
more
flexible
"factor
analysis"
system.
The
system
analyzed
stocks
by
how
their
price
moves correlated with factors such as the market indexes, inflation,
the
price
of
gold,
and
so
on.
This
better
managed
risks.
Princeton-
Newport
managed
to
launch
the
improved
system,
called
STAR
(short
for
"statistical
arbitrage"),
the
month
after
Giuliani's
raid
on
the Princeton
offices.
STAR made a return of 25percent, or 20 per
cent
after
fees.
Thenthe
partnership
dissolved
and
the
idea
was
put
aside
for
a
third
time.
After
Princeton-Newport
closed,
Thorp
took
some
time
off.
He
was
out of the
business
of
investing
other
people's
money
for
about
a
year.
Like
a
compulsive
gambler,
he
could
not
stay
away
long.
He
discovered
some
irresistible
opportunities
in
Japanese
warrants.
By
late 1990, he was trading them.
One of
Thorp's
former
investors
suggested
that he start a
new
statistical
arbitrage
operation.
Thorp
decided
to
start
a
new
hedge
fund,
Ridgeline
Partners,
for
this
purpose.
"I
had
an
interest
list
that
had
accumulated,"
Thorp
said,
of
people
"looking
to
invest
in any
thing
I
might
be
doing.
So
I
just
made
phone
calls
and
before
the
day
was
done,
we
were
'full.'
"
Ridgeline
Partners
began
business
in
August
1994-
3i8


## Page 325

Signal
and
Noise
Ridgcline's
capacity
was
capped
at
about
S300
million.
By
ex
pansive
1990s
standards,
that
was
only
a
midsize
hedge
fund.
Thorp
wanted
to
make
sure
he
could
keep
oversight
on
his
staff.
He
also
wanted
the
fund
small
enough
that
its
own
actions
did
not
adversely
affect
returns.
As
it
was,
Ridgeline
traded
about
4
million
shares
per
trading
day.
It
was
routinely
accounting
for
something
like
half
ofa
percent
of the NYSE
volume.
The
operation
was
highly
automated.
On
a
typical
morning,
when
Thorp
first
logged
onto
his
trading
computers,
it
was
three
hours
later
in
New
York
and
something
like
a
million
shares
had
al
ready
been
traded.
Steve
Mizusawa
had
joined
the
new
venture.
It
was
Mizusawa's
job
to
scan
the
Bloomberg
news
for
any
surprise
an
nouncements
that
could
upset
the
trades.
Because
of their
unpre
dictability,
mergers,
spin-offs,
and
reorganizations
were
bad
for
the
scheme.
At
the
announcement
of
such
news,
Mizusawa
put
the
af
fected
companies
on a
"restricted
list"
of
stocks
to
avoid
in new
trades.
According
to
Thorp,
each
trade
had
about
a
half-percent
edge.
Half
of
that
went
to
transaction
costs.
The
remaining
quarter-
of-a-percent
profit
on
each
trade
added
up
to
handsome
returns.
Ridgeline
did
even
better
than
Princeton-Newport
did,
averaging
18 percent per year after
fees
from 1994 to 2002.
As
a
demonstration
that "fat
tails"
need
not be
fatal,
in
1998,
the
year
of the
Russian
default,
Ridgeline
Partners
made
a
return
of
47
percent
after
fees.
Ridgeline
had
much
competition.
Among
the
most
successful
operations
are
Ken
Griffin's
Citadel
Investment
Group,
James
Si-
mons's
Medallion
Fund,
and
D.
E.
Shaw
and
Co.
Each
is
larger
than
Ridgeline
was,
managing
billions
of
dollars.
The
managers
are
more
or
less
in
the
Thorp
mold:
Simons
is
a
former
SUNY
Stony
Brook
mathematician,
Shaw
a
Stanford-educated
computer
scientist,
and
Griffin
a
Harvard
physics
undergraduate
who
began
trading
in
his
dorm
room.
Frank
Meyer,
one
of
Princeton-Newport's
early
in
vestors,
set up
Griffin's
hedge
fund.
Medallion
Fund's
employees
include
astrophysicists,
number
theorists,
computer
scientists,
and
linguists.
Job
applicants
arc
ex-
319


## Page 326

fortune's
formula
pected
to
give
a
talk
on
their
scientific
research.
"The
advantage
scientists
bring
into
the
game,"
explained
Simons,
"is
less
their
mathematical
or
computational
skills
than
their
ability
to
think
sci
entifically.
They
are
less
likely
to
accept
an
apparent
winning
strat
egy
that
might
be
a
mere
statistical
fluke."
Each
statistical
arbitrage
operation
competes
against
the
others
to
scoop
up
the
so-called
free
money
created
by
market
inefficiency.
All
successful
operations
revise
their
software
constantly
to
keep
pace
with
changing
markets
and
the
changing
nature
of
their
com
petition.
The
inexplicable
aspect
of
Thorp's
achievement
was
his
continu
ing
ability
to
discover
new
market
inefficiencies,
year
after
year,
as
old
ones
played
out.
This
is
a
talent,
like
discovering
new
theorems
or
jazz
improvisations.
Statistical
arbitrage
is
nonetheless
a
few
de
grees
easier
to
understand
than
the
intuitive
trading
of
more
con
ventional
portfolio
managers.
It
is
an
algorithm,
the
trades
churned
out
by
lines
of
computer
code.
The
success
of
statistical
arbitrage
operations
makes
a
case
that
there
are
persistent
classes
of
market
inefficiencies
and that
Kelly-critcrion-guided
money
management
can
use
them
to
achieve
higher-than-market
return
without
ruinous
risk.
For that
reason,
funds
like
Ridgeline,
Medallion,
and
Citadel
probably
pose
a
clearer
challenge
to
efficient
market
theorists
than
even Berkshire Hathaway.
In
May
1998
Thorp
reported
that
his
investments
had
grown
at
an
average
20
percent
annual
return
(with
6
percent
standard
devi
ation)
over
28.5
years.
"To
help
persuade
you
that
this
may
not
be
luck,"
Thorp
wrote,
"I
estimate
that
...
I
have
made
S80
billion
worth
of
purchases
and
sales
('action,'
in
casino
language)
for
my
in
vestors.
This breaks down into something like one and a quarter
million
individual
'bets'
averaging
about
865,000
each,
with
on
av
erage
hundreds
of'positions'
in
place
at
any
one
time.
Over
all,
it
would
seem
to be a
moderately
'long
run'
with
a
high
probability
that the
excess
performance
is
more
than
chance."
320


## Page 327

Signal
and
Noise
Hong
Kong
Syndicate
At
a 1998 UCLA
CONFERENCE,
Eugene
Fama
"pointed
to me
in
the
audience
and
called
me
a
criminal,"
said
Robert
Haugen.
Haugen's
"crime"
was
that he
was
a prominent
academic
criticof the
efficient
market
hypothesis.
Fama
"then
said
that he
believed
that
God
knew
that
the
stock
market
was
efficient."
The
efficient
market
hypothesis
is far
from
dead.
The
rhetoric,
as strident as
ever,
provides
scant
evidence
that the
track
records
of
a
few
successful
hedge
funds
have
changed
many
minds.
The
story
of the
Kelly
criterion
began
with
bookies
and
horse
races.
The one
milieu
where
Kelly's
system
has
attained the status of
orthodoxy
is
neither
Wall
Street's
canyons
nor
the
groves
of
aca
deme.
It is Hong
Kong's
racetracks.
In
the
past
few
decades,
gamblers
have
begun
to
discover
how
inefficient
the
"market"
of
sports
bets
is.
This
realization
began
in
the
early
1980s
with
the
Las
Vegas-based
"Computer
Group"
of
Michael
Kent,
Ivan
Mindlin,
and
Billy
Woods.
They
had
a
factor-
analysis
system
that
looked
at
college
football
and
basketball
statis
tics
and
decided
which
teams
to bet
on,
at
what
point
spreads.
News
of the
Computer
Group's
predictions
spread
so
quickly
that
it
cut
into
the
group's
profits.
Others
piggybacked
on
the
group's
bets,
af
fecting
the point
spread.
On
Super
Bowl
Sunday
of
1985,
the
FBI
raided
Computer
Group
affiliates
at
forty-three
locations
in
sixteen
states.
The Com
puter Group had been
placing
bets at sports
books
all
across
the
country
in
order
to
minimize
the
effect
of
its
own
wagers
on the
321


## Page 328

fortune's
formula
odds.
The
government
argued
that
this
constituted
a
bookmaking
operation.
People
were
indicted,
the
Computer
Group
dissolved,
and
ultimately
the
charges
were
dropped.
In
1993
Ed Thorp
was
approached
by a
secretive
computer sci
entist
who
was
just
finishing
his
Ph.D.
at
UC
Irvine.
The
computer
scientist
had
a
program
to
identify'
favorable
wagers
on
basketball
and
other
pro
games.
He
had
discovered,
for
instance,
that
teams
that
had
to
travel
to
the
city
in
which
a
game
was
played
tended
to
do
poorer
than
a
team
that
didn't
have
to
travel.
A
team
that
had
to
play
a
number
of
games
in
a
row
did
poorer
on
average
than
a
team
given
more
rest
between
games.
These
variables
were
not
properly
weighted
in
bookies'
odds.
Thorp
was
impressed
enough
to
put
up
S50.000
for
an
experi
ment.
To
minimize
copycat
betting,
they
decided
that the
person
playing
the
bets
should
defy'
the
stereotypes
about
what
a
successful
bettor
would look like. A female friend
of
the
computer
scientist
agreed
to
play
the
role.
She
moved
to
Las
Vegas
for
the
term
of
the
experiment.
Sports
betting
has
several
advantages
over
blackjack.
It is
possi
ble
to
place
very
large
bets,
spreading
among
multiple
bookies
when
necessary.
There
is
no
pressure
to
place
camouflage
bets
when
no
fa
vorable
opportunity
exists.
The
computer
system
identified
wagers
with
a
typical
edge
of 6
percent.
They
used
the
Kelly
criterion
to
size
the
bets.
Wagers
ranged
from
a
few
hundred
dollars
into
the
thousands
as
the
bankroll
grew.
They
placed
anywhere
from
five
to
fifteen bets a
day.
Over
a
period
of
101
days
in
early
1994.
the
team
racked
up a
profit
of
$123,000
on
the
S50,ooo
bankroll.
They
almost
literally
broke the bank at one
down-at-the-hecls
sports book
called
Little
Caesar's.
It wentout of
business
during
the
experiment,
and Thorp
suspects
their
winnings
were
a
factor.
The
team
called
it
quits
because
the
system
required
having
someone
in
Las
Vegas
to
place
the
bets.
The bettor
had
to
transport
lots
of
cash,
and
that
made everyone nervous.
322


## Page 329

Signal
and
Noise
The
problem
with
winning
at
blackjack
and
sports
betting
is
that
sooner
or later a
big
guy
in a suit
tells
you
to
leave.
The
successful
player
is
winning
from
the
house.
In the
1970s
Alan
Woods
was
a
professional
blackjack
player
coping
withthis
very
issue.
He
had
read
Thorp's
blackjack
book
and
wondered
whether
it
would
be
possible
to
take
a
similar
approach
to
horse
racing.
The
winning
purses
come
out of the
pockets
of the
great
mass
of
bettors.
The
track
always
gets
its cutand
has
no
reason
to
care
who
wins.
In
1984
economists
William
T.
Ziemba
and
Donald
B.
Hausch
published
a
book
with
the
Thorp-inspired
title
Beat
the
Racetrack.
In
this
and
other
publications,
the
authors
showed
how
it
was
possible
to
find
arbitrage
opportunities
at
the
racetrack
and
to
use
Kelly's
system
for its
ostensible
purpose,
of
betting
on
horses.
Ziemba
and
Flausch's
experience
was
mainly
with North Ameri
can
tracks.
By
1984
Woods
had
determined
that
the
best
place
to
bet
horses
was
Flong
Kong.
Horse
racing
is
the
only
form
of
legal
gambling
in
Hong
Kong,
and it
is,
according
to an
official
web
site,
"byfar the most popular form of
recreation."
About Sio
billion
is wa
gered
on
horses
in Hong
Kong
each
year.
That
averages
to about
Si,400
for
every
man,
woman,
and
child
in
Hong
Kong.
More
is
wa
gered
on
some
Hong
Kong
races
than
in
an
entire
year
of
betting
at
some
U.S.
and
European
tracks.
Bets
are
accepted
by
cell
phoneand
Internet.
Racing
in Hong
Kong
is run by the
Jockey
Club,
a not-for-profit
organization
that
takes
in
about
S2
billion
a
year.
The
club
has
a
squeaky-clean
reputation.
Fixed
races
are bad for the bottom line.
The
Jockey
Club
runs
two
racetracks,
the
British
colonial
Happy
Valley
and
the
newer,
high-tech
Sha
Tin.
The
Hong
Kong
racing
scene is
relatively
insular.
Florses
and
jockeys
have
little reason to
run
elsewhere.
That too
is
good
for
a
computer
system,
for thereare
fewer
"unknown"
horses
without
track
records.
Woods
partnered
with
Bill
Benter and Walter Simmons in the
"Hong
Kong Syndicate."
Benter
wrote the software,
Simmons
as
sembled
the
historical
data
on
horses
and
jockeys,
and
Woods
put
up the
seed
money,
about
Si50,OOQ.
It
took
several
years
oflaborto
323


## Page 330

FORTUNE
S
FORMULA
get
the
system
operating.
Benter's
computer
model
used
a
fractional
Kelly
system
to
prescribe
the
optimal
portfolio
of
bets.
Kelly's
edge/odds
formula
ignores
the
effect
of
the
bettor's
own
wa
ger
on
pari-mutuel
odds.
A
bettor
who
places
a
large
wager—large
relative
to how
much
is
already
riding
on the
horse—will
lower
the
odds
and
the
potential
winnings.
Benter
had
to
use
a
more
complex
version
of the
Kelly
formula
that
takes
this
into
account.
The
effect
of a
successful
betting
operation's
own
wagers
on the
odds
limits
profits
more
than
the
usual
overbetting
concerns.
This
was
one
rea
son
for
favoring
Hong
Kong
and
its
large
pari-mutuel
pools.
Running
a
computer
betting
team
is
labor-intensive.
Up to a
hundred
people
are
needed
to
hustle
to the
betting
windows
and
to
continually
update
the
model's
database.
Benter's
model
uses
not
only
published
data
like
jockey
and
finish
position
but
some
130
variables.
The
syndicate
hired
people
to
pore
over
videos
of
each
race,
gleaning
data
such
as
whether
a
horse
was
bumped
in
the
turn
and
how
well
it
recovered.
The
first
winning
season
was
1986-87.
Almost
as
soon
as
the
money
started
coming
in,
Benter
and
Woods
fought
over
the
divi
sion
of
profits.
The
syndicate
split
up,
each
partner
taking
a
copy
of
the
software.
Within a
few
years,
Benter,
Woods,
and
Simmons
were
each
multimillionaires.
Woods
has
a
tragic
flaw
for a
scientific
bettor:
he
talks
about
his
betting.
"I
would
have
benefited
by
not
telling
anybody
about
this—
thus
not
tipping
off the
several
other
computer
teams
that
have
since come in here and made their own
millions,"
he told one jour
nalist.
"But that is an
extremely
difficult
thing to do. I just could not
keep my mouth shut."
William Ziemba estimates that a first-rate Hong Kongcomputer
team can
make
as muchas Sioo
million
in a good
season,
with about
halfthat
going
to the
team
leader.
Woods
himself
says
he
has
made
S150
million.
To
Ziemba,
the
races
are an
instructive
model of the
securities markets. It is the same
fallible
humans who set prices for
technology
stocks
and
show
bets.
Both
sets
of
speculators
are
moti
vated
by
desire
for
gain.
This
does
not
guarantee
perfect
market
efficiency.
324


## Page 331

Signal
and
Noise
Woods
lives
the
life
of one of the more
benignly
dissolute
James
Bond
villains.
He
makes
his home in
Manila,
close
enough to Hong
Kong
in a
world
of
fiber-optic
cables
transmitting
bits
that
mean
money.
Now
in
his
late
fifties.
Woods
is
a
white-haired
recluse
who
rarely
leaves
his
luxury
high-rise
apartment
and
his
shapely
female
en
tourage.
If
he
needs
anything,
he
has
his
maid
or
his
Filipino
girlfriend
get
it
for
him.
"I
like
going
to
the
seedy
girlie
bars
in
Makati,"
he
ad
mitted
in one
interview.
"I goout
only
a
few
nights
per
month,
buton
those
nights,
I
tend
to
come
home
with
two
girls,
or,
usually,
more."
Woods
takes
a
perverse
pride
in
saying
that he
has
not
watched
a
horse
race
in
person
in the
past
eighteen
years.
He
does
not
find
horse
races
that
interesting.
Results
arrive
as
instant
messages
from
his
agents
at the
track,
punctuated
by
the
appropriate
smiling
or
frowning emoticons.
Nearthe top of the
late
1990s
stock
market
bubble,
Woods
sold
short
the
NASDAQJndex.
It
was
an
outright
gamble
that
the
bub
ble
would
burst,
and the
timing
was
wrong.
Woods
says
he lost
Sioo
million.
"When
you
look
at
how
much
money
I
have
consistently
made from the
horses,
from
1987
onward,
compared to what I've
done
in the market," he said, "horses would seem to be a far safer in
vestment
than
stocks."
The
Dark
Side
of
Infinity
Claude
Shannon
died
the same year as HAL—2001—on
February
24.
Among
the
hundreds
of
obituaries
were
a
few
that
mentioned
Shannon's
influence
on
thinking
about
gambling
and
325


