There’s a strong chance that the average person on the street has never heard
of Edward O. Thorp. For those who engage in blackjack or hedge fund management
on a regular basis, however, his name may loom as large as anyone else in those
fields of endeavor.
If you fall into the former category, it’s our hope that this Edward Thorp
biography can familiarize you with one of the titans of statistical gambling.
For those who already have a basic knowledge of the man, our detailed biography
of his life is sure to present some facts that have previously slipped between
the cracks. In either case, you should come away from this article with a
newfound appreciation for a true pioneer.
Edward Oakley “Ed” Thorp was born in Chicago, Illinois on August 14th, 1932.
His father was a veteran of World War I, and the senior Thorp had met his future
bride after returning home from combat.
Thorp’s father was a strong proponent of education, and he worked hard to
make sure his son would have a solid foundation of knowledge to draw upon
throughout his life. The benefits of the elder Thorp’s efforts were evident
early on, as Edward could mentally calculate the number of seconds in a year by
the age of seven.
When America entered World War II, Thorp’s father was once again called upon
to serve his country. The absence of the family breadwinner created difficulties
when it came to paying the bills, so Edward’s mother took a job at Douglas
Aircraft to make ends meet.
With his father gone and his mother working, the only child of the Thorp
family was left with lots of free time. Instead of getting in trouble, however,
he pursued a diverse number of hobbies ranging from making explosives (and
detonating them) to playing chess with opponents via a HAM radio.
His father managed to survive yet another world war, and the elder Thorp
relocated his family to Lomita, California when Edward was 10. Ed’s desire for
knowledge and overall intellect continued to flourish, despite being enrolled in
a school that was rated as one of the worst in the area.
Higher Education and Teaching
After graduating from high school, Thorp used his overall intellect and keen
talent for math to gain acceptance to UCLA. He received his bachelor’s degree in
physics in 1953, and this was followed by a master’s degree in 1955.
He then set his sights on a doctoral degree in mathematics, and during this
period he became interested in the math associated with gambling (specifically
roulette). He decided to dispute the long-held notion that games of chance
couldn’t be beat.
Thorp received his PhD in mathematics in 1958, and he began working as a
professor at MIT the following year. He held this position until 1961, when he
transferred to New Mexico State University and taught mathematics until 1965.
At this stage, Thorp began his long affiliation with the University of
California, Irvine. He taught mathematics at the college from 1965 to 1977, and
then became a professor of both mathematics and quantitative finance from 1977
A Wearable Computer
While teaching at MIT, Thorp continued his fascination with using mathematics
to crack the secrets of gambling. He spent hours observing the various games,
and he noted one element that stood out above all others. In a game such as
roulette, each spin was independent of one another, which meant that the odds
were the same regardless of when or where it was played. Blackjack, however, had
odds that varied, as cards being dealt from a deck altered the probability for
future hands (at least until the deck was reshuffled).
Around this time, Thorp read an article about blackjack strategy in a
statistical journal. This further fanned the flames of interest, and he decided
to take his wife on a trip to Las Vegas. While the couple enjoyed modest success
at the blackjack table, Thorp left convinced that a perfect system of play
existed. All it required was someone to come along and discover it.
To help in his initial efforts, Thorp used two main tools. The first was an
IBM 704 computer, which Thorp was able to operate after teaching himself the
computer language known as FORTRAN. The second was the Kelly criterion, a
formula developed in 1956 by J.L. Kelly, Jr. to determine the ideal size of a
series of wagers.
As his research intensified, he brought fellow mathematician Claude Shannon
on board. Claude and his wife would accompany the Thorps on trips to Vegas, and
this led the two men to create the first pocket-sized computer for the purpose
of advantage play (which is now illegal under modern-day casino rules).
At the time, a deck of cards wasn’t reshuffled after every hand, so it was
much easier to keep track of which cards had been played and which remained.
This was a major factor in helping Thorp create his system, and casinos later
adopted a policy of shuffling after every hand in order to combat would-be card
Following careful research and analysis, Thorp created several strategies
that he felt provided the player with a stronger chance of winning. His favorite
was known as the 10 Count System, and it’s explained in the following section.
The 10 Count System Explained
First presented in Edward Thorp’s book, Beat the Dealer, the 10 Count System
is a method that allows players to increase their odds of winning while playing
blackjack. It’s by no means the earliest example of a card counting system, but
it’s notable for being the first made widely available to the general public.
The importance of this fact can’t be overstated, as it opened up gambling and
the game of blackjack to a whole new pool of players.
