A Man for All Markets: From Las Vegas to Wall Street, How I Beat the Dealer and the Market

by Edward O. Thorp

model is a simplified version of reality, like a street map that shows you how to travel from one part of a city to another or the vision of a gas as a swarm of tiny elastic balls ceaselessly bouncing against one another. I learned that simple devices such as gears, levers, and pulleys follow basic rules. You could discover the rules by experimenting and, if you got them right, could then use the rules to predict what would happen in new situations. Most amazing to me was the magic of a crystal set—an early primitive radio made with wire, a mineral crystal, and headphones. Suddenly, I heard voices coming from hundreds or thousands of miles away, carried through the air by some mysterious process. The notion that things I couldn’t even see followed rules I could discover just by thinking—and that I could use what I discovered to change the world—inspired me from an early age. Because of circumstances, I was largely self-taught and that led me to think differently. First, rather than subscribing to widely accepted views—such as you can’t beat the casinos—I checked for myself.

de ludo aleae (“Book on Games of Chance”) was instrumental in the later development of probability, but, unlike Thorp’s book, was less of an inspiration for gamblers and more for mathematicians. Another mathematician, a French Protestant refugee in London, Abraham de Moivre, a frequenter of gambling joints and the author of The doctrine of chances: or, a method for calculating the probabilities of events in play (1718) could hardly make both ends meet. One can easily count another half a dozen mathematician-gamblers, including greats like Fermat and Huygens—who were either indifferent to the bottom line or not particularly good at mastering it. Before Ed Thorp, mathematicians of gambling had their love of chance largely unrequited.

True success is exiting some rat race to modulate one’s activities for peace of mind. Thorp certainly learned a lesson: The most stressful job he ever had was running the math department of the University of California, Irvine. You can detect that the man is in control of his life. This explains why he looked younger the second time I saw him, in 2016, than he did the first time, in 2005. Ciao, Nassim Nicholas Taleb

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By the time I took chemistry in the eleventh grade, I had been doing experiments for a couple of years. Enjoying the theory as well as having fun, I read a high school chemistry book from cover to cover. I fell asleep at night mentally reviewing the material, a habit that proved, both then and later, remarkably effective for understanding and permanently remembering what I had learned. Our

I didn’t expect to win, since the odds were slightly against me, but as I expected to build a device to successfully predict roulette and had never gambled before, it was time to get casino experience. I knew virtually nothing about casinos, their history, or how they operated. I was like a person who had glanced at recipes but never been in a kitchen.

Facing four hundred million man-years of calculations, with a resulting railroad car full of strategy tables, enough to fill a Rolodex five miles long, I tried to simplify the problem. I

The $32 loss was well within the range of possible outcomes predicted by my theory, so it didn’t lead me to doubt my results.

With nothing more for me to learn that day, I left, poorer once again but, I hoped, wiser.

A young reporter for the Post named Tom Wolfe followed up after my talk with an interview. The Post ran his story, “You Can So Beat the Gambling House at Blackjack, Math Expert Insists.” He was curious rather than skeptical, sympathetic but probing. Wolfe later became one of America’s most famous authors.

By this time, Washington’s airports were buried in two feet of snow, so I boarded a train for Boston. During the long ride back I wondered how my research into the mathematical theory of a game might change my life. In the abstract, life is a mixture of chance and choice. Chance can be thought of as the cards you are dealt in life. Choice is how you play them. I chose to investigate blackjack. As a result, chance offered me a new set of unexpected opportunities.

This plan, of betting only at a level at which I was emotionally comfortable and not advancing until I was ready, enabled me to play my system with a calm and disciplined accuracy. This lesson from the blackjack tables would prove invaluable throughout my investment lifetime as the stakes grew ever larger.

dealing hands at high speed, blowing cigarette smoke at me, and engaging me in complicated conversations. Meanwhile, I was keeping track of the cards, calculating the percent advantage and my bet size, then playing out my hand using strategies that varied depending on the count. The key was to take it one step at a time, adding a new difficulty only after I became comfortable and relaxed with what I was already doing. What had seemed daunting finally became easy.