## Page 332

FORTUNE
S
FORMULA
investment.
"Perhaps
the
impact
Shannon
and
Kelly
have
had
on
finance
can
now
best
be
measured
by
the
number
and
quality
of
Wall
Street
firms
that are
actively
recruiting
mathematicians
and
information
theorists."
wrote
Elwyn
Berlckamp.
Tragically,
Shannon
saw
little
of the
1990s'
developments
in
mathematical
finance
or the
equally
impressive
developments
in in
formation
theory.
His
memory
lapses
worsened
and
were
diagnosed
as
symptoms
of
Alzheimer's
disease.
Shannon
would
be
driving
in
thecar
and
realize
hedid
not
know
where
he
was
going.
In
collect
ing
his
scientific
lifework
for
book
publication
by
the
IEEE,
Shan
non
found
it
impossible
to
remember
where
he
had
put
many
of
his
files.
When
he
did
find
papers,
he
often
had
no
memory
of
writing
them.
Still
physically
vigorous,
Claude
would
take off and
have
trouble
finding
his
way
home.
He
failed
to
recognize
his
own
children.
By
1993
Betty
had little
choice
but to put her
husband
in a
Medford,
Massachusetts,
nursing
home.
She
visited
him
daily.
Shannon
was
a
tinkerer
to the
end,
customizing
other
patients'
walkers
and
taking
apart the home's fax machine.
Ed
Thorp
closed
Ridgeline
Partners
in October 2002. He
seems
to
have
shown
good
timing.
The
return
of
statistical
arbitrage
opera
tions
has
mostly
been
unexceptional
since
2002.
Perhaps
the
mar
ket
has
adapted—or
perhaps
it
is
only
waiting
for
somebody's
new
and improved software.
The Thorps
recently
endowed
a
chair
at the
University
of Cali
fornia
at
Irvine
mathematics
department.
The gift
consists
of one
million
dollars
to
be
invested
entirely
in
stocks,
with
the
university
limited
to
withdrawing
only
2
percent
a
year.
The
fund
is
expec
ted to
compound
exponentially
in
inflation-adjusted
dollars.
Ulti
mately,
Thorp
hopes,
it
will
fund
the
most
richly
endowed
university
chair
in the
world,
and
will
help
draw
exceptional
mathematical
talent
to
UC
Irvine.
Besides
running a
fund
of
funds
and
managing
his own
invest
ments,
Thorp is
exploring
new
investment
and
gambling
opportu-
326


## Page 333

Signal
and
Noise
nitics.
He
cagily
described
one he
had
recently
discovered.
Fie
told
me it is a
widespread
form
of
gambling,
"something
available
in the
Eastern
Hemisphere,"
that
can
take
a
million-dollar
bankroll.
"You
can make about S2.000 an
hour,
but it's
work.
If I could
figure
out
how to make it better, it would be a lot of fun. I've got a whole the
ory
worked
out, and
nobody
else
anywhere
knows
this
theory.
The
people
whooperate this
gambling
situation
have
no
clue."
People
remain
polarized
over the
Kelly
criterion.
Each
side has de
fined
the debate so
narrowly
that its
own
position
is
incontestable.
Each
believes
its
opponents
areabout to be swept
aside
by the
good
sense charitably ascribed to
posterity.
In a recent letter, Samuelson told mc that a heretic is born every
minute.
By
"heretic"
he meant
someone
subscribing
to
logarithmic
utilityand/or the
false
corollary.
When I told Thomas Cover that I
was
writinga bookon this
subject,
he
said
it
was
a storywith
every
thing
except
an
ending.
Like
many
of the
Kelly
people.
Cover
sees
the story as
incomplete
because
it
does
not
include
mainstream
economists recanting their errors.
The
Kelly
cultists
feel
themselves
surrounded
by the indifferent
and
skeptical.
Nils
Hakansson
estimates that no more than
io
per
cent of
M.B.A.
programs
bother to
mention
the
Kelly
criterion (a
situationhe
describes
as
"shameful").
"The
Kelly
criterionis
integral
to the
way
we
manage
money,"
wrote
chairman
Bill
Miller
in the
2003
annual
report of the
Lcgg
Mason
Value
Trust.
But
Miller
says
that
"my
guess
is most
portfolio
managers
arc
unaware
of it, sinceit
did not arise from the
classic
work of
Markowitz,
Sharpe, and oth
ers in the
financial
field."
Investment manager Jarrod Wilcox told
mc the subject is still
"fringe."
The idea pops up in the strangest
places.
It has gained currency
in the
cryonics
subculture,
those
people
who
plan
to
have
their bod
ies frozen at death for potential reanimation by the
medical
nano-
tcchnology
of a
remote
future.
(Thorp
has
arranged
to
have
his
body
frozen.)
The
unlikely
connection is the need to set up a trust
fund to
pay
for ongoing
refrigeration.
Art Quaife, director of the
327


## Page 334

FORTUNE
S
FORMULA
International
Cryonics
Foundation
and
chairman
of its
Suspension
Funds
Investment
Committee,
argued
that a
Kelly
investment
pol
icy"should handilybeat the
published
investment
policies
of other
cryonics
organizations."
To
a
limited
extent,
the
Kelly
criterion
has
enteredthe
company
of
pi and the golden section as one of those rare mathematical ideas
that captures the imagination of nonmathematicians.
There
is
something numinous about
Kelly's
"coincidental"
link between
gambling
and the theory
underpinning
our
digital
age
and the fact
that a
simple
rule
turns
out to be
optimal
in
several
distinct
ways.
Thomas
Cover
compares
the
Kelly
"coincidences"
to the
way
that pi
turns up in contexts that
have
nothing to do with
circles.
"When
something
keeps
turningup
like
that,"
he
suggests,
"it
usually
means
it's
fundamental."
Coverisgettinginto the
hedge
fund
business
himself.
Hisplanis
to
use
the
universal
data
compression
algorithms
devised
for the In
ternet to
wring
profits
from
pairs
of
volatile
stocks.
In
marketing
his
fund,
Cover
has
run into
resistance
from
conventionally
trained
economists
and
financial
advisers.
For
many
people
in
finance,
terms
like
information
theory
and
the
long
run
still
raise
red
flags.
A
Wharton
School
professor
was
quizzing
Coveron behalfof poten
tial
investor
GordonGetty
(who
did not
invest).
The Wharton pro
fessor
objected to Cover's talk of
compound
return rates as time
goes to
infinity.
He informed Cover that "there's a dark side to
infinity."
Paul
Wilmott wrote that
"life,
and
everything
in it,
is
based
on
arbitrage opportunities and their
exploitation."
This
idiosyncratic
view is interesting for its candor. The defenders of free markets are
often at
pains
to
insist
that
market
prices
are
"fair"
prices
and no
one
"exploits"
anyone.
Wilmott
proposes
instead
that
many
of the
market's participantsare
always
trying to take the
maximum
advan
tage
of
people
who
know
less
than
they
do.
We
are
unlikely
to get
very
far
in
understanding
markets
by
pretending
otherwise.
Theop
erative model is
Kelly's
gambler,
or
perhaps
Dostoyevsky's
The
Gam
bler
(who
finds
that
"people,
not
only
at
roulette,
but
everywhere,
do
nothing
but try to
gain
or
squeeze
something
out of one
another").
328


## Page 335

Signal
and
Noise
"You've
heard of
Kuhn's
paradigm
shift?
This is what's going on
here," Jarrod Wilcox said recently of the ongoing
Kelly
criterion
controversy.
"Until youget one of the leading
lights
at
MIT
or Stan
ford to endorse it, you're not goingto
have
the
paradigm
shift...
At
one point I
was
so daring as to submit a paper to
The
Journal
of
Fi
nance.
The
review
said,
'This contradicts everything
we've
learned in
finance.' Well, it
really
doesn't. But it contradicts so many things
that
are
so
well
established
that
the
claws
come
out."
329


## Page 336

NOTES
PROLOGUE:
THE
WIRE
SERVICE
3 Origin of
Payne's
wire
service:
[Allan]
May1999.
4 "It is myintention to
witness
the sport of
kings":
[Allan]
May
1999.
4
"Yes,
of course I do":
[Allan]
May
1999.
5 "If people
wager
at a
racetrack":
Quoted from
John
Cooney's
The
Annenbergs
in May1999.
6
AT&T
history:
Sec
New
York
Times.
July
23,
2004,
C3.
6 "These applicants must know that a
majority":
Fonzi1970,
75.
8 Mercury in catheter:
Fonzi
1970,74.
9
"Go
to hell": Reid
and
Dcmaris
1963, 27.
9
Trans-American,
Ben
Siegel
background:
See
Reid
and
Dcmaris
1963,12-29.
9
Mobsters
took over at time of
Siegel's
death: Lait and Mortimer
1950,
212.
9 "In my opinion, the wire
service":
May1999.
10 "How can we curb
gambling":
Tuohy 2002.
10
Counterfeit
Kcwpie
dolls.
Tropical
Park:
Sec Stuart 198s.
1962.
IO
"I feel like I'm getting shot":Stuart
1985.
176.
10 "In the old days. I met
everybody":
Stuart 1985,180.
11
$25,000 bet on Truman:
Life.
Mar.
26,
1951,
33-39.
11
Kefauver
rated
Zwillman
leader
of
mob:
Stuart
1985,
173.
I.
ENTROPY
15
"It's said that it is one of the few
times":
Biographical
film,
Claude
Shannon:
Father
of
the
Information
Age.
produced by UCSD Jacobs
School,
2002.
331


## Page 337

Notes
15
"The moment I met
him":
Minsky,
e-mail. This is a longer version
of a quote used in Johnson 2001.
16 "It's likesayinghow much
influence":
Morgan
1992.
16 "Mewrote beautiful
papers":
Waldrop2001.
17
"Shannon
became
less
active
in
appearances":
Samuelson,
personal
letter,
June 28,
2004.
17 "Claude'svisionof
teaching":
Waldrop 2001.
17
"had a
vcr)'
peculiar
sort of
mind":
Coughlin
2001.
17 "Some wondered whether he was
depressed":
Samuelson,
personal
letter,
June
28,
2004.
17 "One unfamiliarwith the man might
easily
assume":
"Reflectionsof
Some
Shannon
Lecturers"
1998, 19.
18 Five feet ten:
Letter,
Shannon
to
M.G.E.
Paulson-Ellis.
March
8,
1982,
Shannon Manuscript Collection, Manuscript Division, Li
brary
of
Congress
(hereafter
"Shannon's
papers,
LOO")
18
Appearance
with
beard:
Photograph
in
Shannon's
papers,
LOC.
18
Dixieland
music:
Biographical
film.
Claude
Shannon:
Father
oj
the
Infor
mation
Age,
produced by UCSD
Jacobs
School,
2002.
18
Juggled
four or
five
balls,
small
hands:
Livcrsidgc
1987
and
Elwyn
Bcrlckamp in "Reflections of Some Shannon Lecturers" 1998, 20.
18
Atheist:
Livcrsidge
1987;
"Claude
Elwood
Shannon:
Information
Theorist." article byTimothy M.
Johnson,
dated February10, 1982,
in Shannon's papers, LOC. This unpublishedarticle appears to be a
student
paper prepared from an interview with Shannon.
18 Watergate poem:
"Washington
Fall-out,"
typescript in Shannon's
papers,
LOC.
18
Listof
"Sometime
Passions":
This ison a paper in
Shannon's
hand
writing,
in
Box
13,
Folder
1,
of
Shannon's
papers,
LOC.
18
Enjoyed
burlesque theater:
Livcrsidgc
1987.
19 Family history: Letter, Shannon to Shari
Bukowski,
October
20,
1981,
Shannon's papers, LOC.
19
Distant
father:
Livcrsidgc
1987.
19 Used barbed wire for
telegraph:
Shannon biography in Shannon
1993;
also
biographical
film,
Claude
Shannon:
Father
of
the
Information
Age.
produced by UCSD
Jacobs
School,
2002.
19
Messenger
for
Western
Union:
Wikipcdia
entry for
Claude
Shan
non,
cn.wikipedia.org/wiki/Claudc
Shannon.
19
Didn't
know
what he
wanted
to do,saw
postcard:
Livcrsidgc
1987.
20
Bush
insisted that Shannon be accepted into mathematics depart
ment:
Livcrsidgc
1987.
21
"Apparently,
Shannon is a
genius":
Letter,
Vannevar
Bush to Bar
bara
S.
Burks,
Jan.
5,
1939.
Bush
Manuscript
Collection,
Manuscript
Division,
Libraryof
Congress.
332


## Page 338

Notes
21
"a
decidedly
unconventional
type
of
youngster":
Letter,
Vannevar
Bush
to
E.
B.
Wilson,
Dec.
15.1938,
Bush's
papers,
Library
of
Con
gress.
22
Mathematical
connection
between
heredity
and
relativity:
Letter,
Shannon
to
Vannevar
Bush.
Mar.
8,
1940.
in
Bush's
papers,
Library
of
Congress.
22 Intended to
publish
genetics
dissertation:
See the letters between
Bush
and
Shannon
in
Bush's
papers.
Library
of
Congress.
22
Rediscovered
five
to ten
years
later:
See
Shannon
(1993),
where
ed
itors Sloaneand
Wyncr
address
this
issue.
22
Meeting
with
Norma,
courtship,
honeymoon:
Norma
Bar/.man,
in
terview.
22 "Do you think it would be worthwhile": Letter.
Shannon
to Van
nevar
Bush,
Mar.
8,
1940,
Bush's
papers.
Library
of
Congress.
23
Worked
on
topology:
Letter,
Weaver
to
Vannevar
Bush,
Oct. 24.
1949,
Bush's
papers,
Library
of
Congress.
23
"He got so he didn't want to
see
anyone
anymore":
Norma
Barz-
man,
interview
23
"for a time it
looked
as
though":
Letter.
Weaver
to
Vannevar
Bush.
Oct.
24,1949,
Bush's
papers.
Library
of
Congress.
24 Description, history of
SIGSALY:
Booneand Peterson
2000.
25 "A secrecy system is almost identical": Chin. Lin. Mcferron. et al.
2001,
50.
25
"were so
close
together
you
couldn't separate
them":
Kahn
1967.
744-
26
Conversation
aboutbit,
ban:
Modges
1983,
249-50.
26
"It's
a
solid-state
amplifier":
Livcrsidgc
1987.
27
Meeting,
courtshipof
Moore:
Betty
Shannon,
interview.
27 "One
was
married,
and the
other":
Betty
Shannon,
interview
27
Planned
to
write
book
on
information
theory:
See
letters
between
Riordan
and
Shannon
dated
Feb.
9
and
20,
1956,
Shannon's
papers.
LOC.
Riordan
pitched
the
book
toan
editor
from
John
Wiley
who
was
enthusiastic.
Shannon
thanked
Riordan
but
admitted
that
he
still hadn't gotten around to a first draft.
27 "I am havinga very
enjoyable
time here at
M.I.T.":
Letter, Shannon
to
FIcndrik
Bode,
Mar.
15.
1956,
Shannon's
papers,
LOC.
27
"Foreign
visitors
often spend a day at
Bell
Laboratories":
Letter,
Shannon
to H. W
Bode,
Oct.
3,1956,
Shannon's
papers,
LOC.
28
"flattering":
Letter,
Shannonto H. W
Bode.
Oct.
3,1956,
Shannon's
papers,
LOC.
28
Affiliation
with
Bell
Labs
through
1972:
Coughlin
2001.
28
Salary
of S17000:
Letter.
M. G.
Kispert
to Shannon,
Feb.
15,
1957.
Shannon's papers, LOC.
333


## Page 339

Notes
28 "started
disappearing
from
the
scene":
Fano,
interview.
28
Interrupted
oboe
practice:
Chiu,
Lin,
Mcfcrron.
ct
al.
2001,
59.
28
"Me
slept
when
he
felt
like
sleeping":
Chiu,
Lin,
Mcferron,
et
al.
2001,45.
28
Minsky
comment
about
why
Shannon
quit
working
on
information
theory:
Livcrsidgc
1987.
28
Fano
on
Shannon's
knowledge
of
problems:
Reported
by
Boris
Tsy-
bakovon
http:
"chnm.gmu.edu/tools/surveys/responscs/80/.
28 "I
just
developed
different
interests":
Liversidge
1987.
29
"Will
robots be
complex
enough
to be
friends":
Livcrsidgc
1987.
29 "Dear
Sir:
Your
mechanical
robot
Bel":
Letter to
Shannon
from
Daniel J.
Quinlan,
Shannon's papers, LOC.
29
"We
really
are not
approaching
you
accidentally":
Letter.
Philip
M.
McCallum
to Claude Shannon, May 26,
1983,
Shannon's papers,
LOC.
30 "Letters I've
procrastinated":
Waldrop
2001.
30
Born
about
1898;
son
(Caesar)
not
sure:
Forbes
(uncredited
writer),
June
1,1970,
22-23.
30
Kimmel
biography:
Ruchman
2000 and
unpublished
interview
with
Jack
Newton;
Tudball
2003. 30;
Bruck
1994;
Thorp,
interview.
Peter
Ruchman
interviewed
gambler
Jack
Newton,
who knew
Kim
mel.
Hesentpartof
this
unpublished
material
regarding
Kimmel
to
Ed
Thorp, who
forwarded
it to
me.
30
Zwillman
biography:
SeeStuart
1985.
31
Chose number with fewestbets: Smart
1985,
29.
31
Storyabout
Kaplus
shooting:
Stuart
1985,
42.
32
40
percent
of
imported
liquor:
Stuart
1985.
53-
32
Kimmel
won
parking
lot in crap
game:
Bruck
1994.
29.
33
Kimmel
mortgaged
parking
lots:
Bruck
1994,
32,
which
quotes
Ed
die
Hand
on
this.
33
Taught
himself
calculus,
trigonometry,
probability:
This
is
from
Pe
ter Ruchman's interview with Jack Newton, some
of
which was
published
in
Ruchman
2000.
Ed
Thorp
believes
that
Kimmel
had
little
understanding
of
math.
33
Birthdays
bet.
fly
on
sugar
cube
rigged
with
DDT:
Thorp,
interview.
33
Kimmel
let
Adonis
use
parking
lot:
Bruck
1994.
3°.
34
Compared
to the
National
Association
of
Manufacturers:
Sec
Stu
art
1985.
72.
34 1930 report on New
York
City
rackets:
Coe 2003.
35 Involved with Annenberg's General News: Stuart 1985,
H5-
35
Muzak investment,
Chicago
Crime Commission report: Stuart
1985,140.
35
"said
he'd
get
Longy
if it
was
the last
thing
he
did":
Stuart
1985,
45.
334


