The Business of Hedges, Bets, and Blackjack

By James Case

A Man for All Markets: From Las Vegas to Wall Street, How I Beat the Dealer and the Market. By Edward O. Thorp. Courtesy of Random House.

The basic details of Edward O. Thorp’s legendary career are well known. As a postdoctoral instructor at the Massachusetts Institute of Technology (MIT), he programmed the school’s brand-new IBM 704 computer—in the then-brand-new FORTRAN language—to calculate the odds of winning a hand of blackjack dealt from an incomplete deck. Following coverage of the feat in both Sports Illustrated and Life magazine, Thorp’s book Beat the Dealer became a New York Times best seller, heightening interest in casino blackjack for years to come. Not long thereafter, in collaboration with Claude Shannon, Thorp developed a “wearable computer” that enabled the pair—working as a team—to beat the house at roulette. Rather than pursue that opportunity, however, the two parted ways, focusing separately on Wall Street: the biggest casino of all. In 2014, Celebrity Net Worth placed Thorp at number 36 on its list of 50 richest hedge fund managers, with a fortune estimated at $800 million.

A Man for All Markets describes Thorp’s struggle, as a child of the Great Depression, to attend college, much less forge an academic career. Learning first to count and then to read, young Edward was devouring classics such as Treasure Island, Gulliver’s Travels, and King Arthur and the Knights of the Round Table by age six. When challenged by a stranger amused to find one so young in possession of Charles Dickens’ A Child’s History of England, the prodigy responded by naming every English monarch from King Arthur through Queen Victoria.

The Thorp family moved from Chicago to Lomita, Calif., on the eve of World War II, in search of factory work. With both of his parents working long hours, Thorp was obliged to find his own amusement outside of school. Increasingly, he found it in science.

Thorp won California’s competitive high school physics exam, entitling him to first pick among the scholarships offered that year by in-state institutions. He started school at the University of California, Berkeley as a chemistry major in the fall of 1950, but switched to physics after one semester and soon transferred to the University of California, Los Angeles (UCLA) to be closer to home.

Despite receiving a scholarship to Columbia University, Thorp remained at UCLA upon graduation due to financial reasons, quickly completing his masters and the course work for a Ph.D. He married his undergraduate classmate Vivian Sinetar and embarked on a thesis regarding the shell structure of atomic nuclei, which required a number of advanced math courses. Ultimately, this prompted a switch to mathematics, and a thesis pertaining to compact operators on Banach spaces.

Following the completion of his thesis at UCLA in 1958, Thorp worked there as an instructor for a year. Because Las Vegas offered packages that included cheap lodging, meals, and A-list entertainment, he and Vivian decided to vacation there during Christmas break. Having long believed it possible to develop a winning strategy for roulette, Thorp planned to use the visit to conduct feasibility studies. Before leaving, however, he learned of a recently published strategy for blackjack. Devised by four army mathematicians led by Roger Baldwin using desktop calculating machines during World War II, it reduced the odds favoring the house to a mere 0.62, substantially lower than any other game in town. In the process of losing $8.50 of his $10.00 stake while following an abbreviated form of the Baldwin strategy, Thorp became hooked on blackjack.

Back in Los Angeles, Thorp located the journal article describing the strategy and experienced an immediate “ah-ha” moment. He realized that all the probabilities in the article had been calculated as if each hand was dealt from a fresh, randomly-shuffled deck, whereas casino hands were typically dealt from depleted decks, devoid of the most recently played cards. Depending on which cards were missing, a depleted deck could be more or less favorable to the house than a fresh deck. And by betting heavily when the deck is in the players’ favor, and lightly (if at all) when it isn’t, an individual can expect to win in the long run. The only remaining questions were which depleted decks were favorable to whom, and how to recognize the promising ones in real time.

