The Perfect Bet

by Adam Kucharski

  In fact, it could be argued that our entire notion of randomness is an abstraction. When we say a coin has a 50 percent chance of coming up tails, or that a roulette ball has a 1 in 37 chance of landing on a particular number, we are using an abstraction. In theory we could write down equations for the motion and solve them to predict the trajectory. But because coin flips and roulette spins are so sensitive to initial conditions, it is difficult to this do in reality. So, instead we approximate the process and assume it is unpredictable. We choose to simplify an intricate physical process for the sake of convenience.

  In life, we must often choose (either consciously or subconsciously) what abstractions to use. The most extensive abstraction would not omit a single detail. As mathematician Norbert Wiener said, “The best material model of a cat is another, or preferably the same, cat.” Capturing the world in such detail is rarely practical, so instead we must strip away certain features. However, the resulting abstraction is our model of reality, influenced by our beliefs and prejudices.

  Sometimes abstractions have tried to deliberately influence people’s perceptions. In 1947, Time magazine published a double-page map of Europe and Asia. Titled the “Communist Contagion,” the map’s perspective had been altered so the Soviet Union—colored in an ominous red hue—loomed over the rest of the world. The map’s creator, a cartographer by the name of R. M. Chapin, continued the theme in subsequent issues. In 1952, a piece called “Europe from Moscow” featured the USSR rising up from the bottom of the image, its borders forming an arrow that pointed toward the West.

  Even if the bias is not deliberate, models inevitably depend on their creators’ aims (and resources). Recall those different horse racing models: Bolton and Chapman’s model had nine factors; Bill Benter used over a hundred. Researchers have to tread a fine line when deciding on an abstraction. Simple models risk omitting crucial features, while complicated models may include unnecessary ones. The trick is to find an abstraction that is detailed enough to be useful, but simple enough to be implementable. In blackjack, for instance, card counters don’t need to remember the exact value of each card; they just need enough information to tip the odds in their favor.

  Of course, there is always a risk of picking the wrong abstraction, which leaves out a critical detail. Émile Borel once said that, given two gamblers, there is always one thief and one imbecile. This is not just the case when one gambler has much better information than the other. Borel pointed out that in complex situations, two people could have exactly the same information and yet come to different conclusions about the probability of an event. When the pair bet together, Borel said each one would therefore believe “that it is he who is the thief and the other the imbecile.”

  Poker is a good example of situation in which choice of abstraction is important. There are a huge number of possible moves in poker—far too many to compute—which means that bots have to use abstractions to simplify the game. Tuomas Sandholm has pointed out that this can cause problems. For instance, your bot might only think in terms of certain bet sizes, to avoid having to analyze every possible wager. Over time, however, the bot’s view of reality will not match the true situation. “Your belief as to how much money is in the pot is no longer accurate,” Sandholm said. This can leave you vulnerable to an opponent using a better abstraction, which is closer to reality.

  The problem doesn’t just appear in poker. The entire casino industry is built on the assumption that the games are random. Casinos treat roulette spins and blackjack shuffles as unpredictable and rely on customers sharing that view. But believing an abstraction doesn’t make it correct. And when someone comes along with a better model of reality—someone like Edward Thorp or Doyne Farmer—that person can profit from the casinos’ oversimplification.

  Thorp and Farmer were both physics students when they began their work on casino games. In subsequent decades, other students and academics have followed their lead. Some have targeted casinos, while others have focused on sports and horse racing. Which raises the question: Why is betting so popular among scientists?

  IN JANUARY 1979, A group of undergraduates at Massachusetts Institute of Technology set up an extracurricular course called “How to Gamble If You Must.” It was part of the university’s four-week-long independent activities period (IAP), which encouraged students to take new classes and broaden their interests. During the gambling course, participants learned about Thorp’s blackjack strategy and how to count cards. Soon some of the players had decided to try out the tactics for real; first in Atlantic City, and then in Vegas.

  Although the players had started with Thorp’s methods, they needed a new approach if they were going to be successful. As Thorp had discovered, it was difficult to get away with solo card counting. Players have to raise their bets when the count is in their favor, which means they are likely to attract the attention of casino security. The MIT students therefore worked as a team. Some players would be spotters, whose job it was to bet the minimum stake while keeping track of the count. When the deck was sufficiently in their favor, the spotters would signal to another group—the “big players”—who would come and throw lots of money at the table. To help conceal their roles from security, the team exploited common casino stereotypes. Smart female students would put on low-cut tops and pretend to be dumb gamblers, all the while keeping count of the cards. Students with an Asian or Middle Eastern background would play the role of a rich foreigner, happy to spend their parents’ money.

  Although its members changed over time, the MIT team continued to take on the casinos for many years. The contrast with life in Massachusetts could not have been larger. Instead of dorm rooms and Boston rain, there were hotel suites, sunny skies, and huge profits. During the Fourth of July weekend in 1995, the team was so successful that when they met by the pool at the end of the trip, one of them was carrying a gym bag holding almost a million dollars in cash. Another time, one of the team left a paper bag containing $125,000 in a classroom at MIT. When they returned, the bag was gone. They later discovered the janitor had stored it in his locker; they only got the money back after six months of investigations by the FBI and Drug Enforcement Administration.