## Page 340

Notes
36
1952
taxlien
against
Zwillman:
Stuart
1985,
198-99.
36
"Take
it
easy,
Don
Vitone":
Stuart
1985,
188.
36
"This isfor
you,
Frank!":
Reid
and
Dcmaris
1963,
69.
37
"gross
casinowinsas of
4/27/57":
Reidand
Demaris
1963,
69.
37
Zwillman
death,
suicide
theory
discounted:
See
discussion
in Stuart
1985.
38
"the
most
precise
man
I
have
ever
met":
Liversidgc
1988,
70.
38
"Queen
Victoria,
I
know
when
her
reign
began":
Tudball
2003,
26.
39
Race
with
adding
machine
for
ice
cream
cones:
Liversidgc
1988,
70.
39
Ed
and
James
left
alone
while
parents
worked:
Thorp,
interview.
39
Ammonium
iodide
stunt:
Thorp,
interview.
39
Robinson
Hall
discussion
of
roulette:
Thorp
1984,
43-46.
41
Blackjack
article:
Baldwin,
Cantey,
Maiscl,
and
McDermott
1956.
41
Playall day for
S6:
Welborn
1974.
42
Blackjack
for
wives
of
craps
players:
Fliltzik
1995,
19.
44
"Are
you
working
on
anything
else":
Thorp
1998.
44
"We
had
a
vety
informal
house":
Chiu,
Lin,
Mcfcrron,
et
al.
2001,
58.
45 Dusty
unicycles
and
penny
farthings:
Liversidgc
1987.
45
Items
in
Toy
Room:
Photo
supplied
by
Arthur
Lewbel.
Five
pianos,
piccolos,
sousaphoncs:
Liversidgc
1987.
45
"What
it
was was
a
collection
of
rooms":
Thorp,
interview.
45
"the
biggest
Erector
set
you
could
buy":
Livcrsidgc
1987.
46
Reconditioned
wheel,
ivory
balls:
Thorp,
interview.
48
Importance
of
tilt;
ice
idea:
Thorp,
interview.
53
Nickthe Greek
story:
Smithand
Noble
1961,
69.
53
"she
wasn't
any
bargain
beauty":
Smith
and
Noble
1961.
70.
53
"Off
and
on.
I
have
been
working
on an
analysis":
Letter,
Shannon
to
Vannevar
Bush,
Feb.
16,1939,
Bush
papers.
Library
of
Congress.
55
Orange
juice
analog)-:
I've
loosely
adapted
a
statement
in
Kelly
and
Sclfridge
1962:
"It
is
impossible
(practically)
to
make
good
syn
thetic orange
juice."
57 "an important
influence
on my
life":
"A
Conversation
with Claude
Shannon,"
transcript
of
interview
with
Robert
Price,
Dec.
20,
1983,
Shannon's papers, LOC.
58 "Entropy
House":
Rogers
n.d.
58
"I didn't
like
the
term":
Aftab,
Cheung,
Kim,
ct
al.
2001.
59
"To
make
the
chance
of
error":
Waldrop
2001.
59
Use
more
bandwidth,
more
power:
Aftab,
Cheung,
Kim,
et
al.
2001,
15-
60 "No
Shannon,
no
Napster":
Waldrop
2001.
60
"proudest
and
rarest
creations":
Quoted
in
Liversidgc
1987.
60 "This,of
course,
involves
not
only":
Shannon
1949.
61
Influence
on
garden
design:
Liversidgc
1987.
335


## Page 341

Notes
61
Scientology
cites
Shannon,
information
theory:
www.dianetics-
theevolutionofascicnce.org/chapters/cos_glossary.pdf.
Philip
K.
Dick
appears
to
allude
to
this
odd
blend
of
science,
religion,
and
science
fiction
in his
1957
novel
Eye
in
the
Sky,
a talc of a
religious
cult that,
"using
the
invaluable
material
of
Shannon
and
Weaver
...[,]
was
able
tosetupthe
first
really
adequate
system
of
communication
be
tween
earth
and
Heaven
..."
61
Hubbard
quote
about
starting
a
religion:
In
1938
George
Orwell
wrote,
"I
have
always
thought
there
might
bea lot of
cash
in start
ing
a
new
religion
. .
."
It's
reported
that
eight
witnesses,
including
writer
Theodore
Sturgeon,
heard
Hubbard
say
this,
or a
close
vari
ant, on five
different
occasions circa the late 1940s.
The
Church of
Scientology
denies
that
Hubbard
made
any
such
claim.
Sec
discus
sion at
www.religio.de/thcrapie/sc/relstart.html.
61
"Information
Theory,
Photosynthesis,
and
Religion":
Elias
1958.
62 Date
of
birth: See
short
bio in
"Contributors"
section
of
IRC
Trans-
actions
on
Information
Theory,
Feb.
1962,
189.
62
Kelly
early
biography:
B.
F.
Logan,
interview;
1930
census
record
for
Corsicana,
Texas.
62 Flierfor
Naval
Air
Force:
B.
F.
Logan
interview;
Newark
Evening
News,
Mar.
19,1965.
63
Kelly
description:
Manfred
Schroeder,
interview.
63 "a lot of fun, the life of the party": B. F. Logan, interview.
63 Took shoes off at
work:
Betty Shannon,
B.
F.
Logan,
interview.
See
also IEEE Oral History of John
Pierce.
63 Interest in guns: B.
F.
Logan,
interview.
63 Resistorcircuits to model
football:
B.
F.
Logan,
interview.
63
Feet
up,
chain-smoker:
B.
F.
Logan,
Manfred
Schroeder,
and
Betty
Shannon,
interviews.
64
Schroeder
and
Kluver
rated
Kelly
second
only to
Shannon:
Schroeder,
interview.
64 Storyabout
climbing
Kresge
Auditorium:
Robert
Fano,
interview.
65
Vocoder
at
1939
World's
Fair:
Lucent
web
site
(http://www.bell-
Iabs.eom/news/1997/march/5/2.html),
Smithsonian
Speech
Syn
thesis
History
Project
(http://www.mindspring.com
-ssshp/ssshp_
cd7ss_
homchtm).
65
"Imagine
that wehad at the
receiver":
Pierce
1980, 140.
65
Kelly's
work
on
speech
synthesis:
Lucent
web
site
(http://www.bell
labs.eom/news/1997/march/5/2.html)
65 "televisiondrama of highcaliber and produced by first-rate artists":
Popular
Mechanics,
1939-
66 FCC ban on
giveaway
shows.
Supreme
Court
decision:
Sec
Business
Week,
Aug.
27,
1949.
and Apr. 10,1954.
336


## Page 342

Notes
66
Contestants
and
areas
of
expertise:
See
DeLong
1991,
180-82.
67
West
Coast
gambler:
Shannon
1956b,
which
says
that
Kelly
"was
in
spired by news reports" about this.
68
"gambler
with
a
private
wire":
Kelly
1956,
918.
76
"Although
the
model
adopted
here
is
drawn":
Kelly
1956,
926.
76
"inside
information":
Thomas
Cover,
interview.
76
AT&T
worried
about
title,
bookies:
Berlekamp
1993.
77
Shannon
rcferecd
Kelly
paper:
Thorp,
e-mail.
77
Photograph
of
Floover
in
sexual
situation:
Summers
1993
claims
that
Meyer
Lansky
had
such
a
photograph.
77
"had
agents
. . .
place
his
real
bets":
Sullivan
1979.
77
Hoover,
Mafia,
and
fixed
races:
Sec
Sullivan
1979;
Kristi and
Mark
Fisher's
"J.
Edgar
Hoover"
at
www.carpenoctem.tV;
mafia
hoovcrj.html.
78
"You'll
never
know
how
many
races":
1993
PBS
show
Frontline.
"The
Secret
File
on J.
Edgar
Hoover."
Sec
www.altcrnatives.com/
crime/hoovcr.html.
II.
BLACKJACK
82
Kimmel
physical
description:
Thorp,
interview.
83 Math paper
"Greek"
to
Kimmel:
Ruchman 2001.
83
90
percent
of
profit
to
Kimmel
and
Hand:
Thorp,
interview.
84
Kimmel
said
he
could
protect
Thorp
from
cheaters:
Thorp,
inter
view
84
Pearl
necklace:
Thorp
(e-mail)
denies
the
amusing
statement
in
O'Neil
1964,
repeated
in
Bruck
1994.
that
they
appraised
the
pearls
and
found
them
to be
worth
S16.
84 Gift of
salami:
Bruck1994,
31.
84 Hand
description:
Thorp,
interview;
also
Ruchman
2000.
84 "What was he a bookie
for?":
Bruck
1994,
32.
84 East Coast
tracks,
El
Rancho
Hotel:
Bruck
1994,
30.
85 Hunt bet a
million
on a
football
game:
Eddie
Hand
claims
this in
Bruck
1994. 32.
85
"Kimmel
is
known
to be a
lifetime
associate":
Bruck
1994,
29—30.
(By
1965.
Ed
Thorp
qualified
as
one
of
the
best-known
gamblers!)
85
Bernstein's
discovery
of
counting:
Peter
Ruchman's
unpublished
in
terview
with
Jack
Newton,
supplied
by
Ed
Thorp.
Bernstein
was
probably
not the
first
to
get
the
idea.
See
the
discussion
of
counting
historyin Thorp
1966.
86
Kimmel
accompanied
by two
women:
Thorp,
e-mail.
87
Kimmel
and
casino
people
not
pleased
to
meet:
Thorp,
interview.
337


## Page 343

Notes
88
Planning
for
Reno
trip:
Thorp
1962,
O'Neil
1964.
89 "No one can
win
all
the
time":
Smith
and
Noble
1961,
31
(which
gives
a
slightly
different
wording)
and
201
(photo
of
sign).
89
Miles
of
one-way
mirrors:
Smithand Noble
1961,
95.
90
Lady
Luck:
See
throughout
Smith
and
Noble
1961.
such
as
35,
79.
90
Lost
savings
in
1929
crash:
Smith
and
Noble
1961.
150.
90
Sheriff
closed
game;
paid
fine:
Smith
and
Noble
1961,
149.
90
Most
guns
had
drawn
blood:
Smith
and
Noble
1961,
37.
90
"You're
not
going
to
shoot
any
dice":
Smith
and
Noble
1961,
166-67.
91
Alcoholic
and
compulsive
gambler:
See
Vogel
1999
(where
craps
dealer
and
family
member
Neil
Cobb
says
Flarold
Smith,
Sr.,
"had
a
problem
with
alcohol")
and
especially
Smith
and
Noble
1961.
Though
the
autobiography
has
Smith
saying
"I
believe
I
was
not,
nor am I
now,
an
alcoholic"
(p.
209), he
makes
a strong
case
for the
opposite
conclusion
throughout.
"Apparently
I
was
a
periodical
[drinker]
whose
periods
crowded
so
closely
on
each
other
at
times
as
to
find
me
drinking
daily
and
weekly
for
weeks
at a
crack.
It
was
bad
in
all
ways
and
this
I
knew
. . . But. . .
[e]vcn
after
twelve
and
thirteen
days
of
steady
drinking
I
knew
salt
from
pepper"
(p.
210).
91
"Cowboying":
Smith
and
Noble
1961,
213.
91 Forced to eat hen manure: Smith and Noble
1961,
137.
91
Dorothy's
infidelity,
divorce
settlement:
Smith
and
Noble
1961,
177-85.
91
First-refusal
stockoption: Smithand Noble
1961,
104.
91
Stock
worth
$8
million:
See
Smith
and
Noble
1961,140.
In
1961
the
casino wasvalued at
S25
million,
and Harold owned a third of it.
92
Saw
moth;
talked
into
entering
"psycho
ward":
Smith
and
Noble
1961,223.
92
Swore
off
alcohol
for
four
years,
then
six:
Smith
and
Noble
1961,
25,
317
93 Joe Bernstein's ace count: Smith and Noble 1961.
118—19.
It is con
ceivable
that
Kimmel
accompanied
Bernstein on this trip, and this
may
have
been
why
Kimmel
did
not
accompany
Thorp
and
Fland
at
Harolds
Club.
94 "He'd watch mc likea
hawk":
Thorp,
interview.
95 "Oh, help me,
please
help
me":
Thorp
1962,
46.
95 "I .. .
will...
not...
leave
...
this
...
place!":
O'Neil
1964.
88.
96 "more trouble than an
S18
whore":
O'Neil
1964, 87.
96 Challenge to pit
boss:
Thorp
1962.
46.
97 $10,000 to S21.000 in 30 person-hours:
Thorp
1966,73.
99
Revell
bet
everything
on
roulette:
Reuters
story,"
Briton
Bets
All
on
Vegas
Roulette
Spin
-and
Wins,"
April
II, 2004.
338


## Page 344

Notes
103
Made
virtual
$24,000
in test
run:
Liversidgc
1987
104
"Everybody
else
was
really,
really
nervous":
Thorp,
interview.
104
"We
didn't
trust
the
casinos
not to
bug
our
rooms":
Thorp,
inter
views.
104
"cased
the
wheels":
BettyShannon,
interview.
104
Description
of
roulette
play:
Ed
Thorp and
Betty
Shannon,
inter
views.
104
Brought
soldering
irons:
Thorp,
interview.
104
Test
of
roulette
computer:
Thorp
1998.
105
"it
was
pretty
clear
to
me
that
this
group":
Thorp,
interview
105 50 percent raise in
salary:
Thorp, interview
105 Ranch house:
O'Neil
1964, 80.
105
"The
Relation
Between
a
Compact
Linear
Operator...":
Thorp
1959.
106 Random House
unenthusiastic:
Thorp,
interview.
106
"System
players!":
Thorp
1966,
65.
107 0.10 percent in
favor
of
player:
This
figure,
cited in the
1966
edi
tion
of
Beat
the
Dealer,
was
due
to
Julian
Braun.
The
Braun
figure
was
still
an
approximation.
Peter
Griffin
later
derived
an
exact
figure
of
0.13
percent
in
favor
of the
optimal
(but
noncounting)
player.
107 "Jack, I
didn't
think
it would be
worth
two cents":
Peter
Ruchman's
interview
with Jack
Newton.
107
"a
promoter
who
manipulated
people":
Thorp,
e-mail
to
Peter
Ruchman,
supplied
byThorp.
107 "The
typical
counter, as the
casinos
see
him":
Hiltzik 1995,18.
107 "To enter a casinowith the
ability":
Snyder
1983.
1998, 2003.
108 "one of those
young
men":
O'Neil
1964,
88.
108 Beard as
disguise:
Thorp
1966,
133-36.
108 Peripheralvision,bargain
breakfasts,
S25,ooo: O'Neil 1964,
88-89.
109 "One of the
most
ingenious
aspects":
O'Neil
1964,
89.
109
"How
the
heck
do I
know
how
he
does
it?":
Vickrey
1993,
61.
110
"All
I
know
ishe
wrote
a
book":
Vickrey
1993.
61.
110
Thorp's
book
compared
to
Kefauver
hearings:
Vickrey
1993,
61.
ill "It
tasted
like
they'd
dumped
a
box
of
baking
soda":
Liversidgc
1988,
72.
in
"I
know
of three
beatings":
Liversidge
1988,
72.
112
"ideal for such torture": Reid and Demaris
1963,
44.
M2
"Now you son of a
bitch":
Reidand Demaris
1963,
44.
112
Head
of
information
coding
and
programming:
Newark
EveningNcws,
Mar. 19, 1965. 15.
113
"Theywerevery
polite":
IEEE Oral Historyof
Manfred
Schroeder,
August
2,1994.
113
"Singing"
computer
voice technically easier: Manfred Schroeder. in
terview.
339


## Page 345

Notes
113
AT&T
concerns
about
2001
film:
IEEE
Oral
History
of
John
Pierce,
August
19-21,
1992.
114
Death
on trip to
Manhattan:
B.
F.
Logan
and
Manfred
Schroeder,
interviews;
Newark
EvcningNews.
Mar.
19,
1965.
15-
All
three
accounts
disagree
on
minor
details.
I
have
mostly
followed
Logan's
account,
which
was
the
most
complete.
Schroeder
remembered
the
cause
of
death asa heart
attack.
The
Evening
News
does
not
give
a
cause.
The
News
says
Kelly
collapsed
"on
the
sidewalk
in
front
of the
company's
[Bell
Labs']
office
at
57
Bethune
St.
Logan
remembers
it
as
being
on
Fifth
Avenue,
near IBM's headquarters.
III.
ARBITRAGE
117
Passed
overfor
tenure,
"disability"
of
being
from
Kansas:
Samuelson
1983.
118
"Let those who
will,
write the nation's
laws":
quoted in Bernstein
1992.
113
118
RUM
Warrant
and
Low-Price
Stock
Sumy.
Bernstein 1992,
115.
119
"almost as if once a
week":
Kendall
1953.
119
"nihilism
. . . strike at the
very
heart of
economic
science":
Samuel
son
1973.
119
Savage
thought
people
who
disagreed
with
him
were
stupid:
See
recollection
of
William
Kruskal
at
http://www.umass.edu/wsp/
statistics
tales/savage.html.
119
"Everhear
of
this
guy?":
Bernstein
1992,
23.
120
"the
mathematical
expectation
of the
speculator
is
zero":
Bachelier
1900.
122
"ridiculous":
Bernstein
1992.
116.
123
"It is not ordained in
heaven":
Samuelson
1974.
19-
123
Research
of
Treynor,
Sharpe.
Black.
Scholes:
Cited in
Samuelson
1974.
17
124
"I'd be a
bum
in the
street":
See
http://wwwrwestga.edu/-bquesty
2002/market.htm.
124
"a loose
version
of the
'efficient
market'or 'random
walk'
hypothe
sis":
Samuelson
1974.*7
125
Samuelson
bought
Berkshire
Hathaway:
Ed
Thorp
brought
this to
my
attention.
125 "In an efficient market": Fama 1991.
126 1970 article proposing three versions: Fama I970-
126
Studies
suggesting
that
private
information
afreets
prices:
Sec
Roll
1988 and Cutler, Poterba, and Summers 1989.
127
"A
respect
for
evidence
compels
me":
Samuelson
1974.
340