The system is meant to be used with a single deck of cards, and the goal is
to reduce the house edge by placing larger wagers when the player has a greater
chance of achieving a valuable hand. Counting begins when a fresh deck of cards
is dealt, and the player is tasked with assigning a numerical value to each
face-up card on the table.
If a card is worth 10 points in blackjack, then Thorp’s system assigns it a
value of negative nine. All other cards, meanwhile, are given a value a four. As
the player keeps a running count of the cards, they can get an idea of when they
have the best chance to receive a 10-point card. For example, a count of zero
indicates that there are 2 1/2 4-point cards for every 10-point card in the deck.
While this system is effective for single-deck games of blackjack, there’s
simply too much variation when it comes to larger decks. Las Vegas initially
tried to counter the 10 Count System by introducing new rules, but players
rebelled and refused to play these games.
Instead, the casinos eventually started introducing games with multiple decks
dealt from a shoe, and they were able to convince players to accept these
changes over time. This has rendered Thorp’s system largely ineffective for most
modern forms of 21, although it would become the basis for more advanced methods
of play over the decades.
Taking on the Casinos
Armed with a winning strategy, Thorp was ready to put his research to the
test by making a serious run at the casino blackjack tables. He understood
bankroll management quite well, however, and he therefore realized he would need
someone to bankroll him.
He found his financial backer in Manny Kimmel, a respected gambler with lots
of money and possible connections to the mafia. Another individual may have also
been present, but the exact details tend to vary from one source to the next.
Kimmel wasn’t named directly in Beat the Dealer, instead being given the moniker
of “Mr. X.”
The first stops on their trek were Reno and Lake Tahoe, and Thorp had been
given a $10,000 investment to play with, courtesy of his newfound partner(s).
One of the main destinations was a now-defunct Reno casino known as Harold’s
Club, and Thorp managed to win $500 within 15 minutes using his system. While
the system didn’t always work, he wound up with an $11,000 profit by the end of
the weekend. After that, he never had to ask Kimmel for another penny.
Thorp eventually moved on to Las Vegas, but his ability to rack up
significant wins drew the attention of eagle-eyed security agents. This got him
ejected from a number of Vegas casinos, and Thorp had to resort to a number of
disguises to keep gaining admittance. In fact, he soon adopted the practice of
carrying a notebook on his trips, allowing him to keep track of his various
affectations and disguises. In addition to blackjack, he put together a baccarat
team that enjoyed a respectable amount of success during this period.
Beat the Dealer: A Winning Strategy for the Game of Twenty-One
Word of Thorp’s system and exploits soon spread throughout the close-knit
community of serious gamblers, and the mild-mannered professor was inundated
with requests for his secrets. Thorp had always enjoyed the intellectual
challenge more than the financial benefits, so he decided to put his thoughts
and theories into book form and make it available to anyone who was interested.
The first edition of Beat the Dealer was published by Vintage Books in 1962.
The tome clocked in at over 200 pages, and it was packed with everything from
card counting systems to tips on how to recognize cheating.
Instead of undergoing the usual peer review process for an academic work,
Thorp simply released it onto the market. Some wondered if the mob might respond
by sending a hitman to assassinate Thorp, but nobody resembling Joe Pesci ever
materialized. Beat the Dealer went on to sell more than 700,000 copies and make
the New York Time Bestseller List, a remarkable feat considering that gambling
was such a niche category in the 1960s.
Despite the success of the book, however, a number of critics argued that the
strategies presented were difficult to apply in real-world situations. Ever the
serious academic, Thorp took these criticisms to heart and set out to further
refine his ideas. Luckily, he would get some serious help in the form of fellow
egghead Julian Braun.
Julian Braun and Hi-Lo Card Counting
The publication of Beat the Dealer drew attention from a lot of individuals,
but one of the most notable was IBM computer programmer Julian Braun. The
mathematician and former Marine wrote to Thorp and requested a copy of his
blackjack computer program, which Edward was happy to provide.
Braun used an IBM 7044 mainframe computer to further refine the strategies
laid out by Thorp, running 9 billion blackjack simulations in the process. Over
the next four years, Braun perfected the Hi-Lo Blackjack System, which was more
accurate that Thorp’s original 10 Count System.
When Beat the Dealer was offered in a revised form in 1966, Braun’s Hi Lo
System was included with the following quote from Thorp,
blackjack calculations, based on his extensions and refinements of my original
computer program, are the most accurate in existence, and he has kindly allowed
them to be used throughout this revised edition.”