Mathematically, interruptions didn’t matter, because my lifetime of playing was just one long series of hands, and chopping it into sessions and playing them at various times and in various casinos should not affect my edge, nor the long-run amount I could expect to win. This principle applies in both gambling and investing.

Countermeasures included reshuffling the pack of cards by the time half or fewer of them had been played. This not only limits the card counter’s chances to make favorable bets, but is also costly for the casino because it slows the game down, fleecing the ordinary players more slowly and reducing casino profits. If one likens a casino to a slaughterhouse for processing players, then more time spent shuffling means less efficient use of plant capacity.

There are as many ways to do this as there are to portray characters in the theater. You can be the drunken cowboy from Texas or the wildly animated lady from Taiwan who can’t wait to get her next bet down. You can be Caspar Milquetoast, the nervous accountant from Indianapolis who has already lost too much down the street. Or Miss Spectacular, who draws all the attention to herself, not to how she bets and plays.

As part of an orchestrated PR follow-up, a Las Vegas Sun editorial of April 3, 1964, assured us that “Anybody who has been around Nevada very long knows that [casinos welcome] players with a system.” “Edward O. Thorp…obviously doesn’t know the facts of gambling life. There has never been a system invented that overcomes…the advantage the house enjoys in every game of chance.” And for the clincher: “ ‘Dr. Thorp may be qualified at mathematics, but he is sophomoric on gambling,’ is the way Edward A. Olsen, Gaming Control Board chairman, put it.” In a nonconfrontational vein, Gene Evans of Harrah’s Club explained that “…the club believes the player may have a better chance when the deck is shuffled every time, because all the Aces and face cards could come up on each deal.”

Still, the fact that blackjack could be beaten led to an upsurge in play.

The casinos introduced technology to stop the counters. Cameras and observers followed the action through one-way mirrors above the tables. Currently, this is automated, incorporating face-recognition software. RFID chips keep track of a player’s bets, and machines can track the cards and check the play of the hands, searching for patterns characteristic of counters. Machines that continually reshuffle the cards proved to be a perfect defense without slowing the game down, but the casinos pay fees to the vendors of the machines. Meanwhile the card counters were developing more techniques for winning.

So this was the setting when Claude Shannon and I, in September 1960, set to work to build a computer to beat roulette. The key fact was that casinos allowed players to bet for a few seconds while the ball was spinning.

“Do you know anyone in Budapest named Sinetar?” I asked. “Of course. They are a famous family,” she replied. “There’s Miklos, the film producer, as well as an engineer, and a psychologist.” “Well,” I said, “they are relatives of my wife.” Me, to Vivian, to a Budapest Sinetar, to my economist seatmate. Two degrees of separation. So far, I’ve never needed more than three to connect with a stranger.

One of us wore the computer, which had twelve transistors and was the size of a pack of cigarettes. Data was input with switches hidden in the wearer’s shoes and operated by his big toes. The computer’s forecast was transmitted by radio, using a modification of the inexpensive, widely available equipment ordinarily used to remotely control model airplanes. The other person, the bettor, would wear a radio receiver, which played the musical tones telling him on which group of numbers to bet. We two confederates would act like strangers.

I was at a point then in life when I could choose between two very different futures. I could roam the world as a professional gambler winning millions per year. Switching between blackjack and roulette, I could spend some of the winnings as perfect camouflage by also betting on other games offering a small casino edge, like craps or baccarat. My other choice was to continue my academic life. The path I would take was determined by my character, namely, What makes me tick? As the Greek philosopher Heraclitus said, “Character is destiny.” I unfreeze time and watch us head for the roulette tables.