## Page 346

Notes
127
"Random
Walk
Cosa
Nostra"
nickname:
Lowenstein
2000,
35,
which
quotes
fund
manager
Victor
Niederhoffer.
127
"Unless
you're
working
in a
certain
way":
Fano,
interview.
128
"would
call
someone
at MIT
and
they'd
say":
Fano,
interview.
Ed
Thorp
likewise
reports
a
sense
that
he
was
"fighting
the
establish
ment"
and
says
he
decided
"not
to
waste
time
trying
to
publish
pa
pers
I
didn't
need
to
publish"
on
market
inefficiency.
128
"I
have
a
nice
wife,
wonderful
kids":
Barzman
2003,
379.
128
"Are
you
happy?":
Barzman
2003,
379.
129 "Entirely without
funds":
Letter, Vannevar Bush to Barbara S.
Burks,
Jan.
27,
1939,
Bush's
papers,
Library
of
Congress.
129
Complained
new
furnishings
were
like
stage
set:
Norma
Barzman,
interview.
129
Saving
in
zero-interest
checking
account:
Hershbcrg
n.d.
[1986].
129
"I've
always
pursued
my
interests":
Quoted
in
Lewbel
2001.
129
"When
he
was
working
on a
theory":
Chiu,
Lin,
Mcferron,
et
al.
2001,
63.
129
"Once
he
was
done
with
something":
Betty
Shannon
quoted
in
Chiu, Lin, Mcferron, et al. 2001, 60.
129 "I've spent lots of
time":
Quoted in
Lewbel
2001.
129
Shulman's
list
story:
Bernstein
1984,135.
130
Legend
of
uncashed
checks
in
office:
Sec
Coughlin
2001;
Liversidge
1987
130
Books
read.
Where
Are
the
Customers'
Yachts?:
Hershbcrg
n.d.
[1986].
131
"Usually
in
my
experience":
Samuelson,
personal
letter,
June
28,
2004.
131
"You
weren't
affected
by your
success
in the stock
market":
Liver
sidge
1987
(Library
of
Congress
transcript).
131
"Certainly
not":
Liversidge
1987
(Library
of
Congress
transcript).
132
Writing
theories
on
napkins:
http:/,
chnm.gmu.edu/tools/surveys/
responses/80/
132
Euler's
investments:
Thorp
1969,
citing
G.
Waldo
Dunnington's
Carl
Friedrich
Gauss,
Titan
of
Science
(1955).
132
"I
can
calculate
the
motions
of
heavenly
bodies":
Quoted
in
Dunbar
2000,
1.
132
Arbitrage
comment:
Chiu,
Lin,
Mcferron,
et
al.
2001,
59.
133
"The
Portfolio
Problem":
Shannon
1956b,
Shannon's
papers,
LOC.
The
lecture
notes
have
a
cover
sheet
incorrectly
identifying
them
as
notes taken by Peterson. Peterson has informed me that the notes
were
written
by Shannon himself as a
handout
for the class.
135
"You
know the
economists
talk about the
efficient
market":
Liver
sidge
1987.
136
Codex
history:
Aftab,
Cheung,
Kim,
et
al.
2001,
20-21.
341


## Page 347

Notes
136
Told
Berlckamp
it
was
not
the
time
to
buy
stocks:
Berlekamp
in
"Reflections
of
Some
Shannon
Lecturers"
1998, 20.
137
Equation
on
blackboard,
explanation:
Thorp,
interview.
138
Zwillman's
widow
claimed
to
own
Kinney:
Bruck
1994.
32-
139
"Service
isour
middle
name":
Bruck
1994.
41-
139
"One
day,
a
black
guy
came
in":
Bruck
1994.
42.
139
Funeral
business
more
profitable
than
parking
lots:
Bruck
1994.
28.
139
Ross
a
card-counter:
Bruck
1994,
39.
139
Over$30a
share:
See
Bruck
1994.
57
140
Caesar
Kimmel
share
value:
Forbes,
June
I,
197C
22.
140
"I've
lived
with
this
over
the
years":
Forbes,
June
1,1970,
22-23.
141
Sio
billion
revenue,
$15
billion
market
value:
Bruck
1994,
272.
141
Kimmel's
death,
Ivi's
age:
Bruck
1994.
242.
141
"I
realized
that if I
pushed
it":
Liversidge
1988,
70.
142
"I
learned
an
expensive
lesson":
Thorp,
interview.
142
"promptly
went
down
the
tubes":
Thorp,
interview.
142
Steak
knives
defective:
Thorp,
interview.
142
Sidney
Fried,
RHM
Warrant
Service:
Thorp,
interview.
142
"I
got
thinking
about
what
it
is":
Thorp,
interview.
145
Long-short
trades
Kelly-optimal:
Thorp
1998,
21-22.
146
"clique
of
group
theorists":
Thorp,
interview.
146
Kassouf's
Ph.D.
thesis
on
warrants:
Kassouf
1966.
146
Weekly
research
seminar,
no
students:
Thorp,
interview.
147
$40,000
to Sioo.ooo in
two
years:
Navsweek,
Dec.
18,
1967;
Laing
1974-
147
"after
several
false
starts,
I
have
finally
hit
pay
dirt":
Letter,
Ed
Thorp
to
Claude
Shannon,
dated
Dec.
23,
1965,
in
Shannon's
pa
pers, LOC.
148
PQ^See
Samuelson
1974.
148
"They
have
too
high
an
I.Qjbr
that":
Samuelson
1974.19-
148
"we'd
get
a
certain
cachet":
Thorp,
interview.
149
"staggering":
Tudball
2003.
32.
149
"Just
as
astronomers
loathe
astrology":
Samuelson
1968.
150
"We
had
a
different
degree
of
daring":
Thorp,
interview.
150
S2.000
attorney
fee:
Thorp,
interview
and
e-mail.
151
Thorp
looked
at
list
when
Regan
left;
concluded
he
would
be
cho
sen: Thorp, interview.
151
"He
was
going
to
do
the
things
I
didn't
want
to
do":
Thorp,
inter
view.
152
"speculative
tools
used
for
conservative
ends":
Loomis
1966,
240.
152
Two
hundred
hedge
funds
by
1968:
Gabelli
1995-2003.
153
Survivor
bias
in
TASS
hedge
fund
returns:
van
der
Sluis
and
Posthuma 2003; see also Flulbert 2003.
342


## Page 348

Notes
153
Meeting
with
Warren
Buffett:
Thorp,
interview.
153
Got
leads
at
courthouse;
met
Evans
brothers:
Thorp,
e-mail.
153
Evans
and Mario
Puzo:
Patterson 2003.
154
Evans
interview
in
pool;
asked
same
questions
repeatedly:
Thorp,
interview,
154 Fund's
investors:
Kandel
1969.
154
"The
question
wasn't
'Is
the
market
efficient?'
":
Thorp
2004-5.
155
Thorp
had
version
of
Black-Scholes
formula
by
1967:
Thorp,
inter
view
and
e-mail.
155
Hedge
fund
returns:
Thorp,
e-mail.
The
figures
in
Ziemba
2003
are
higher
(they
may
not
include
fees?).
155
Mizusawa
needed
only
five
hours
of
sleep:
Thorp,
e-mail.
156
"But I don't think I'll be
able":
Weiss
2004.
156
Resorts
International
deal:
Tobias
1984,
69-70.
157
Committed
150
percent
to
arbitrage:
Thorp
1971.
157
"Sleep
at
night"
test:
Thorp,
interview.
159
"No
one
who's
been
with
me
for
five
years":
Bruck
1988.
83.
159
"Michael
is
the
most
important
individual":
Bruck
1988,
84.
159
"Someone
like
Mike
comes
along
once
every
five
hundred
years":
Bruck 1988. 84.
160
Saw
Milken
behind
a
pane
of
glass:
Thorp,
interview.
160 "Whatare
you
talking
about?"
Bruck
1994,
216.
160
Milken
told
friend
he
liked
Ross,
thought
they
were
similar:
Bruck
1994.
215.
161
Equity
for
bond
buyers
went
to
Milken:
Sec
Stewart
1991;
also
Bruck 1994, 216.
161
Contracted
pupils
in
poker
games:
Lowenstein
2000,
29.
163
"For a
while":
Dunbar
2000.
40.
163
"Although
our
trading
didn't
turn
out
very
well":
Dunbar
2000.
40-41-
164
Tested
Black's
formulas
on
HP
computer:
Thorp,
interview
and
e-mail.
164 "a
masterpiece":
Thorp,
e-mail.
164
"I
never
thought
about
credit,
actually":
Thorp,
interview.
165
Changed
fund
name
in
1974:
Kurson
2003.
165
Returns:
Thorp,
e-mail.
$20
million:
Laing
1974.
166
"Playing
the
Odds":
Laing
1974.
166
"In
some
cases,
the
funds'
trading
is
dictated":
Laing
1974.
166
"an
incipient
but
growing
switch":
Laing
1974.
166
"just
oneof
many
tools":
Laing
1974.
166
"The
whole
computer-model
bit
is
ridiculous":
Laing
1974.
167
"The
better
one
was
one
of
those
crazy
funds":
Laing
1974.
167
Lost
S107.000
on
U.S.
Financial:
Laing
1974.
343


## Page 349

Notes
167 Phoned attorneys: Laing 1974.
167
Asked
money
managers
if
they
beatthe
market:
Bernstein
1992,
75;
Thorp, interview.
168
Capital
Asset
Pricing
Model:
Sharpe
1964.
168
AMC
convertible
bond
deal:
Kurson
1999a,
42-44-
169 "Situations that
simple":
Kurson1999a,44-
171
Sharpe
on
"active"
and
"passive"
investors:
Thorp,
interview;
see
also Sharpe 1991.
172
The
Sting
inspired
by
delayed
wire
service
con:
Cooney
1982,
76.
I
am
all
but
certain
that the
alias
"Kelly,"
adopted
by
Robert
Red-
ford's
character,
isa
coincidence.
But
screenwriter
David
Ward
was
well
versed
in
the
history
of the
wire
services
and
associated
confidence
games.
One
character
makes
a
reference
to
tapping
into
"Moe Annenberg's wire."
172
"Why
aren't
you
out
there
doing
it?":
Liversidgc
1988,
74.
172
Thorp
made
$6
million:
Thorp,
interview;
see
also
Financial
World.
July
14,1987,109,
which
estimates
Thorp's
1986
earnings
as
"a
hefty
$8 million to S9 million."
172
Newman
concerned
about
tax-related
trades,
government
scrutiny:
Thorp, interview.
172
"I've estimatedfor
myself":
Thorp,
interview.
174
Dorchester,
Belvedere
partnership:
Bruck
1988,
81-82.
175
Capital
about
$60
million:
Ziemba
2003,151.
176
Profit
in
AT&T
deal:
Spanier
1988,
35-36.
Kurson
2003
says
the
deal
"enriched
Thorp's
investors
by
S2.5
million."
177
S&P
futures
trading:
Tobias
1984,
68- 72.
177
Return
figures:
Thorp,
e-mail.
178
"Taking
candy
from
a
baby":
Baldwin
1986.
178
"near
the
rumors,
information
and
opportunities":
Wiles
and
Hum
1986.
178
Quit
teaching
jobin
1982:
Baldwin
1986.
178 Mod shirts and
sandals:
Laing
1974.
178
Bombshelter:
Liversidge
1988,
70.
182
IV.
ST.
PETERSBURG
WAGER
"Peter
tosses a coin":
Bernoulli
1954-
182
Ducat
worth
S40: See
Bernstein
1996.
lo6n.
183
"Although
the
standard
calculation":
Bernoulli
1954.
183
Keynes's
book:
Keynes
1921.
183
Mentioned
by
von
Neumann
and
Morgenstern;
other
economic
thinkers:
See list
of
references
in
Bernoulli
1954, 35.
344


## Page 350

Notes
184
"The
value
ofan
item
must
not
be
based
on
its
price":
Bernoulli
1954.
24.
185
"In the
absence
of the
unusual":
Bernoulli
1954,
25.
186
"As
the
quantity
of
any
commodity":
Jevons
1986.
186
"prototype
for
Everyman's
utility
function":
Savage
1954,
94.
Savage
adds,
however,
that
"it
cannot
be
taken
seriously
over
extreme
ranges."
187
"hold
any
terrors
forthe
economist":
Samuelson
1969,
243.
187
"bliss
level":
Stephen
Ross
mentions
the
term
in
a
passage
quoted
in
Goldman
1974, 98.
188
"ifa
speculator
is
in
the
habit
of
risking
his
capital":
Williams
1936,
453-54-
190
"Nature's
admonition
to
avoid
the
dice
altogether":
Bernoulli
1954,
29-
190 "It
may
be
reasonable
for
some
individuals":
Bernoulli
1954,
29.
191
"Since
all
of our
propositions
harmonize":
Bernoulli
1954,
31.
192 Lastman hired before
Depression:
Bibb
Latane.
e-mail.
192
February
17,1956:
McEnally
1986,
29.
192
Presented
geometric
mean
principle
at
1956
Cowles
seminar;
Markowitz present: Latane
1978,
395.
192
"To
suppose
that
safety-first
consists
in
having
a
small
gamble":
Let
ter,
John
Maynard
Keynes
to
F.
C.
Scott,
dated
Feb.
6,
1942,
in
Keynes 1983,12:81-83.
194 1959 article: Latane 1959.
194
Latane
had not
heard
of
Kelly
at timeof
Cowles
seminar:
See
foot
note6 on
page
147
of
Latane
1959,
which
cites
Kelly
and
Shannon.
195
Markowitz
learned
of
Latane's
work
via
Tobin,
1955-56:
personal
letter, October 25.2004.
Markowitz
said he didn't remember hear
ing Latane speak in 1956.
195
Chapter
in
Portfolio
Selection:
"Return
in
the
Long
Run,"
Markowitz
1959.116-25.
196
"Kelly[-Breiman-Bernoulli-Latane
or
capital
growth]
criterion":
Thorp
1971.
197
"the
idea
that
we
should
pick
the
investment":
McEnally
1986,
22.
201
"the
Kelly
criterion
should
replace
the
Markowitz
criterion":
Thorp
1969,
292.
202
Samuelson
attended
regular
meetings
on
investing
organized
by
Shannon:
Betty
Shannon
and
Thomas
Cover,
interviews;
Paul
Samuelson,personal letter. June 28,2004. Cover wasunder the im
pression
(from
speaking
with
Claude)
that
these
meetings
were
at
the
Shannon
home.
Betty
said
they
were
at
MIT;
it
was
a
series
of
meetings on jugglingthat were held at their home.
202
1971
MIT
talk:
No
one
today
is
sure
about
the
year.
In
Liversidge
1987
Shannon
says
the
talk
was
"some
twenty
years
ago."
Hershberg
345


## Page 351

Notes
n.d.
[1986]
puts
it
"fully
17
years
ago,"
apparently
based
on
Claude
and
Betty's
recollections
at
that
time.
Though
undated,
the
Flcrsh-
berg
article
was
almost
certainly
written
in
1986,
as
it
is
mentioned
in
letters
from
Hershberg
to the
Shannons,
dated
June
23
and
Au
gust
28,1986,
in the
LOC.
204
Description
of
rebalancing
in
MIT
talk:
see
David
Forney
in
chnm.gmu.edu/tools/surveys/responses/80/;
also
Liversidge
1987
204
"being
whose
facilities
are
so
sharpened":
Maxwell
1871.
206
Bennett's
explanation
of
Maxwell's
demon:
Bennett
1982.
207
"is
in
effect
possessed
of a
'Maxwell's
Demon'
":
Samuelson
1974,
19
20S
"Naw.
The
commissions
would
kill
you":
David
Forney
in
http://chnm.gmu.edu/tools/surveys/responses/80/.
208
Constant-proportion
rebalanced
portfolios
discussed
by
econo
mists:
Rubinstein
1991 and Booth and Fama 1992.
209
"As
pointed
out to meby
Professor
L.
J.
Savage":
Latane
1959.
210
"Our
analysis
enables
us
to
dispel
a
fallacy":
Samuelson
1969,
245-46.
210
"somewhat
mystifying
. . .
Professor
Savage
has
informed
me":
Samuelson
1969.
245.
210
"provides
an
effective
counter
example":
Samuelson
1969.
246.
211
Shannon
unaware of Samuelson's article, reaction: Cover,
interview;
letter,Thomas Coverto
Claude
Shannon,
dated
July
5,1985.
Shan
non's papers, LOC.
211
Rubinstein endorsed, then
recanted:
See Rubinstein
1975
and Ru
binstein
1987.
212
"Fromthis
indisputable
fact":
Samuelson
1971,
898.
212
"The
Kelly
view,
that
maximizing
investment
growth
of
value":
Hunt
2000,
3.
213
"automatically
built
in":
Hakansson
1971,
555.
213
Auto
accident
analogy:
Wilcox,
interview.
The
1996
U.S.
death
rate
from
auto
accidents
was
16.2
per100.000.
Were
this the only
cause
of
death,
the
average
life
span
would
beabout
6,170
years.
216
Kelly
system
maximizes
median
wealth:
Sec
Hakansson
1971.
217
"As
Gertrude
Stein
never
said:
Epsilon
ain't
zero":
Samuelson,
1963,
6.The
literary
reference
is
unclear.
I
was
unable
to
find
any
Stein
comment that sounds like it could have been the basis for Samuel
son's
"Epsilon
ain't
zero."
One
quote
attributed
to
Stein
(it
could
describe
the
Kelly
criterion
controversy)
is:
"Thereain't no
answer.
Thereain't
gonna
be
any
answer.
There
never
has
been
an
answer.
That's
the
answer."
218
"Again
the
geometric
mean
strategy
proves
to
be
fallacious":
Merton
and
Samuelson
1974.
76.
346