Arriving at MIT in the fall of 1959, Thorp was pleased to discover that the school’s IBM 704 could carry out a thousand man-years of routine calculations in a mere ten minutes of run time. Yet his work was still frustrating; results took two to three days after a job (deck of punched cards) was placed in the queue. Thorp’s first discovery, made by avoiding some of the approximations used by the Baldwin team, was that their strategy actually reduced¹ the house advantage to a mere 0.21! His second was that the 48-card deck missing all four aces gave the house a 2.72 percent advantage, far greater than the 0.21 of a fresh deck. This realization showed that the odds can shift significantly after only four cards have been played. By the fall of 1960, Thorp completed his calculations, used the results to develop a variety of more or less complicated winning strategies, made a “proof-of-concept” visit to Las Vegas, and prepared to publish his findings.

To reach the largest possible audience, he asked Claude Shannon to submit his paper to the Proceedings of the National Academy of Sciences. After a searching cross examination, Shannon agreed to do so, and directed Thorp to a paper by John Kelly containing a now-famous (if still somewhat controversial) formula for choosing the fraction of one’s current endowment to wager on a sequence of promising, though risky, propositions.

With his knack for detecting statistically advantageous wagers and the Kelly rule for exploiting them, Thorp was ready for an assault on the financial markets. In collaboration with Sheen Kassouf, an economist at the University of California, Irvine (where Thorp taught math and finance between 1965 and 1982), he wrote a book called Beat the Market, explaining a few of the ways to do exactly that. In 1969, at the suggestion of Warren Buffett, Thorp formed a hedge fund called Convertible Hedge Associates (later renamed Princeton Newport Partners, or PNP), with offices in Newport Beach, Calif., and Princeton, N.J. The West Coast operation, managed by Thorp, identified promising trades and communicated them to the East Coast division, which made the trades and sought additional investors.

In early 1973, Thorp received a preprint of a paper by Myron Scholes and Fischer Black that rigorously derived a formula for evaluating certain options about which Thorp presumed no one else knew. Having deduced it by what he calls “plausible mathematical reasoning,” Thorp had been using the now-famous Black-Scholes formula since 1967. But once it entered the public domain, he realized that he would have to develop new tools to stay ahead of the competition.

In December 1987, operatives of the International Revenue Service, the Federal Bureau of Investigation, and the U.S. Postal Service raided the Princeton office of PNP. The five top people were indicted and tried on 64 charges of stock manipulation, stock parking, and tax, mail, and wire fraud. All were convicted on multiple counts. As a result, Thorp elected to close the operation down. At no time was he, or anyone else in the West Coast office, accused of any wrongdoing.

Thorp is able to estimate the amount of money he might have made, had PNP remained in business, merely by reflecting that a market-neutral hedge fund operation—the Citadel Investment Group—was built on the PNP model by former hedge fund manager Frank Meyer and investment prodigy Ken Griffin. Beginning with a few million dollars in 1990, when Thorp became the group’s first limited partner, it has produced annualized gains of about 20% through 2015, when Griffin’s net worth was estimated at $5.6 billion. During much of that time, Thorp continued to act as an informal consultant and benevolent guru to a variety of investment startups.

Thorp dwells at length on the criminal behavior he has encountered over the years, from plagiarism in academic life to dirty tricks in casinos to white collar crimes reported in the Wall Street Journal. Neither the powers in academic life, the Nevada state gaming commission, nor the U.S. Securities and Exchange Commission seems prepared to confront the malfeasance that surrounds them. Protect yourself, he warns. No one else is likely to do it for you.

Upon closing PNP’s doors in 1987, Thorp paused to reflect on the nature of time. How you spend it, he decided, is what counts in the long run, and there are tradeoffs to be made between time, health, and wealth. What seems to please Thorp most is the knowledge that, simply by thinking about problems of interest, he has been able to change the way people choose to live their lives and occupy their time.

¹Around 1980, as computers became powerful enough to require no approximations, researchers discovered that the Baldwin strategy actually placed the house at a 0.13 disadvantage, even without counting cards!

James Case writes from Baltimore, Maryland.