Like all forms of card counting, Hi-Lo requires the player to assign a
specific value to each visible card. In this case, the values are as follows:
2 through 6 = +1
7 through 9 = 0
10 through Ace = -1
This is known as a “balanced system,” as the count of all cards in the deck
equals zero. High cards are more beneficial to the player, so their value is set
at -1. Low cards, meanwhile, benefit the dealer, so their value is set at +1.
When the count is high, this means more high cards should exist in the hand, and
therefore the player should place larger wagers.
To properly use the system, you must keep up with the running count and the
true count. The former is just what it sounds like: a running total of the value
of all cards played during a hand. The true count, meanwhile, allows the player
to determine if they truly have an edge over the dealer.
In a single deck version of the game, the true count is determined by
dividing the running count by the number of cards yet to be played.
Unfortunately, it’s almost unheard of to find a single-deck game of blackjack
these days, so the player is now required to estimate the number of decks still
in the shoe and divide this by the running count.
Additional Literary Works
While most gamblers and members of the general public remember Thorp for Beat
the Dealer, he wasn’t content to rest on his laurels as an author. He has penned
a number of other works, and all of these are still in print.
A Man for All Markets: From Las Vegas to Wall Street, How I Beat
the Dealer and the Market (2017)
A comprehensive look at Thorp’s life,
from his time as a card counter to his career as an investor.
A Winning Bet in Nevada Baccarat (2013)
A re-publication of a
1963 research journal article entitled “A Favorable Side Bet in Nevada
The Mathematics of Gambling (1984)
An analysis of gambling games
such as blackjack, baccarat, and backgammon, as well as tips on proper money
management. Most of the items in this book are reprinted columns that Thorp
wrote for Gambling Times magazine.
Beat the Market: A Scientific Stock Market System (1967)
takes his skills at mathematics and analysis and applies it to the world of
Elementary Probability (1966)
A scientific text on mathematics
In addition to the books listed above, Thorp has written a wide range of
academic papers on game theory, functional analysis, and probability.
After Beat the Dealer became a sensation, Thorp found it increasingly hard to
enter a casino without being spotted and ejected by security. He therefore
decided to take a break from the world of gambling, turning his attention
instead to investing.
Working alongside Sheen Kassouf, Thorp used his knowledge of statistics and
analysis to find and locate pricing anomalies in the securities market. This led
to the invention of delta hedging, as well as the creation of what’s now known
as the Black-Scholes formula.
In 1967, Thorp published his findings and advice in a book titled Beat the
Market. While it didn’t sell as well as Beat the Dealer, it had a major
long-term impact on the world of investing. Two years later, Thorp and partner
Jay Regan would launch the first market-neutral derivatives based hedge fund
(known as Princeton/Newport Partners).
While still teaching, Thorp founded Edward O. Thorp & Associates, which he
continues to run as of this writing. His first hedge fund returned 15.1% over 19
years, while his overall personal investments have yielded an average return of
20% for 28.5 years (as of 1998).
Induction into the Blackjack Hall of Fame
In 2002, it was decided that the Blackjack Hall of Fame would be created to
honor the contributions of various men and women to the game of 21. The initial
ballot was appropriately comprised of 21 players, experts, and authors, and
voting was held in order to cull down the list. Casino owners and the general
public were invited to participate, although those who derived their primary
income from blackjack had the greatest influence on the voting process.
The first class of the Blackjack Hall of Fame was announced at the 2003
Blackjack Ball, which is always held in a secret location to elude minions of
the casinos. A total of seven individuals were inducted, and Thorp was among
those honored. The complete list included the following:
Edward O. Thorp
In 2003, Edward O. Thorp and his wife, Vivian, donated $1 million to the
University of California, Irvine, to attract promising mathematicians to the
college. According to Thorp,
“Vivian and I have greatly benefited from the
knowledge I have acquired in mathematics and my association with the
mathematical community. It’s our chance to give back, in a modest way, to
mathematics, mathematicians, and a great university.”
As you might have guessed, Edward Thorp has used his mathematical genius to
make himself a multi-millionaire. While his blackjack endeavors brought him a
certain level of fame and a sizable return on Beat the Dealer, it was his
transition to the world of investing that moved him up several tax brackets.
Now in his golden years, Thorp enjoys semi-retirement with his wife and
family. His legacy in the world of gaming is assured, and he also enjoys the
respect of his peers throughout the mathematics community. Not bad for a kid who
used to pass the time by blowing things up.
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