## Page 352

Notes
218 "Given the qualifications": Latane 1978.
397.
218 "spare the dead":
Samuelson
1979,
306.
218
"It is
surprising
to
note":
Ophir
1978,
103.
219
"We
heartily
agree
that
the
corollary
is
false":
Thorp
1971.
219
"has
nothing
to
do
with
the
value
function":
Kelly
1956,
925-26.
219 "My position as to the usefulness of G
...
I have never considered
G":
Latane
1978, 310.
219 "We are not interested in utility
theory":
Bell
and Cover 1980,162.
220 "it is
difficult
to
identify
the
underlying
utilities":
Latane
1978,
310.
220 Markowitz
articles:
Markowitz
1972
and
1976.
220
"What
about
the
argument
that
expected
average
compound
re
turn": Merton and Samuelson 1974.
221
"most
people
I
talk
to
say
'Yeah,
sounds
great
to me'
":
Thorp,
in
terview.
221
"a private
institutional
investor":
Thorp
1971,
reprinted and
revised
in
Ziemba
and Vickson 1975, 612.
221
"Institutional
investor"
was
Convertible
Hedge
Associates:
Thorp,
e-mail.
221
Fund's
cumulative
gain:
Thorp
1971.
221
"Proponents
of
efficient
market
theory":
Thorp
1971.
221
"We
consider
almost
surely
having
more
wealth":
Thorp
1971.
224 "a
person
accepting
Latane's
[line
of
reasoning]
has
to
forgo":
Ophir
1979.
303.
225
Leverage
justified with
stocks:
Rubinstein
1991;
Rotando and
Thorp
1992;
and
especially
Thorp
1998.
Thelatter
shows
thatopti
mal
leverage
is
acutely
sensitive
to the
interest
rate
charged.
225
"What I think he
was
trying
to
say":
Thorp,
interview.
226 "Why then do somestill think they
should
want":
Samuelson
1979,
305.
226 "No need to say
more":
Samuelson
1979,
306.
227
"Reviewers
who are best
placed
to understand an author's
work":
Begley
2004.
229 i/h
rule
an
approximation
for
blackjack,
exact
for
continuous
bet
ting:
SeeThorp 1997
(revised
1998),
IO.
229
"All
serious
gamblers
use
something
close
to the
Kelly
criterion":
http://may.casin0citytimes.com/articles/li3i.html.
229 "a certain John L
Kelly":
"The
Kelly
Criterion
Defended"
on
Predict-A-Win
for
UK
Football,
http://www.prcdict-a-win.co.uk
ba_tkcd.php.
230
"The
next
time
some
tout in a
bad
suit
advises
you":
http://www.
professionalgambler.com/behind.html.
230
"according
to expert
researcher
Dr.
Nigel
E.
Turner,
Ph.D..
Scien
tist":
http://www.professionalgambler.com/binomial.html.
347


## Page 353

Notes
230 "We have no evidencethat
Buffett":
Flagstrom
2000,128.
231
"My
experience
has
been
that
most
cautious
gamblers
or
investors":
Thorp
1997
(revised
1998),
10.
231
"bright
clear
line":
"Gambling.
Investment,
and
the
Kelly
Crite
rion,"
http://www.fricndlymachine.eom/2003/n/gambling_invest.
html.
233
"Those
individuals
or
institutions
who are long term com
pounders":
Thorp
1997
(revised
1998),
38-
On
reading
the
present
work.
Thorp
spotted
a
minor
typo
in the
1997
article,
which
has
been
corrected
here
("a
lesser
fraction"
rather
than
"a
lesser
func
tion").
234
Market
caps
on
position
sizes;
use
of
Kelly
criterion
as
conceptual
guide:
Thorp,
interview
and
e-mail;
see
also
Thorp
1971.
235
Lost
$2
million
and
made
$2
million;
Octoberabout
even:
Thorp,
e-mail; Liversidge 1988.
235
34 percent: Ziemba 2003,
151.
236
"So
improbable
is
such
an
event":
Rubinstein
1988.
237 "If I did use
some":
Letter,
Paul
A.
Samuelson
to Thomas M. Cover,
dated
September
7,
1988
(supplied
by
Cover).
237
"complete
swindle
. . .
mathematicians
who
ignore
remainders":
Letter, Paul A. Samuelson to
Thomas
M. Cover,
dated
Nov.
2,1988
(supplied
by
Cover).
237
"If I
like
your
ways":
Letter,
Paul
A.
Samuelson
to
Thomas
M.
Cover,
dated
May
16,
1991
(supplied
by
Cover).
V.
RICO
241
Boesky
said
father
ran
delicatessens,
actually
ran
topless
bars:
Stew
art
1991,41.
241
Claimed
he
worked
for
U.S.
Information
Agency
but no
record:
Stewart
1991,42.
241 Boeskybio: Stewart 1991,42~43-
242 Unlisted phone number: Hicks
1982.
242 "Ivan, you little
pig":
Stewart
1991,
45.
243
Nickname
"Piggy":
See
Kinkead
1984,
102.
243 "The maximumpermitted by
law":
Kinkead
1984.
105.
243 "Not at
all":
Kinkead 1984, 104.
243
"You
are
insinuating
improprieties":
Kinkead
1984.105.
245
Boesky's
payment to
Siegel:
Stewart
1991.
H3-
245
Boesky
told
Siegel
he
was
a CIA agentin Iran:Stewart
1991,
42.
246
Siegel
suspected
assassination:
Stewart
1991.177.
246 "What's the matter,
Marty?":
Stewart 1991,
178.
348


## Page 354

Notes
247
"Boesky's
competitors
whisper
darkly":
Kinkead
1984-
247 Criminal connections of Harold Giuliani. Leo D'Avanzo: See Bar
rett
2000,13-66.
248 Picture of Nixon as dartboard: Barrett
2000,
53.
248
RICO
named for
Little
Caesar
character:
The
law's
author, G. Robert
Blakey
of
Notre
Dame
Law
School,
refused
to
confirm
or
deny
this
story.
See
http:
www.snopes.com
language
acronyms
rico.htm.
249
Supreme
Court
ruling
on
scope
of
RICO:
U.S.
v.
Turkette,
452
U.S.
576
(1981).
249 "I dreamed up the
tactic":
Giuliani
2002,
214.
249 "Rudydecided that RICO
would
be his
Excalibur":
Barrett
2000,
147
250
Friends
suspected
Ross
bought
the
chips:
Bruck
1994.
97
251
Ross a
card-counter:
Bruck 1994. 39-
251
"I felt at the end of the year that I had netted out":
Bruck
1994.
160.
251
Solomon
Weiss
prosecution:
Bruck
1994,
108-63.
Nickname
of
Charles
Kimmel:
Bruck
1994,
146.
252 Caesar Kimmel's failed restaurant venture, retirement: Bruck 1994.
207-10.
252
Flat Fleet
Feet:
See
http://www.arlingtonpark.com/bet_the_races/
understanding
horses.html.
252 Ross'sinterview and Giuliani'sstatement: Bruck1994.
i59~6o.
253
FBI
tapes,
wealthiest
gangster:
See
Bruck
1994.
239.
253
"We
own
Kinney":
Bruck
1994,
239.
This
was
reported by two FBI
investigators
and
may
not be quite
verbatim.
253
"Fat
Tony"
a friendof
Kimmel's:
Bruck
1994,
242.
253
Cafaro's account of labor
racketeering:
Bruck1994. 239-42.
254
"a
devil's
pact
with
La
Cosa
Nostra
. . .
careful,
surgical
action":
Newsweek.
July
11,
1988,
33.
254
"Freedom
is the
willingness
of
every
single
human
being":
Barrett
2000,
6.
254
132
assistants in 1986: Barrett
2000,138.
254
"would
review
press
releases
like they were
indictments":
Barrett
2000,
148.
254 "He wanted to
achieve
the Thomas Dewey identity": quoted in
Barrett
2000.
161.
255
Prosecutors
noted
parallel
between
Mafia
and
Wall
Street
criminals:
Stewart
1991,
404.
255
"There's a lot of money to be
made":
Stewart I99L 84-
255
"Greed is all
right":
Stewart
1991,
261.
256 "I
doubt
that":
Stewart
1991, 349.
256 "I know":
Stewart
1991, 350.
349


## Page 355

Notes
256 Doonan was
"Bill":
Stewart 1991.
363.
256 Giuliani approved Freeman arrest: Stewart 1991.379.
257
"You've
got to be
careful":
Stewart 1992,
336.
257
"I'm very
close
to the
people
buying
the
stock":
Stewart
1991,194.
258 "I
didn't
leave":
Stewart
1992,407.
259
Description
of tax
implications
of
parking:
Forbes,
Oct. 2,
1989,
222.
259 "didn't have the manpower to sort out": Stewart
1991.
408.
259 Hale's grand jury
testimony:
Stewart
1991.
407-8.
260
Details
of
raid:
Stewart
1991,
409;
Tudball
2003,
34;
Wall
Street
Jour
nal,
Jan.
13,
1988,
24;
Thorp,
interview.
The
Wall
Street
Journal
says
that
six
hundred
boxes
of
evidence
were
taken.
260 1985trades:
Wall
Street
Journal,
Mar.
21,1989,
A12.
260 "Were you parking for
them?":
Stewart
1991,
410.
261
"We were hopingyou
would
be
willing
to cooperate with
us":
Wall
Street
Journal.
Mar. 21, 1989, A12.
261
Thought raid was
nonsense:
Tudball
2003, 34.
261
"Everybody
lawyercd
up":
Thorp,
interview.
261
$15
million
withdrawn
after
raid;
some put in
wives'
names:
Baird
and Vinson 1990, 1028.
262 20 percent
interest;
Milken
helping
Mattel:
Tudball
2003,
34;
Busi
ness
Week,
Aug.
14,
1989,
46.
262
C.O.M.B.'s
business:
The
company
now
appears
to be out of
busi
ness. It took out ads in
The
Wall
Street
Journal;
see, for instance,
Sept.
28,1988,
p. 10.
262
Stock-manipulation
scheme:
Tudball
2003,
34;
Stewart
1991,
411;
Business
Week,
Aug.
14,1989,46.
262 "It's not fun
anymore":
Stewart
1991,
412.
262
"You're
a
sleazebag":
Stewart
1991,
412.
263 "I think I'd be very
good":
New
York
Times.
Dec.
3.
1987.
263 "I
cannot
leave unless I'm sure":
New
York
Times,
Jan.
11,
1988.
264 "It
would
be wrongfor me to
leave
this
office
now":
Barrett
2000.
172.
264
Coached
by
attorneys,
asked
for extra
time:
Wall
Street
Journal,
Mar.
21.
1989,
Al2.
264 Cap saying
suit
HAPPENS:
Stewart 1991,435.
264 "I carried plenty of positions": Stewart 1991,
411.
265
Charges
"too
complicated"
for
jury:
Stewart
1991,
435.
265
"If 1
do.
I'm
going
to
take
the
Fifth":
Thorp,
interview.
265
"My
theory
on
taking
the
Fifth
was,
I
didn't
know
anything":
Thorp, interview.
265
"not a
novel
approach
. . .
when
we
believe
the
magnitude
of the
crime
warrants
it":
Wall
Street
Journal.
Aug.
12,
1988,
4.
265
"You'd
have
to bea
fool":
Wall
Street
Journal.
Aug.
4.
1988.
350


## Page 356

Notes
265
Giuliani
denied
making
offer:
Wall
Street
Journal,
Aug.
4,
1988.
266 "If
you
cooperate,
fine":
Wall
Street
Journal,
Aug.
5.1988,
3.
266
Harvard
and
Weyerhaeuser
invested
in
fund:
Wall
Street
Journal.
Sept. 28, 1988. 10.
266
"frightening... It
seems
clear":
Wall
Street
Journal,
Aug.
4,1988.
266
Paid
taxes
twice:
Thorp,
interview;
Tudball
2003,
34;
Wall
Street
Jour
nal,
Jan. IO, 1989.
266 "My
personal
opinion is that he
was
afraid":
Thorp,
interview.
267 Giuliani threatened to support defendants: Stewart
1991,
438.
267
Reversed
threat to
dismiss
charges
against
Milken:
Stewart I99L
438.
267
Jones
and O'Neil met with
prosecutors,
letter about
refreshed
memory:
Wall
Street
Journal.
Mar.
21.1989,
A12.
268 Thorp
unaware
of stock
parking,
manipulation:
Sec
Tudball
2003,
34-
268 "We didn't
really
connect
well
as
people":
Thorp,
interview.
268 View of
Princeton-Newport's
record
as
definitive
example:
See
comments
quoted in Tudball 2003.
270
"add
or
subtract
something
like
$5
from
the
buy-back
price":
Wall
Street
Journal.
Mar. 16,1989.
270 Stocksparked, recipientsof list:
Wall
Street
Journal.
Mar.
15,
1989. A6.
270
"Told
me it
was
illegal":
Wall
Street
Journal.
March
16,
1989.
270 "a long
litany
of
lies":
Wall
Street
Journal,
Mar.
22.1989.
270 "vety
seriously":
Wall
Street
Journal,
Mar.
23,1989.
A3.
271
"psychiatric
counseling
on the
advice
of her
lawyer":
Watt
Street
Jour-
nal.
Mar. 24, 1989. B3.
271
"I don't
have
to showyou any stinkin'
badges":
L.
Gordon Crovitz
writingin
The
Wall
Street
Journal,
Oct. 4.1989. A30.
271
"Arnold
Schwarzenegger
couldn't
play
a
scarier
role":
Letter
from
Martin I. Klein to
The
Wall
Street
Journal,
Nov.
13,1989.
271
"
'imaginative'
prosecutions
under
RICO . . .
bargaining
tool":
Wall
Street
Journal.
Jan. 26,1989.
271
Law
changed
so that
both
sides
of
hedge
short-term:
Forbes.
Oct.2,
1989,
222.
271
Former IRS commissioner not allowed to testify: Tobias 1989-
271
"I did not commit a crime":
Wall
Street
Journal.
July
11.
1989-
272 "the judge
seemed
to be
saying
byhis
sentence":
Tobias
1989.
272 "When half the leadershipof your firm is
convicted":
Schine
1989-
272 "The destruction of wealth was
huge":
Thorp,
interview.
272 "There
was
an
explosion
in the
hedge
fund
world shortly after":
Thorp,
interview.
273 "we'd be billionaires": Thorp, interview.
274 "You're all right": Stewart 1991,430.
351


## Page 357

Notes
VI.
BLOWING
UP
277 Bettingon
blackjack,
horse
race,
Cubs
games:
Lowenstein
2002, 6.
278
Interest
in horses:
Dunbar
2000,109.
278 Rosarybeads in his
briefcase:
Lowenstein
2000,
9.
278 "It'sgonna be a great
investment":
Thorp,
interview
(this isThorp's
recollection
of what he
was
told).
278
Like
having
Michael
Jordan and
Muhammad
Ali:
Lowenstein
2000,
31.
278
"martingale man . .. The generalchatter": Thorp,
interview.
279
Possible
30 percent return after
fees:
Lowenstein
2000,
35.
279
Harvard
invested
in
LTCM:
William
Ziemba,
interview.
279 Gray market in
shares,
10 percent premium: Dunbar
2000,169.
280
$7.1
billion by October
1997:
Perold
1999,
C12.
280 "many went
kicking
and
screaming":
Loomis
1998,
114.
280
Samuelson's
doubts: Lowenstein
2000,
71.
280
Vacuuming
nickels
pitch:
Lowenstein
2000,
34.
281
Investortold return
was
67
basis
points:
Loomis
1998,114.
281
Role of Merton, Scholes, in fund: see Lowenstein
2000,
65.
281
"There aren't that many opportunities":
Lowenstein
2000,
33-34.
285 I percent chance of 20 percent
loss:
Loomis
1998,114.
285 "I've got a bad
feeling
about this ..
.":
Wilmott 2001,
356.
286
"We
spenttime
thinking
about
what
happens
if
there's
a
magnitude
ten earthquake in
Tokyo":
Dunbar
2000,187
287
Boesky
offered expertise to
Russia:
Stewart
1991,
532.
287
Caesar
Kimmel ran Moscow casino: Bruck 1994,
11.
287 S4.5
billion
of
S17
billion
loan
went
to
offshore
accounts:
Dunbar
2000.
200.
288 "Where are
you?":
Lowenstein
2000,156-57.
288
"A
banker is a
fellow
who lends
you
his
umbrella
when the sun is
shining":
Kargin
2004, 2.
289 "John. I'm not sure it's in your
interest":
Lowenstein
2000,153.
289 "When they
first
started
losing":
Wilcox,
interview.
289
Fisher's
visit,
details
of "Risk
Aggregator":
Lowenstein
2000,
186-89.
290 "I'm not
worried
about
markets
trading
down":
Lowenstein
2000,
189.
290 S28 million down from Si.8 billion: See Dunbar
2000,
224, and
Lewis
1999.
31-
Lewis
putsthe
sixteen
partners'
loss
at
"roughly
S1.9
billion."
290 Merton lost
SlOO
million:
William
Ziemba
(interview)
said he had
heard this figureas a rumor.
352


## Page 358

Notes
291
"ten or
15
guys
with an
average
[Qofmaybe
170":
Loomis
1998,116.
291
"Aman who
risks
hisentire fortune acts likea simpleton": Bernoulli
1954.
29.
291 "Flow the
Eggheads
Cracked":
Lewis
1999.
291
"swappedtheir laurelsfor the booby
prize":
Loomis
1998,
in.
291
Leverage
figures
for
investment
banks:
Pcrold
1999,
A23.
292 "People think that if things arc
bounded":
Thorp,
interview.
293 "had
forgotten
the
predatory":
Lowenstein
2000,173.
293 "When the young Fis[c]her
Black
had crossed the Charles river
bridge":
Dunbar
2000,
224.
294
Enron,
telecommunications,
portfolio
insurance
as
"overbetting":
Wilcox
2000,
2003,
2004.
294 "I could see that they didn't understand":Tudball 2003.
295 "a
whole
lot of bets on
Southeast
Asian
debt":
Thorp,
interview.
298
Contrast of two
mappings:
See
Figure
1 in
McEnally
1986,
which
I
haveadapted here.
299 "Convergence trades are a
real
snake pit":Thorp, e-mail.
300
Koonmen
bio,
Eifuku
history:
Senderand
Singer
2003.
300 UBS was LTCM's largest
investor:
Lowenstein
2000,
158.
302 "preserve and
maximize
any remaining
equity":
Posted on Turtle
Trader web site,
www.nirtletrader.com/trading.html.
302 "John Koonmen will try to contact each
investor":
Posted on Turtle
Trader
web
site,
www.turtletrader.com/trading.html.
302 Shannon on
hedge
fund
manager's
motives:
I am referring to the
untitled and undated
(evidently
circa
1961)
notebook in
Shannon's
papers,
LOC.
303 Overlap
between
hedge
fund
managers
and
gamblers:
Thorp and
Ziemba both
make
this point
(interviews).
304 "Likeall of life'srich emotional
experiences":
Schwed 1940, 70.
VII.
SIGNAL
AND
NOISE
307 28 percent
return:
I
lershberg
n.d.
[1986].
307 I lershberg thought of writing an article on the Shannons' investing
success:
Letters, Philip Hershberg to Claude and Betty Shannon,
dated June 23 and August 28.
1986.
with Shannon's papers. LOC.
Betty Shannon supplied me with a transcript of the
interview.
308 "In a
way,
this is close to some of the work I
have
done": Hershberg
n.d.
[1986].
Similar
views
on the part of Shannon are
expressed
in
Philip Hershberg. e-mail.
308
Tried
Kentucky
Fried Chicken: Hershberg n.d.
[1986].
353