  The MIT blackjack team has become part of gambling legend. Journalist Ben Mezrich told their story in the best-selling book Bringing Down the House, and the events later inspired the film 21. Unfortunately, for modern students, however, the exploits of the MIT team have become history in more ways than one. Casinos have introduced lots more countermeasures in recent years, which means teams would struggle to reproduce the sort of success seen in the 1980s and 1990s. In fact, according to professional gambler Richard Munchkin, hardly anyone focuses exclusively on blackjack anymore. “I know very few people—people you could count on one hand—who are making a living only by counting cards,” he said.

  Yet the science of gambling still features at MIT. In 2012, PhD student Will Ma set up a new course as part of the independent activities period. Its official title was “15.S50,” but everybody knew it as the MIT poker class. Ma, who was studying operations research, had played a lot of poker—and won a lot of money—during his undergraduate days in Canada. When he arrived at MIT, word of his success got out, and several people started asking him questions about poker. One of them was his head of department, Dimitris Bertsimas, who also had an interest in the game. Bertsimas helped Ma put together a class to teach the theory and tactics needed to win. It was a legitimate MIT class; if students passed, they could get degree credit.

  The course attracted a lot of attention. In fact, so many people turned up for the first class that they had to move rooms. “It was probably one of the most popular classes during IAP,” Ma said. Attendees ranged from undergraduate business students to PhD mathematicians. Ma’s class also caught the eye of the online poker community. Many incorrectly believed that students were going to use their expertise to build poker software. “Through word of mouth, it somehow got twisted,” Ma said. “They thought it wa
s going to lead to a huge poker bot system with a ton of bots written by MIT students taking all the money.”

  As well as distancing himself from bots, Ma also had to be careful to avoid his course on poker being misinterpreted by the university. “It can be seen as gambling,” he said, “and you’re not supposed to teach gambling at MIT.” He therefore used play money to demonstrate strategies. “I had to make sure I wasn’t taking people’s real money.”

  Ma didn’t have enough time to cover every aspect of poker, so instead he tried to focus on topics that would provide the biggest benefits. “I tried to go through the steepest part of the learning curve,” he said. He explained why players shouldn’t be afraid to go in at the start of a round and the dangers of getting bored with folding and instead playing too many hands. Many of the lessons would be useful in other situations, too. “I tried to put it in the perspective of real life,” Ma said. The poker class covered the importance of making confident moves and of not letting mistakes affect performance. Students learned how to read opponents and how to manage the image they conveyed during games. In doing so, they started to discover what luck and skill really looked like. “I think one of the things poker teaches you very well is that you can often make a good decision but not get a good result,” Ma said, “or make a bad decision and get a good result.”

  COURSES TEACHING THE SCIENCE of gambling have cropped up in other institutions, too, from York University in Ontario to Emory University in Georgia. In these classes, students study lotteries, roulette, card shuffling, and horse races. They learn statistics and strategy, analyzing risks and weighing options. Yet, as Ma found, people can be hostile to the concept of betting in universities. Indeed, many people are against the idea of wagers in any context.

  When people say they dislike betting, what they usually mean is that they dislike the betting industry. Although the two are related, they are by no means synonymous. Even if we never gambled in casinos or visited bookmakers, betting would still permeate our lives. Luck—good and bad—looms over our careers and relationships. We have to deal with hidden information and negotiate in the face of uncertainty. Risks must be balanced with rewards; optimism must be weighed against probability.

  The science of gambling isn’t just useful for gamblers. Studying betting is a natural way to explore the notion of luck and can therefore be a good way to hone scientific skills. Although Ruth Bolton and Randall Chapman’s paper on horse racing predictions gave rise to a multi-billion-dollar betting industry, it was the only article Bolton wrote on the topic. She has spent the rest of her career working on other problems. Most of them revolve around marketing, from the effects of different pricing strategies to how businesses can manage customer relationships. Bolton admits that the horse racing paper could therefore seem like a bit of an outlier on her CV; at first glance, it doesn’t really fit in with her other research. But the methods in that early racetrack study, which involved developing models and assessing potential outcomes, would go on to shape the rest of her work. “That way of thinking about the world stayed with me,” she said.

  Probability theory, which Bolton used to analyze horse races, is one of the most valuable analytical tools ever created. It gives us the ability to judge the likelihood of events and assess the reliability of information. As a result, it is a vital component of modern scientific research, from DNA sequencing to particle physics. Yet the science of probability emerged not in libraries or lecture theaters but among the cards and dice of bars and game rooms. For eighteenth-century mathematician Pierre Simon Laplace, it was a strange contrast. “It is remarkable that a science which began with the consideration of games of chance should have become the most important object of human knowledge.”

  Cards and casinos since have inspired many other scientific ideas. We have seen how roulette helped Henri Poincaré develop the early ideas of chaos theory and allowed Karl Pearson to test his new statistical techniques. We also met Stanislaw Ulam, whose card games led to the Monte Carlo method, now used in everything from 3D computer graphics to the analysis of disease outbreaks. And we have seen how game theory emerged from John von Neumann’s analysis of poker.