The MIT Media Lab lists our device as the first of what would later be called wearable computers, namely, computers that are worn on the body as part of their function. In late 1961 I built the second wearable computer, a knockoff to predict the wheel of fortune or money wheel. As in the roulette computer, my device used the toe-operated switch for input, the speaker for output, and just a single unijunction transistor; it required only one person. Matchbox-sized, it worked well in the casinos, but the game had too little action to conceal the spectacular consequences of my late bets. Several times when I placed bets on 40:1 as the wheel was spinning, the croupier would give the wheel an extra push.

To find out, Bill Walden and I proved what we called the Fundamental Theorem of Card Counting, which says, in a precise mathematical way, that the advantage from card counting becomes better as more cards are seen. This means the best situations come toward the end. We found that even those were tiny and rare.

well-known joke is, “How do you tell whether a mathematician is an introvert or an extrovert?” Answer: “If he looks at his shoes when he talks to you, he’s an introvert. If he looks at your shoes, he’s an extrovert.”

Much of what I read was dross but, like a baleen whale filtering the tiny nutritious krill from huge volumes of seawater, I came away with a foundation of knowledge. Once again, just as with casino games, I was surprised and encouraged by how little was known by so many. And just as in blackjack, my first investment was a loss that contributed to my education.

Having learned the folly of anchoring from my investment experience, I have seen that it can be equally foolish on the road. Being a more rational investor has made me a more rational driver!

After these lessons from Mr. Market, I was tempted to believe that the academics were right in claiming that any edge in the markets is limited, small, temporary, and quickly captured by the smartest or best-informed investors. Once again, I was invited to accept the consensus opinion at face value, and once again I decided to see for myself.

Warren was a high-speed talker with a Nebraska twang and a stream of jokes, anecdotes, and clever sayings. He loved to play bridge and had a natural liking for the logical, the quantitative, and the mathematical. As the evening went on, I learned that he focused on finding and buying into undervalued companies. Over a period of several years, he expected each of these investments to substantially outperform the market, as represented by an index such as the Dow Jones Industrial Average (DJIA) or the Standard & Poor’s 500 (S&P 500). As his mentor Ben Graham did before him, Warren also invested in warrant and convertible hedging and merger arbitrage. It was in this area that his and my interest overlapped, and where Buffett, unknown to me, was vetting me as a possible successor to manage investments for the Gerards.

As we chatted about compound interest, Warren gave one of his favorite examples of its remarkable power, how if the Manhattan Indians could have invested $24, the value then of the trinkets Peter Minuit paid them for Manhattan in 1626, at a net return of 8 percent, they could buy the land back now along with all the improvements. Warren said he was asked how he found so many millionaires for his partnership. Laughing, he said to me, “I told them I grew my own.”

Vivian’s insights helped me cope with the cast of characters I was meeting in the investment world, many of whom seemed to be lacking a moral compass. She was fascinated by people. It had become second nature to take the bits and pieces someone told her about themselves and build a unified life story, which she analyzed and checked for consistency. As a result my wife was an almost unerring judge of character, motives, and expected future behavior. I was repeatedly amazed when she applied this to business and professional people I introduced her to for the first time.

What the hagglers and the traders do reminds me of the behavioral psychology distinction between two extremes on a continuum of types: satisficers and maximizers. When a maximizer goes shopping, looks for a handyman, buys gas, or plans a trip, he searches for the best (maximum) possible deal. Time and effort don’t matter much. Missing the very best deal leads to regret and stress. On the other hand, the satisficer, so-called because he is satisfied with a result that is close to the best, factors in the costs of searching and decision making, as well as the risk of losing a near-optimal opportunity and perhaps never finding anything as good again.

Focused on Princeton Newport, I lost track of Warren after 1969. Then in 1983, I heard about the remarkable growth of a company called Berkshire Hathaway. Not knowing it was to become Warren’s investment vehicle, I had stopped paying attention to it back in 1969. The stock price then was $42 a share, if you could find anyone to trade with. It was now publicly trading at over $900. I knew at once what this meant. The “cigar butt” had become a humidor of Havanas. Despite its having increased by a multiple of more than 23 in fourteen years, I made my first purchase at $982.50 a share and continued to accumulate stock. By