## Page 359

Notes
308 "If
we
try it and don't
like
it":
Hershberg
n.d.
[1986].
309 "is a verydifficult
field":
Letter,
Shannon to Dr.George A. Roberts,
Nov. 5,1978. Shannon's papers, LOC.
309 Warren Buffett praised
Singleton:
Quoted in Train 1980.
309 Downloadedstock
prices:
Arthur
Lewbel,
interview.
309 Portfolio value on Jan. 22,
1981:
computer printout in Shannon's
papers, LOC (this is on the backof a sheet
filled
with
juggling
ma
chine diagramsand
formulas!).
310
"We
have
not, at any time in the past 30
years":
Hershberg
n.d.
[1986].
310
"I am
willing
to
borrow
on our
investments
if
necessary":
Hersh
berg
n.d.
[1986].
311
Check-printer
company
returns:
Hershberg
n.d.
[1986].
313
"I
have
personally
tried to
invest
money":
Roll
and
Shiller
1992.
313
Weather
effect:
Hirshleifer and
Shumway
2001.
314
"Then some
business
school
professor":
Buffett
1984.
Fred
Schwed,
Jr.,'s
Where
Are
the
Customers'
Yachts?
makes
a similar
case,
in equally
amusing
terms
(pp.
159-61).
Shannon
cited
Schwed's
1940 bookas
his
favorite
on
investing.
316
Returns
for
1980-82:
Ziemba 2003.
317
Bamberger
forbidden
to go into computer
room:
Thorp
2004—5.
317
"How often do you havea tuna salad
sandwich":
Thorp
2004—5.
318
"I had an interest
list":
Thorp, e-mail.
319
Mizusawa
scanned
news;
"restricted
list":
Thorp
2004-5.
319
18
percent after
fees:
Computed
Irom
data
supplied
by Thorp,
e-mail.
319
47 percent
return:
Kurson
2003; Thorp,
e-mail.
320 "The
advantage
scientists
bring into the
game":
Turtle Trader web
site,
www.turtletradcr.com/trader-simons.html.
320 20 percent return and 6 percent standard
deviation:
Thorp
1997
(revised
1998),
38.
320 "Tohelp
persuade
you":
Thorp
1997
(revised
1998).
38.
321
"pointed to me in the
audience":
Flaugen
1999, quoted in
Thorp
2004-5.
322 Sports betting
system,
experiment: Thorp,
interview;
also
Thorp
1997 (revised1998).
323
"by far the most
popular
form
of
recreation":
www.hong-kong-
racing.com/trackside.html.
323
More
wagered
on
single
races
than in
year's
betting
elsewhere:
www.hong-kong-racing.com/trackside.html.
323
Si50,000
seed
money:
Kaplan
2003.
324
Kelly
formula
that
takes
into
account
effect
of bet on
odds:
See
Benter 1994 and
Kallberg
and Ziemba
1994-
354


## Page 360

Notes
324
"I
would
have
benefited
by
not
telling
anybody":
Kaplan
2003.
325
"I likegoingto the
seedy
girlie
bars
in
Makati":
Kaplan
2003.
325
Instant
messages:
Kaplan 2003.
325
Lost
Sioo
million
by
shorting
NASDAQ^Kaplan
2003.
325
"When
you
look
at
how
much
money
I
have
consistently
made":
Kaplan 2003.
326
"Perhaps
the
impact
Shannon
and
Kelly
have
had on
finance":
Golomb.
Berlekamp,
Cover,
et
al.
2003,
11.
326 Alzheimer's
symptoms:
Robert
Fano,
interview.
Put in home in
1993:
Chiu,
Lin,
Mcferron,
et
al.
2001.
Tinkering
with
walkers,
fax
machines:
Coughlin 2001.
326
Exponentially
growing
endowmentfor UC
Irvine:
Thorp,
e-mail.
327
"something
available
in the
Eastern
Hemisphere":
Thorp,
interview.
327
Fleretic
born
every
minute:
Samuelson,
personal
letter, June 28.
2004.
327
A story with
everything
except
an
ending:
Thomas
Cover,
e-mail.
327
10 percent of
M.B.A.
programs,
"shameful":
Hakansson.
interview.
327
"The
Kelly
criterion
is
integral":
Legg
Mason
Value
Trust2003 an
nual report, 5.
328
"should
handily
beat the
published
investment
policies":
Quaife
1993-
328
"When something
keeps
turning up
like
that":
Cover,
interview.
328 "there's a dark side to
infinity":
Cover,
interview.
328
"life,
and
everything
in
it":
Wilmott 2001,146n.
328
"people,
not onlyat
roulette":
Dostoyevsky
1966.
329
"You've
heard of
Kuhn's
paradigm
shift?":
Wilcox,
interview.
355


## Page 361

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Omar,
Pearl
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Sneha
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Louis
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1964.
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1986,
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Wayne
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Norma (2003).
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This
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David
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367


## Page 372

ACKNOWLEDGMENTS
Ed
Thorp
has
been
especially
gracious
and
helpful,
contributing
time,
ad
vice,
photocopies,
and
speedy
replies
to
e-mails.
Ed
read
an
early
version
of
the
manuscript
and
helped
to
improve
its
accuracy.
The
Claude
Shannon
collection
at the
Library
of
Congress
was
an
invaluable
resource,
the
more
so
since
Shannon
never
chose
to
publish
anything
on
investing.
I
am
par
ticularly
indebted
to
Philip
I.
Hershbcrg
for
asking
Shannon
many
of
the
questions
I
would
have
wanted
to
ask
him.
Ben
Logan
and
Manfred
Schroeder
shared
their
memories
of
John
Kelly
Jr.,
and
Mr.
Logan
was
re
sponsible
for
locating
the
photograph
of
Kelly.
Thanks
also
go
to
Robin
Baddcrs,
Norma
Barzman,
Gary
Browning.
Erin
Campbell,
Thomas M.
Cover,
Ed
Eckert,
Robert
Fano,
Dave
Finni-
gan,
G.
David
Forney,
Jr.,
Robert
Gallagcr,
Adam
Grossberg,
Nils
Hakans
son, Larry
Flussar,
Henry
Landau.
Bibb
Latane,
Arthur
Lewbel,
the staff of
the
Library
of
Congress
Manuscript
Division.
Flarry
M.
Markowitz.
James
Massey.
Allan
May,
Judy
McCoy,
Robert
C.
Merton,
Marvin
Minsky,
Ellen
Neal,
Joe
Olive,
W
Wesley
Peterson,
Linda
Pringle,
Rick
Ross,
Paul
A.
Samuelson,
Betty
Shannon,
Neil
J.
A.
Sloane,
Kim
Spurr,
Jarrod
Wilcox,
Neelima
Yeddanapudi,
and WilliamT. Ziemba.
369


## Page 373

INDEX
active investing,
169-71
Adonis, Joe, 33,34, 35,36
Allison, FIcrb.
288-89
Amber
Arbitrage
Fund,
300
American Express,270
American Motors
Corporation
(AMC), 168-69
American Telephone and Tele
graph Company
(AT&T),
5-6,
12,25,113,
164,170,175-77;
Bell Labs,
15,
17,
18, 22, 23, 26,
54. 61, 63,
75-77.
112-14.
129-30.
309: breakup,175-
77; monopoly, 6, 63,
136,
i75—77;
vocoder, 65; wire
lessees,
6
America
Online,
141
Annenberg, Moe, 5,
6—7,
35,
65
Annenberg,
Walter,
65
anti-Semitism,
117
arbitrage, 132-35, 144-45,
159.
162,
165, 178, 241, 294;
bond,
277-
78,
299-300;
definition
of,
132-33;
Kelly
formula and, 133-
35. 145, 169;
racetrack,
321-
25; risk,
241-42;
statistical.
315-20,
326
arithmetic
mean,
189-91,
193,
198,
207
Arizona,
12
Armstrong, Mike, 263
Arrow,
Kenneth,
183
Arsenault,
Jack,
265-66
artificial
intelligence,
28-29, 45.
60
Atkinson,
T R., 158
Atlantic
City,
34,
156
Baby
Bells,
175-76
Bachelier,
Louis, 119-21, 122, 130;
"A
Theory of
Speculation,"
119-20
backgammon,
49, 300
Baesel, Jerome, 315-16
Baird. Bruce. 258, 264,
265-66
Baldwin,
Roger,
41-42
Bamberger,Jerry, 317-18
bandwidth, 54-55. 59, 74
Bank
of
China,
279
bankruptcy, 50.
51,
168, 272
Barrett, Wayne, 249
Barron's,
142, 307
Baruch,
Bernard,
130
baseball, 68, 84
Basel
Committeeon
Banking
Supervision,
285
basketball, 321. 322
Bear
Stearns,
288
371


## Page 374

Index
Beat
the
Dealer
(Thorp), 105-109,
no,
139
Beat
the
Market
(Thorp and Kas
souf), 149,150,163
Beat
the
Racetrack
(Ziemba and
Hausch),
323,
324
Bell.
Alexander
Graham,
5
Bell.
Robert,
219
Bell
Journal
of
Economics
and
Manage
ment
Science,
164
Bell Labs. 15. 17. 18, 22, 23,
26-28.
54,61,63,75-77112-14.
129-30.
309; Project X,
24-25
Bell
System
Technical
Journal,
26,76,
196
Belvedere
Securities,
174
Bender, John,
300
Bendix,
245
Bennett,
Charles,
205,
206
Benter.
Bill,
232-33,
323, 324
Bergcr.
Toby,
15
Berkman.
Paul, 259,
262,
267,
270
Berkshire
Hathaway,
124,125,
230,
268,
269,
307,
320
Berlekamp,
Elwyn.
17,
75,136-37.
326
Bernoulli,
Daniel,
181-88.
192.
194.196, 209,
291;
Hydraulica.
181;
St. Petersburg
wager,
183-
91
Bernoulli, Jakob,
102-103,
181;
law
of large numbers, 102-103
Bernoulli,
Johann,
181
Bernoulli,
Nicolas,
182, 183
Bernstein,
Joe. 85. 93
bet-it-all system,99
betting
systems,
51-52,
97;
bet-it-
all, 99:
fixed-wager,
98, 99.
IOO;
Kelly.
97-103;
martingale,
52,
97,
99-100.
278: proportional.
98-103;
see
also
blackjack;
gam
bling;
horse
racing;
Kelly
system;
specific
systems
"bet your
beliefs,"
71-72,
145
binary digits,
16,
25,
74
bit,
25-26
Black. Fischer, 123,
162-65
blackjack.
41,
141,
157,194~95. 224,
250-51, 322-23;
analysis,
4I~44;
casinos,
41-43,
82-97,
105-12,
322-23; diversification and,
233-34;
goal,
82-83;
Kelly
sys
tem for,
82-97,
109; rules,
82-83.86-87,93.
no-ii;
Thorp
system,
41-44.
81-97,
104,
105-12,
141
Black
Monday
crash
(1987).
235-36,
269,
284,
294
Black-Scholes
formula,
155,
162-67,
236
Blakey,
G. Robert, 248
"blowing up," 284
Bode.
Flendrik,
27
Boesky,
Ivan,
241-46, 286; convic
tion and imprisonment, 272,
273;
insider trading,
243-46,
. 247. 255-57, 267, 272
Boesky
Corporation.
242, 243
Bonanno.
Joe,
M<jh
of
Honor,
249
bonds,
173,
277;
arbitrage,
277-
78,
299-300;
convergence
trades,
280-81;
convertible,
153-55. 165,
167,168-69,
262,
299-300;
government,
277,
280-81,
288; junk, 159-61,168,
259,
264,
272;
zero-coupon,
173-75
bookmaking,
3-6,
32,
84-85,
247;
casino,
8
Boolean
algebra,
20
bootlegging,
32,33-37
BOSS
Partners,
317-18
Boston
Globe,
The.
81
Breiman,
Leo, 196
Brillouin,
Leon,
205
Brownian
morion.
121
372


## Page 375

Index
Buffett,
Warren.
124-25, 150. 152.
268,
269,
288, 291, 307, 314;
Kelly
systemand,
153.
230
Burks.
Barbara.
21
Bush.
Vannevar,
19-20.
21, 22. 53.
54
Business
Week.
272, 291
Butcher
&
Shcrrerd.
151
Caesars
Palace,
Las
Vegas,
250
Cafaro,
Vincent.
253
Cage,
John,
61
Cameron.
Dort,
159
Capital Asset Pricing
Model.
168
capital growth
theory,
196
Capone, Al,
7,
34
Carberry. Charles,
255.
258
card-counting.
85, 96.
105-109,
157;
Beat
the
Dealer
on.
105-109;
Thorp's
blackjack
system,
41-44.
81-97,104.105-109:
see
also
blackjack;
Kelly
system
Carnation-Nestle
merger. 246
Casanova,
52
casinos,
8,
33—35.
5L 134. 187, 250.
256, 283, 322-23; blackjack,
41-43,
82-97.
105-12.
322-23;
bookmaking.
8; cheating
dealers.
84,
87-88.
93-94,
96. 106, 108,
112;
corruption, Hi-12; edge,
41-42, 49.
51;
Kelly
systemin,
82-97,
98-103;
Nevada. 8, 9,
35.37,41-43.53.82,86-97.
104-105,
106, 108,
110-12,141;
New
Jersey,
33-34,
156;
organ
ized
crime
and,
33-37,
no,
112;
"professor
stopper."
Ill;
roulette.
40-44,
90,
103-105;
Russian.
287;
see
also
specific
casinos
CBS
Television,
66
Central Intelligence
Agency
(CIA),
29. 245
chance.
56-57.
I97~98
cheating,
53,
84, 90, 106;bycasino
dealers,
84,
87-88,
93~94-
96.
106.108.112
Chicago.
4.
38.
174.
277;
commod
ity
markets.
118;
organized
crime,
4. 7, 8. 9, 35
Chicago
Board
of
Exchange.
164
Chicago Crime Commission. 35
Chow,
Andrew,
281
Churchill,
Winston,
24
Cincinnati.
3
Citadel
Investment
Group,
319.
320
Cities
Service,
244
Clarke.
Arthur
C.
113 14
codes and ciphers, 29. 55,58, 67,
125-26;
Enigma. 25. 26;
SIGSALY
and. 24 25
Codex
Corporation.
136
Cohen.
Carl,
no
Cohn,
Flarry,
32
coin
toss,
314
Columbo crime
family.
251
C.O.M.B..
262
Combination.
7-10,
34—35,77,
253
Commission
case,
253 54, 255
Communism.
77, 128: fall of.
286-87
Computer
Group,
321
22
computers.
15,
16,42, 43. 60, 164;
Differential Analyzer,
19-20;
option-pricing
formulas.
164-67;
roulette,
103-105,
130;
singing.
113;
sports betting and.
321-25; stock
market
and.
164-67,
177,
292-93.
309-20
Congress,
U.S..
174.
175.
271;
Ke
fauver hearings.
9-12,
35,
77,
125:
RICO
legislation,
248-
49
Coniston
Partners,
257
Conseco,
282-83
373


## Page 376

Index
constant-proportion
rebalanced
portfolio,
208-209
Continental
Press Service, 7,
8-12
convergence
trades, 280-81, 299
convertible
bonds,
153,
154-55,
165, 167,
168-69,
262,
299-
300
Convertible Hedge
Associates,
152-58,
221;
investors,
153-54
Cootner,
Paul.
The
Random
Character
of
Stock
Market
Prices,
142
corporate
raiding, 159
Cosa
Nostra,
II, 251,
253-54
Costcllo, Frank, 10. n. 34,35.
36-37
77-78,
248
Cover, Thomas, 209.
211,
219,
237,
327. 328
craps,
42
Credit
Lyonnais,
290
cryonics.
327-28
cryptography,
24-26,
29, 55,58,67,
125-26
D'Amato, Alfonse,
263-64
Darrow,
Clarence,
4
Dartmouth
College,
28
Datamarinc
International.
310.
311
D'Avanzo,
Leo, 247,
248
delta
hedging,
145,
147-50,163—
64
Deluxe,
311
Depression.
38,192,
247
Desert
Inn, Las Vegas,
no
D. E. Shaw and Co., 319
Detroit,
241
Deuce-Dealing Dottic,
no
Dianetics,
61
Differential
Analyzer,
19-20
digital media,
15,
16,
55,
59-60,
114
digital speech. 113-14
Dillinger,
Ray,
231
diversification,
134,192-201,
290;
Kelly
system and, 233-35
DNA,
16. 21
Dodd. David, 130
Donaldson,
Lufkin &
Jenrette,
166
Doonan.
Thomas,
256,
260-61
Dorchester
Government
Securi
ties.
174
Dostoyevsky,
Fyodor,
The
Gambler,
328
doubling
down,
no
doubling
up.
see
martingale
system
Dow Jones
Industrial
Index, 124,
228;
Black
Monday
crash
(1987),
235,
269, 284.
294
Drexel Burnham Lambert, 159,
160,
255,
259,262; bankruptcy
272;
investigation,
259-68,
270-72
drug
dealing,
249
Dudley, Flomer,
64-65
Dunbar.
Nicholas,
Inventing
Money,
293
Econometrica,
188,191
economics,
117-28,
130,
226
edge,
41-42,
49.
51.
68, 97
edge
(formula),
86-87, 97
edge/odds
(formula).
72-75, 82, 86,
191.215,324
efficient
market
hypothesis,
123-28,133,152,169,235,243.
280.
312-13, 320, 321
Eifuku Master Trust,
300-301,
303.313
Einstein, Albert,
15,
23,73,
121,
309
Elias, Peter,
17,
61
Enron,
294
entropy,
57-58,
76,
205,
206-207;
concept of,
57-58
envy.
224
equivocation,
71-75
Ernst, Henry, 132
ESP, 47,
90,
123
eugenics, 21
374


## Page 377

Index
Evans, Bob, 153-54
Evans,
Charles,
153,154
expectation,
50,102-103,182
"fair"
wager,
189-91
Fama, Eugene, 123,125-27. 208.
321
Fano,
Robert.
16, 28, 58, 59, 64,
127—28
faro,
52-53,
181
fat tails,
292, 294,
296-97
FDIC,
197
Federal
Bureau
of
Investigation
(FBI),
7.
37 77-78,
85,
253-54.
260,
321;
J. Edgar Hoover and,
77-78
Federal
Communications
Com
mission
(FCC). 66
Federal
Reserve,
U.S.,
289
Federal
Reserve
Bank
of
New
York, 289,
290
Feldman,
Julian, 146
fiber-optic cable.
16,
54
Finncgans
Wake
(Joyce),
61
Fisher,
Peter,
289-90
fixed-wager
system,98,
99,100
Flamingo hotel and
casino.
Las
Vegas,
8, 9, 35
football,
84, 85.
321-22
Forbes
magazine,
140,178
FORTRAN,
43
Fortune
magazine, 60, 152.243, 247,
280,
291
Freeman,
Robert,
256, 257.
262,
265
Friden Company,
161,
242
Fried,
Sidney,
142
Friedman,
Milton,
183
Fry,
Thornton.
22, 23
futures,
176-77.236
Gabor,
Denis,
205
Gambino crime
family,
251
Gambler,
The
(Dostoyevsky),
328
gambler's ruin,
49-53.
54. 98,
147,
284,
291
gambling,
10,
12,
289. 303-304;
blackjacksystem,
82—97,
105-109;
Kefauver
hearings,
9-12,
35. 77. 125;
money
man
agement
systems,
49-53,
97-103;
roulette prediction,
40-49,103-105;
wire
service
and, 3-6,
12;
see
also
specific
games
Gauss, Carl Friedrich, 132
Gelbaum,
David, 156
General
News
Bureau,
4-5,
6-7,
35
genetics,
21-22
Genovese,
Vito,
II, 36
Genovesecrime
family,
II,
251,
253-54
geometric mean,
189-91,194-201,
207,
208,
210-n,
218, 225, 226,
234, 236;
criterion,
194-201,
210
geometric
random
walk,
122,
203-204
Gerard, Ralph.
153
Germany,
26; Enigmacipher,
25,
26;
World
War
II,
24,25
Getty,
Gordon, 328
Getty Oil, 245
Giuliani,
Harold,
247-48
Giuliani, Rudolph,
247-54,
318;
background
of,247-48;
Boesky
investigation, 255-57;
Commis
sion
case,
253-54,
255; as
New
York
mayor,
254,
267,
270; polit
icalaspirations, 263,
267,
27O;
Princeton-Newport
case,
258-
73;
as prosecutorof
organized
crime,
248-54;
RICO
and.
249-54,
265-68,
271
GKOs,
287-88
Gladstcin.
Mike,
166
375


## Page 378

Index
global
economy,
234,
289-90
global fund, 234
G«_ = R-
73-75.
112
gold,
132,
144, 167
Goldman
Sachs, 166, 256, 290, 301
Golomb,
Solomon
W,
16
Google. 229
Gould,
Jay,
132,
144
government bonds,
277,
280-81,
288
Graham, Benjamin, 130,
153
Grand,
Paul, 265
Great
Britain,
24,118,155,
243;
cryptography,
24-25,
26; World
War
II,
24-25
Greater
New
York News Service, 5
Green,
Hetty, 130
Green
Felt
Jungle,
The
(Reidand De
maris).
112
Greenwich,
Connecticut,
286
Griffin, Ken, 319
Guldimann,
Til,
284
Gulf
Oil. 244
Gutfreund,
John,
277-78
Hagstrom,
Robert,
The
Warren
Buf
fett
Porfolio,
230
haircuts,
282-83
Hakansson,
Nils,
211,
213,
218, 327
Hale, William,
257-62,
270
half
Kelly,
231-33
Hand, Eddie, 84, 86,
88-89,
92-97,
106
Hanson,
Mark,
270
Harland, John
PL,
310,
311
Harlow, Jean, 32
Flarolds Club, Reno,
89-93,
106
Flarrison,
Carter
II,
4
Flarrison, Charles William, 135-36
Flarrison
Laboratories,
136,312
Hartley Ralph, 57
Flarvard University,
117,
220, 266;
as
LTCM
investor,
279,
290
Harvey's Wagon Wheel, 95
Haugcn, Robert,
321
Hausch,
Donald
B.,
Beatthe Race
track,
323
Hawkins,
Greg,
283,
287
FIDTV,
16
hedge
funds,
124,152-58, 294, 302,
313,
315-20,
328;
Convertible
Fledge
Associates,
152-58,
221;
definition
of,
152;
LTCM deba
cle, 278,
279-304;
Princeton-
Newport
Partners,
165-67,
172-78,
220,
231,
234-35,
257-73.
3I5-20;
returns,
303;
Ridgeline
Partners, 318-20, 326;
stock parking,
259-62,
264-68,
270-72
Hershberg.
Philip,
307-308,
310,
3ii
Hewlett-Packard,
136,
310,
311,
312
Hewlett-Packard
9830A
computer,
164
Hickman, W Braddock,
158,
159
"high-low,"
106
High-Risk
Opportunities
Fund
(HRO). 287-88
Hilibrand,
Larry,
289,
290-91
Hong
Kong
horse
racing,
321-25
Hong Kong
Syndicate,
323-25
Hoover,
J.
Edgar,
37,
254;
gambling
habit
of,77-78;
organized
crime
ties,
77-78
horse
racing,
3, n, 68,
69-75,
84,
85.133-34.
233, 252, 278;
arbi
trage,
321-25;
"bet your
beliefs"
system,
71-72,145;
fixed, 73,
77-78, 85; Hong
Kong,
321-25;
Kelly
system and,
69-75,145.
321-25; organized crime and,
77-78;
pari-mutuel betting,
69—70;
wire
service
results,
3-6,
12
Horwitz,
Leonard,
250, 251
376


## Page 379

Index
Hubbard,
L.
Ron.
61
Hudson
&
Manhattan
Railroad, 34
Hunt.
B. F.,
212
Hunt.
PI.
L..85
IBM.
43. 114,
205,
206
IBM
704
computer.
43,113
index funds, 125.134. 169, 170,
224-25,
234
Indicators
Project,
315-17
inflation,
134
"information
age,"
60-61
information
theory,
15,
16,
25-26,
54-62,
64,
67,
69,
70,
73. 103,
125-26,
135,
196; influence of,
58-62
inside
information.
35,
66-78,
135,
163,
243-74;
Boeskycase,
243-46,
247
255-57,
267, 272;
Giuliani investigation, 258-73;
Milken
and,
255,
256-68,
271,
272;
Princeton-Newport
case.
258-73
Institute for Advanced
Study,
23,
57
Internal
Revenue
Service
(IRS),
35-36,
271
International
Monetary Fund, 287
Internet,
6, 15, 55, 74,
114.125.
131.
229-30
Inventing
Money
(Dunbar), 293
Italian
organized
crime,
7,
II,
33.
36,140,
251,
253-54
Jamie
Securities,
273
Januaryeffect,
313
Japan. 72.
155,
234,
299-301,
318
Jevons, William Stanley.186
Jews, 36. 117;
anti-Semitism,
117; in
organized crime,
7,
36;
Russian,
286
Jockey
Club.
323
Jones,
Alfred
Winslow,
130, 152
Jones, Lisa
Ann,
259-61,
264,
267,
270-71
Journal
of
Banking
and
Finance,
225
Journal
of
Finance,
The,
127,
329
Journal
of
Political
Economy,
194
Journal
of
Portfolio
Management,
127
Journal
of
the
American
Statistical
Associa
tion,
149
Joyce,
James.
Finnegans
Wake,
61
J.
P.
Morgan,
284-85,
290
junk bonds, 159-61,
168,
259, 264,
272
Kalb Voorhis, 242
Kaplus,
Leo,
31
Kassouf,
Sheen,
146-50,
151;
Beat
the
Market,
149,150,163
Kefauver,
Carey Estes.
9-12
Kefauver
hearings,
9-12,
35,
77.
125
Kelly,
David,63
Kelly,
John
L.,
Jr.,
62-67,176,181,
188,191,194,196,
201,
219,
229,
244, 286,
297,
326;background
of,
62-63;
at Bell Labs,
63-64,
75-77. 112-14;
death
of,
114;
idea for gamblingsystem, 67,
68-75,
n4; 1956 paper
by,
62,
75-77
191.!94. J96. 199; Shan
non
and,
64. 67, 77, 112;voice
synthesis
research,
64-65,
113-14;
sec
also
Kelly
system
Kelly.
Karen, 63
Kelly,
Lillian. 62
Kelly.
Mildred, 63
Kelly.
Patricia. 63
Kelly
criterion,
67-78,
133,
196-
97,
208;
analysis
of, 97-103: ar
bitrage
and,
133-35.
145.
169;
for
blackjack.
82-97,
109; in casi
nos,
82-97,
98-103;
debate,
209-36,
327-29;
diversifica
tion and, 233-35;
equations.
377


## Page 380

Index
Kelly
criterion
(owr.)
72-75,
112, 191, 324;
fractional
approach, 231-33; horse racing
and,
69-75,
145.
321-25;
idea
for,
67,
68-75;
legacy
of, 327-
29;
LTCM
debacle
and,
294-
99; vs.
Markowitz
criterion,
197-201;
Samuelson's
criticism
of,
210-21,
225-27, 230, 237;
snapshot of, 227-29; sports bet
ting and, 321-25;stock market
and, 145,
147,157,
169, 178,196,
201,
224,
234-35,
269.
294-99,
320;
volatility,
231-33;
web sites,
229-30,
231
Kelly
formula,
see
Kelly
criterion
Kendall, Maurice, 118-19
Kennedy,
John
F.,
118,
248
Kennedy,
Joseph,35
Kennedy,
Robert,
35,
248
Kent, Michael, 321
Keynes,
John
Maynard,
117
145,
192-93;
Treatise
on
Probability,
183
Kidder
Peabody,
244,
245,
247
Kimmel,
Caesar,
138-39,140,160,
251-52,
286-87
Kimmel,
Charles,
251
Kimmel,
Emmanuel,
30-37,
82,
138-41,
152,
251;
blackjack
sys
tem and
casino
test
backing,
82-97,
107;bookmakingopera
tions,
84-85;
death of,
141;
park
ing lot business, 32,
33,
82,
138-41,
253
Kinney National,
253-54
Kinney parking lots, 32,
33,
138-40,
163, 250,
253-54
Kinney Service
Corporation,
138-40
Kinney System Parking Corpora
tion,
32, 33,
138-40,
163
Kiriyenko,
Sergei,287
Kirkland, Weymouth, 7
Kleinrock, Len, 130-31
Kluver,
Billy,
61,
64
Koonmen. John.
299-302
Kouri,
Don,
154
Kozmetsky,
George,
136
Kubrick.
Stanley,
113-14
labor unions, 250; corruption,
253-54
Laemmle,
Carl,
53
Landauer.
Rolf,
206
Landis, Kcnesaw
Mountain,
4
Lansky,
Meyer,
34, 36,77
Las
Vegas,
8, 40, 84, 322;casinos,
8. 9. 35. 37.
41-43.
51.104-105,
108,
110-12
Las
Vegas
Resort Flotel Associa
tion,
no
Latane, Henry, 191,
192-97,
209-n,
218-20,
224;
"Criteria
for
Choice
Among
Risky
Ven
tures," 194;
geometric
mean
criterion,
194-201
lawof
large
numbers,
102-103
Lehman
Brothers,
288, 291, 299
leverage,
225;
Boesky
and,
243;
fat
tails and,
296-97;
LTCM deba
cle, 287-301; Milken and, 255
Levine,
Dennis,
255-56,
267
Levor,
Norma,
22, 23,
128-29
Lewis, Michael, 291;
Liar's
Poker,
277-78
Life
magazine,
108,109
Little,
Arthur
D,
162
Little
Caesar
(film), 248
Liversidge,
Anthony,
131
loan
sharking,
10,247
Lochbaum, Carol,
113
Logan, Ben, 63,
112
logarithmic
utility,
185-88, 2IO
log-normal, 122
London,
155,
313
Longcrstacy,
Jacques, 284
378


## Page 381

Index
Long-Term
Capital Management
(LTCM), 278,
279-304.
313:
collapse of,
287-301;
investors,
279-80,
285.290;
leverage,
280-301;
returns,
279-80.
304;
Russian
GKO
trade,
287-88,
290,
294,
299
Los
Angeles,
8, 9,
159,
160; Mc-
Carthyism.
128
lotto,
122
Louisiana,
IO
Lowenstein,
Roger,
278;
When
Genius
Failed,
292-93
Luciano,
Lucky,
8,
33,
34,36
luck,
90,123,
215—17
Lynch,
Gary, 267
Lynch,John, 7
MacDougall,
Michael,
106
MacMahon,
Lloyd,
248
Maddux,
John.
226-27
Mafia,
II, 140,
251;
see
also
organized
crime
Magee,
John. 130
Mandelbrot,
Benoit,
130
Man
of
Honor
(Bonanno), 249
Mapes Hotel, Reno,
86-88,
94
margin trading. 130
marked
cards,
96
Markowitz, Harry,
192-95,
211,
220,
310, 327;
mean-variance
theory,
192-201.
236;
Portfolio
Selection,
195
martingale system.
52,
97,
99-100,
278
Martin
Marietta,
245
Masco.
310,
311
Massachusetts,
12
Massachusetts
Institute
of
Tech
nology,
15,
17,
19-22,
27-30.
42-43,
49,
64,
67, 81, 105.
117-18,
127-28,
130-33,
162,
163.
202,
211
Mathematical
Theory
of
Communication,
The
(Shannon
and
Weaver).
60
Mattel.
262,
264
Mattone.
Vinny. 288
Maultasch.
Cary, 262
Maxwell, James
Clerk,
204-207;
Theory
of
Heat,
204
Maxwell's
demon,
204-208
McCallum, Philip
PL.
29
McCarthyism, 128
McCulloch,
Warren,
61
McEnally,
Richard W,
197,
298
McLuhan.
Marshall.
60-61,
62;
Understanding
Media.
60
mean-variance
analysis,
192-201.
218, 236,
294.
298
Medallion
Fund, 319,
320
media,
IO.
n.
60.
8l;
effect
of
in
formation theory on,
58-62;
on
LTCM
debacle,
291;
on orga
nized
crime,
251, 252; on
stock
market,
127,
166, 265,
271-72,
291;
see
also
specific
publications;
television
Menger. Karl, 186
mergersand acquisitions,
161,
163,
242; Boeskyand. 243 46
Meriwether,
John.
277-78;
LTCM
debacle,
278,
279-301
Merrill
Lynch,
259, 279, 283, 288,
290
Merton.
Robert
C.
161-65,
211.
214.
220-21.
226.
236,
242.
278;
at
LTCM.
278, 281,
290,
291-94
Merton,
Robert
K.. 161
Meyer.
Frank.
319
Miami.
10,
35
Milgram.
Stanley,
49
Milken, Lowell. 174. 263
Milken.
Michael.
158-61,
174, 255;
conviction and
imprisonment.
272;
insider trading,
255,
256-
379


## Page 382

Index
Milken,
Michael
(conr.)
68,
271,
272;
Thorp
and, 160,
257-59
Miller,
Bill, 327
Miller, J. R., 230
Mindlin,
Ivan, 321
Minsky,
Marvin,
15,
28
Mizusawa,
Steve,
155, 319
mobile phones, 16.55,56, 74
Modest,
David,
286
momentum
investors,
316
Mondayeffect,
313
Montana,
12
Moran,
"Gorgeous
Gussic," 84
Moretti.
Willie.
IO-II,
33, 35. 125
Morgan
Stanley,
291,
317-18
Morgenstern, Oskar, 130,183
Morse
code,
55. 58
Motorola,
136. 310,
311
Moynihan, Daniel Patrick, 263
Muiheren,
John,
273-74
multiple
decks,
in
mutual funds,
125,
127,152,
167,
176,
220,
314
Muzak
Corporation,
35
NASA,
59
NASDAQJ25
Nash, John, 17
National
General,
163
Nationwide
News Service, 5
Natomas.
245
Nature,
226
Naval
Research
Logistics
Quarterly.
196
Neutra,
Richard.
39,
40
Nevada, 8, 53;casinos, 8, 9, 35,
37,
41-43.
53. 82,
86-97
104-5.
106,108,
110-12,
141
NevadaGambling Control
Board,
106
Newark,
32-33,138
Newberg, Bruce,
259-60,
262,
264,
267
"A New
Interpretation
of Informa
tion Rate"
(Kelly
1956
paper),
62,
75-77.191.
194. 196,
199
New
Jersey,
10. II, 12.22, 30, 32,
138, 140;
casinos,
33-34,156;
organized crime, 32-33
Newman, Paul, 172
New Mexico State
University,
105,
146
New
Orleans,
4
Newton.
Isaac, 132
Newton,
Jack, 106
New York, 8, 23. 84,
155.
277. 288.
313;
organizedcrime.
IO,
34-37,
249-52,253-54
Nor
York
Magazine,
254
New
York
Times,
The,
263
Nov
York
Times
Magazine,
The,
291
Nick the
Greek.
53
9/11
terrorist
attacks, 254
Nippon Telephone and
Telegraph,
301
Nitti,
Frank.
7
Nixon,
Richard,
248
Nobel
Prize.
127, 291
nontransirive
dice,
153
NTT
DoCoMo,
301
numbers
racket, 31-32, 35
Nyquist, Harry, 57
Oakley-Sutton
Management,
165,
257
Obermaier,
Otto,
263
O'Neil,
Brian,
267
onetime pad, 24
Ophir,
Tsvi,
218-19, 224
options,
see
stock options
organizedcrime, 4, 7-12,
33,
77,
90,140,
247-48;
bootlegging
and,
32-37;
casinos and, 33-37,
no,
112;
Combination,
7-10,
34-35.
77. 253;
Commission
case,
253-54,
255;
Giuliani
as
380


## Page 383

Index
prosecutor
of,
248-54;
horse
racing and,
77-78;
Italian,
7.
n.
33. 36, 140,
251.
253-54; Jewish,
7,
36;
Kefauvcr
hearings.
9—12,
35, 77, 125;
RICO
suits,
248-54;
Russian,
286-88,
290;
wire
service,
7-12,
35
Orwell, George,
61
overbetting,
100-102,
157,
195,
233,
293. 303;
LTCM
debacle
and,
293-99
Ovitz.
Mike, 279
Paik, Nam June, 61
pari-mutuel betting,
69-70,
324
"parrot
effect,"
113
Payne,John,
3-5,
12
Payne
Telegraph
Service.
3-4
P/E effect,
313,
315
Perception
Technology
Corpora
tion,
309
peripheral vision, 108
Peterson, W
Wesley,
133
Petrallia,
Robert,
252
Philadelphia,
151
physics,
40, 57-58, 309; quantum.
204-207
Pierce, John,
27,
59, 61,65,
113
"point count"
strategy,
106-107
poker. 49.
161.
277
Pool, Ithiel de Sola, 49
portfolio insurance.
235
portfolio
managers,
167-71,
194,
268, 293,
314-15:
see
also
specific
managers
PQJperformancc quotient), 148
Princeton-Newport
Partners, 165-
67, 172--78,
220,
231,
234-35,
257-73.
278, 279.
315-20;
AT&T
deal,
175-77;
Black
Monday crash and,
235,
269;
diversification,
234; FBI raid,
260-62,
253;
Indicators
Project,
315-17;
insidertrading
investi
gation, 258-73; liquidation of.
267-68,
272-73,
318;
returns,
268-69,
303;
RICO
charges,
265-68,
271;
S&P
futures
trade,
176-77; stock parking.
259-62,
264-68.
270-72
Princeton
University,
166:
see
also
Institute for
Advanced
Study
probabilitydistribution. 134-35.
143
Proceedings
of
the
National
Academy
of
Sciences,
The,
43
ProJ'essional
Gambler
Newsletter,
230
"professor
stopper,"
in
Prohibition,
32, 33 35
Project
X,
24-25
proportional betting,
98-103
prostitution,
10, 53,
90
Public
Enemy
(film),
32
Pultc Home Co., 270
Puzo,
Mario,
I53~54;
The
Godfather,
•53-54
Quaife, Art, 327-28
Quantum
Fund.
300
quantum theory,
204-207
Quarterly
Journal
ofEconomics.
188
quiz shows,
66-67,
77
Rabinowitz, Jack, 267
Racing
Form.
5
radio,
66
Ragan, James, 5, 7,8
Rain. Douglas,
114
Random
Character
oj'Stock
Market
Prices,
The
(Cootner).
142
random
events, 46, 182
randomness,
46,
56-57;
of
stock
prices,
118-28,
130, 142.
143-46,
162
random noise,concealing
messages
with,
24-25
?8l


## Page 384

Index
random
walk, 50,
120-21,
202;
geometric,
122,
203-204;
of
stock prices,
120-28,
130.
142,
143-46,
162
Random
Walk
Cosa
Nostra.
167
Rauschenberg, Robert,
61
Reagan,
Ronald,
248
Regan,
James
"Jay,"
150-58.160,
165,173,
257,
317;
convictionof,
272; insider trading investiga
tion, 257,
261-62,
264-68,
270-73;
Princeton-Newport
Partners.
165-67,173~78,
257-64; zero-coupon bond
scheme.
173-75
Reid
(Ed)
and
Demaris
(Ovid).
The
Green
Felt
Jungle.
112
Reliance
Group I
Ioldings.
174
Reno, 46;
casinos,
53,
86-93
repeatability,
312
13
Resorts
International,
156-57
Revell,
Ashley,
99
Review
of
the
International
Statistical
Institute,
The,
201
Rl IM
Warrant
Service,
118, 142
Richheimer,
Judd, 139
Richman.
Grover,
36
RICO,
248-54.
265,
272-74:
Princeton-Newport
charges,
265-68.
271
Ridgeline
Partners, 318-20, 326
Riordan,
John. 27
risk
arbitrage,
241-42
Riviera, Las Vegas.
112
robotics,
45,
60
Roll,
Richard,
313
Roman,
Benito.
271
Roosevelt.
Franklin
D,
24, 25
Ross, Steve.
139.140-41,160;
racketeering
investigation.
250-52
roulette,
40-41,
70,
90,
102;
com
puter,
103-105,
130;
prediction.
40-41,
44.
46-49.
IO3-IO5;
Thorp
scheme,
39-41, 44,
46-49,103-105;
tilt, 48, 49,
103; wheels,
40-41,
46-49.103
Royal
Statistical
Society,
London,
118
Rubik's
cube,
17
Rubinstein,
Mark,
208-209,
211,
235-36
Ruchman,
Peter,
107
ruin,
gambler's,
see
gambler's
ruin
Russia, 132, 181,
286-88;
casinos,
287; fall
of
communism,
286-87;
post-communist
finance
and organized crime,
286-88,
290,
294, 299,
319
Russian
Mafiya,
287
Saarinen,
Eero,
64
Sahara
Flotel,
Las
Vegas,
93
St.
Petersburg
wager,
181-93
Salerno, Anthony "Fat
Tony,"
253-54.
273-74
Salomon,
Dick, 154
Salomon
Brothers,
277,
280,
290,
291;Arbitrage Group,
277-78
Samuelson,
Paul,
117-24,
127,
131,
142. 148,
149,161,162,183,
187,
192, 202, 207,
210-11,
237, 278,
327;
Economics,
118.
130;on Kelly
criterion,
210-21,
225-27,
230,
237;
"Lifetime
Portfolio
Selec
tion by
Dynamic
Stochastic Pro
gramming." 210; on LTCM,
280; "Why We Should Not
Make
Mean Logof Wealth Big
Though
Years
to Act Arc
Long,"
225-26
S&P futures,
176-77.
236
Sands, Las
Vegas,
no
San
Francisco,
4, 85
Saratoga, 35,85
Sarnoff,
General,
65
382


## Page 385

Index
satellite communications, 59,
"3
Savage,
Jimmie, 119,120, 186. 192.
194,
209-10;
death
of. 218
Scholes,
Myron,123,162-65, 278,
280; at
LTCM,
278,
280-82,
291-94
Schroeder, Manfred, 64,
113
Schultz,
Dutch.
34
Schwcd, Fred, Jr.,
Where
Are
the
Cus
tomers'Yachts?.
130,304
Scientology,
61
Securities
and
Exchange
Commis
sion (SEC).
244,
255,
257,
267
Sega, 301
Senate,
U.S.,
263-64;
Kefauver
hearings, 9-12,
35,
77,
125
Shannon,
Andrew, 44
Shannon,
Betty,
27,
44-46,
61,
65,
104,
129,
132, 137,
307,
326
Shannon, Claude
Elwood,
15-23,
151,
176,181,
211;
Alzheimer's
disease
of,
326;
background
of,
18-19; at Bell Labs,
22-23,
26-
28, 54, 63, 64,
129-30;
death
of.
325-26; first
marriage
of,
22,
23,
128-29;
indifference
to
money,
129-30; information
theory,
15.
16,
25-26,
54-62,
64, 67, 69,
70, 73, 103,
125-26,196;
Kelly
and, 64,
67,
77,
112;
"A Mathe
matical Theory of Communica
tion,"
26; at
MIT,
17,
19-22,
27-30,
67,
130-33, 202; per
sonality of, 17-18,
21.
129;port
folio,
309-12; Project X,
24-
25;
published
articles.
17,
20, 26.
28, 43;
retirement
of, 29, 30; sec
ond marriage of,
27,
44-46.
61,
129, 137;
stock
market
interests.
129,
130-38,
173,
201-209,
226, 302,
307-12;
Thorp
and,
43-49.
81-82,
103-105,107,
130,
137,
147;
Toy Room of,
44-
46,129
Shannon,
Claude
Elwood
(Senior),
19
Shannon,
Margarita,
44
Shannon,
Robert. 44
Sharpe, William,
123.
167-71, 327
Shockley,
William,26
short-selling.
130,
144-45, 202,
259.283
shuffling.
42,88,
93.
96;
multiple
decks,
ill
Shulman. Bob, 129
Siegel,
Ben
"Bugsy,"
7-9,
34,
35;
murder
of, 9
Siegel, Martin,
244-46,
256,
257,
272
SIGSALY,
24-25
Silberstcin,
Ben, 241, 242
silver, 142
Simmons. Cecil,
109-10
Simmons,
Walter, 323. 324
Simons, James, 319, 320
Singer-Friden
merger
(1963),
161.
242
Singleton.
Henry,
136,309
"six
degrees
of
separation,"
49
$64,000
Question,
The
(TV show).
66-67,
77
182
size effect,
313
SIcpian. David, 17
slot machines,
35,
39,41
Smith,
Adam,
117,
243;
The
Wealth
of
Nations.
130
Smith, Flarold S., Jr.,
92-93,
106
Smith,
Harold
S., Sr, 53,
89-93
Smith,
Pappy,
90-91
Smith, Raymond, 91
Smotrich,
Steven, 267, 270
Snyder, Arnold, 108
Sony, 270
Soros, George, 152,268. 269. 288,
300
383


## Page 386

Index
space
program,
59
Sperry Rand.
143
sports
betting,
321-25;
see
also
specific
sports
Standard
&
Poor's
500,124,137,
155,167,
176-77.
228, 268, 269.
279,
280
statistical arbitrage, 315-20, 326;
STAR system,
318
Steinberg.
Saul,
174
Steinhardt,
Michael,
152
Stevenson,
Adlai,
118
stock market, 37,
75-76,
115-78;
active vs. passive investing,
169-
71;
arbitrage profits,
132-35,
144-45, 169;
Black
Monday
crash
(1987).
235-36.
269,284,
294; computers and, 164-67,
177,
292-93,
309-20;
efficient
market hypothesis, 123-28,
133,
152. 169, 235, 243,
280,
312-13.
320,
321;
insider trading,
35,
76,
243-74;
Kelly
system
and,
145.
147,157,
169,178.
196,
201, 224,
234-35,
269,
294-99,
320;
LTCM
debacle,
278,
279-
304; mean-variance
analysis,
192-201,
218, 236, 294. 298;
1929
crash,
236, 244;
Princeton-
Newport
case.
258-73; proba
bility
distribution.
134-35. '43;
randomness of stock prices,
118-28,
130,142,
143-46,
162;
Shannon
and,
129,130-38,
173,
201-209,
226,
302,
307-
12;
Thorp and, 141-78, 201,
220
21.233-35,
258-73.
278,
292, 299,
315-20,
326
stock options,
91,
155,176:
Black-
Scholes
formula,
155,
162-67,
236;
warrants,
118-19,
142-58,
163, 165, 318
stock parking,
259-62,
264-68,
270-72
Stone,
Howard,
138
stop-loss orders, 130
Storer
Communications,
257
Sullivan,
William
C,
The
Bureau:
My
Thirty
Years
in
Hoover's
FBI,
77
Supreme
Court,
U.S.,
66;
United
States
v.
Turkette,
248-50
Sutherland.
William,
28
Szilard,
Leo,
205
Tartaglia. Nunzio.
317,
318
TASS.
153
Tax
Equity
and
Fiscal
Responsibil
ity Act (1982),
175
taxes,
134,172-75;
"creative" shel
ters, 174-75;"stock parking"
dodge,
259-62,
264-68,
270-72
Teamsters
Union,
253-54
Teledyne,
136,
308-309,
310,
311
telegraph, 3-12, 19, 54. 55.244
telephone,
5—6
television,
II, 54,
65-67;
color, 136;
quiz
shows,
65-67, 77; reality
shows, 67
"ten-count"
system, 83
Tennes,
Mont,
4, 5
Texas,
62-63,
85,142
Texas
Instruments,
165
Theory
of
Games
and
Economic
Behavior
(von Neumann and Morgen
stern), 130,183
Theory
of
Heat
(Maxwell),
204
Thorp, Edward Oakley,
38-44,
81-82,
196,
326-27;
back
ground
of,
38-40;
Beat
the
Dealer,
105-109,
no,
139;
Beat
the
Market,
149, 150,163; blackjack
system,
41-44,
81-97,104,
105-12,
141;
Warren
Buffett
and, 153;
casino
tests,
81-97;
384


## Page 387

Index
Convertible
Hedge
Associates,
152-54,
221;
delta
hedging
scheme,
145,
147-50.163-64;
"Fortune's
Formula:
A Winning
Strategy for
Blackjack,"
81-82;
insider trading
investigation,
261-62, 265-68, 272-73;
Life
profile on, 108, 109; Milken and,
160,
257-59;
at
New
Mexico
State,
105,146;
"Portfolio
Choiceand the
Kelly
Criterion,"
221;
Princeton-Newport
Part
ners,
165-67,172-78.
220,
231.
234-35. 257-73. 315-20; Ridge
line Partners,
318-20,
326;
roulette scheme,
39-41,
44,
46-49,
103-105;
Shannon
and.
43-49.
81-82,
103-105,130,
137,
147;
sports betting and,
322;
stock
market
interests,
141-78,
201,
220-21,
233-35,
258-73,
278, 292, 299,
315-20,
326; at
UC Irvine, 146,147,151,178,322
Thorp,
Vivian,
41,81,84, 85, 104,
105,146
Time-Life,
141
Time
magazine, 272
Time-Warner,
141
Tobias, Andrew, 272
Tobin, James, 195
Tokyo,
155,
234,
299-301
Tolson, Clyde, 77
Trans-American
Publishing
and
News
Service,
7-8
Transco
Energy,
270
Treasury bills, 164
Treynor, Jack, 123
Tsybakov,
Boris,
132
Tukcy,
John, 25
Turing, Alan,
24-25,
26
TVGki*,
65
Twain,
Mark,
288
twice-Kelly bet, 231-33
2001:
A
Space
Odyssey
(film),
113-14,
293
UBS,
300
UC
Irvine,
146,147
151,153,168,
178, 322, 326
underbctting.
100-102
Understanding
Media
(McLuhan),
60
United
States
v.
Turkette,
248-50
U.S.
Financial
Corp., 167
Uston.
Ken,
157
utility,
184-88,
218,219-21,
223-25;
logarithmic,
185-88,
210; vs.
wealth,
185,
224
VaR
(Value
at Risk),
284-86,
294,
295
Venetian
casinos,
52
Vickrey,
Vic,
no
vocoder, 65
voice
synthesis,
64-65,113-14
Volstead Act, 32
von
Neumann,
John, 23,
57-58;
Theory
of
Games
and
Economic
Behav
ior,
130,183
Wallace,
Robert.
159
Wall Street, 10. 125,155, 192, 219;
corruption,
243-74; greed,
133.
255;
LTCM debacle,
279-304;
see also
stock
market
Wall
Street
Journal,
The,
166,167, 242,
251, 252,
265-66,
271
Warhol,
Andy,
61
Warner
Brothers, 139, 140, 163
Warner
Communications,
141,
160,
250-52,253
warrants,
118-19,
142-58,
163,165.
318;
hedgingsystem,
145,
147-50,
163-64
Warren
Buffett
Portfolio,
The
(Flagstrom),
230
385


## Page 388

Index
wealth:
disparity
of, 222-25;dis
tribution
of, 216-17: vs. utility,
185,
224
Wealth
of
Nations,
The
(Smith),
130
weather
effect,
313
Weaver.
Warren,
23,
60
Weiss,
Solomon,
250,
251
Wells,
Theodore,
266
Western
Union,
3,19
Wexler, Irving, 5
Weyl, Hermann, 23
wheel
of
fortune,
105
When
Genius
Failed
(Lowenstein),
292-93
Where
Arethe
Customers'
Yachts?
(Schwed),130,304
Whitman,
Gerald,
162
Wiener,
Norbert,
20,
61
Wilcox. Jarrod, 289, 294, 327,329
Williams, John Burr,
188;
"Specula
tion and the Carryover," 188
Wilmott,
Paul, 328;
Paid
Wilmott
In
troduces
Quantitative
Finance,
285
Wilmott
magazine,
294
Winchcll,
Walter,
77-78
wire
service,
3-12, 70,133;
legacy
of,
12;
organized
crime
and,
7-
12,35
Woods, Alan,
323-25
Woods,
Billy.
321
World's Fair (1939), 65
World
War
II,
24-25.
62
Xerox,
136
Yale
University 192
Yilmaz,
Huseyin, 309
Young, Denny, 254
Zarzecki,
Charles,
262,
265, 267,
270
zero-coupon bonds,
173—75
Ziemba,
William,
297-98,
303-
304, 323,324;
Beat
the
Racetrack.
323.
324
Zwillman. Abner
"Longy,"
IO-I2,
31-37,
138,
248, 250; death of.
37
386


## Page 389

"Seldom
have
true
crime
and
smart
math
been
blended
to
gether
so
engagingly."
-Jim
Holt,
The Wall
Street
Journal
'Fortune's Formula
may
be
the
world's
first
history
book,
gambling
primer,
mathematics
text,
economics
manual,
personal
finance
guide
and
joke
book
in
a
single
volume.
Poundstone
comes
across
like
the
best
college
professor
you
ever
had,
someone
who
can
turn
almost
any
technical
topic
into
an
entertaining
and
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lecture."
—David
Pogue,
The
New
York
Times Book Review
|J|
\
"An
amazing
story
that
gives
a
big
idea
the
needed
star
treat-
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Fortune's
Formula
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Peter
L.
Bernstein's
Against
the
Gods,
Nassim
Nicholas
Taleb's
Fooled
by
Randomness,
and
Roger
Lowenstein's
When
Genius
Failed.
All
try
to
explain
why
smart
people
take
stupid
risks.
Poundstone
goes
them
one
better
by
showing
how
hedge
fund
Long-Term
Capital
Management,
for
one,
could
have
avoided
disaster
by
following
the
Kelly
method."
—Peter
Coy,
BusinessWeek
(four
stars)
William
Poundstone
is the bestselling author of nine
nonfiction
books,
two
of
which
(Labyrinths
of
Reason
and
The
Recursive
Universe)
were
nominated
for
the
Pulitzer
Prize.
U.S.A.
$15.00
/ Can. $18.95
Games
/
Business
ISBN-13:
978-0-8090-4599-0
ISBN-10:
0-8090-4599-0
780809"045990
www.fsgbooks.com
Cover
design
by
Jamie
Keenan
Cover
art:
Coins
inside
keyhole
©
Jed
Shaite/Photonica;
Archetype
casino
chips
©
Sidepot
Gaming
Company
k
Hill
and
Wang
A
division
of
Farrar,
Straus
and
Giroux