  The relationship between science and betting continues to thrive today. As ever, the ideas are flowing in both directions: gambling is inspiring new research, and scientific developments are providing new insights into betting. Researchers are using poker to study artificial intelligence, creating computers that can bluff and learn and surprise just like humans. Every year, these champion bots are coming up with new tactics that humans never knew about, or would never dare try. Meanwhile, high-speed algorithms are helping companies make bets and trades automatically, creating a complex ecosystem of interactions that has prompted new avenues of research. Sports analysts, armed with better data and faster computers, are no longer just predicting team results; they are picking apart the roles of individual players, measuring the contribution of chance and skill. From poker to betting exchanges, researchers are developing a deeper understanding of human behavior and decision making, and in turn coming up with more effective gambling strategies.

  THE POPULAR IMAGE OF a scientific betting strategy is one of a mathematical magic trick. To get rich, all you need is a simple formula or a few basic rules. But, much like a magic trick, the simplicity of the performance is an illusion, concealing a mountain of preparation and practice.

  As we’ve seen, almost any game can be beaten. But profits rarely come from lucky numbers or “foolproof” systems. Successful wagers take patience and ingenuity. They require creators who choose to ignore dogma and follow their curiosity. It might be a student like James Harvey, who wondered which lottery was the best deal and orchestrated thousands of ticket purchases to take advantage of the loophole he found. Or a physicist like Edward Thorp, rolling marbles on his kitchen floor to understand where a roulette ball would stop. It might take a business specialist like Ruth Bolton, crunching through horse racing data to find out what makes a winner. Or statisticians such as Mark Dixon and Stuart Coles, reading an undergraduate exam question about soccer prediction and wondering how the methods could be improved.

  From the casinos of Monte Carlo to the racetracks of Hong Kong, the story of the perfect bet is a scientific one. Where once there were rules of thumb and old wives’ tales, there are now theories guided by experiment. The reign of superstition has waned, usurped by rigor and research. Bill Benter, who made his fortune betting on blackjack and horse racing, has no doubts about who deserves the credit for the transition. “It wasn’t as though streetwise Las Vegas gamblers figured out a system,” he said. “Success came when an outsider, armed with academic knowledge and new techniques, came in and shone light where there had been none before.”

  ACKNOWLEDGMENTS

  FIRST, THANKS MUST GO to my agent Peter Tallack. From proposal to publisher, his guidance over the past three years has been invaluable. I would also like to thank my editors—TJ Kelleher and Quynh Do at Basic Books, and Nick Sheerin at Profile—for taking a gamble on me, and for helping me shape the science into a story.

  My parents continue to provide crucial suggestions and discussions on my writing, and for this I am eternally grateful. Thanks also to Clare Fraser, Rachel Humby, and Graham Wheeler for many useful comments on early drafts. And, of course, to Emily Conway, who has been there for me throughout with wise words and wine.

  Finally, I am indebted to everyone who took the time to share their insights and experiences: Bill Benter, Ruth Bolton, Neil Burch, Stuart Coles, Rob Esteva, Doyne Farmer, David Hastie, Michael Johanson, Michael Kent, Will Ma, Matt Mazur, Richard Munchkin, Brendan Poots, Tuomas Sandholm, Jonathan Schaeffer, Michael Small, and Will Wilde. Many of these individuals have shaped entire industries with their scientific curiosity. It will be fascinating to see what comes next.

  NOTES

  INTRODUCTION

  ixIn June 2009, a British newspaper: Ward, Simon. “A Sacked 22-Year-Old Trainee City Trader Today Reveals How He Won a
Staggering £20 Million in a Year . . . Betting on the Horses.” News of the World, June 26, 2009.

  ixHe had a chauffeur-driven Mercedes: Duell, Mark. “‘King of Betfair’ Who Lived Lavish Lifestyle in Top Hotels with Chauffeur-Driven Mercedes and Clothes from Harrods after Conning Family Friends Out of £400,000 Is Jailed.” Daily Mail Online, May 28, 2013. http://www.dailymail.co.uk/news/article-2332115/King-Betfair-stayed-hotels-splashed-chauffeur-conning-family-friends-jailed.html.

  ixThe profitable bets that Short claimed: Wood, Greg. “Short Story on Betfair System Is Pure Fiction.” Guardian Sportblog (blog), June 29, 2009. http://www.theguardian.com/sport/blog/2009/jun/30/greg-wood-betfair-notw-story.

  ixHaving persuaded investors to pour hundreds of thousands: Duell, Mark. “Gambler, 26, Who Called Himself the ‘Betfair King’ Conned Friends Out of £600,000 with Betting Scam to Pay for Designer Clothes.” Daily Mail Online, April 23, 2013. http://www.dailymail.co.uk/news/article-2313618/Gambler-called-Betfair-king-connedfriends-600–000-bogus-betting-scam.html.

  xthe case went to trial: “Criminal Sentence—Elliott Sebastian Short—Court: Southwark.” TheLawPages.com, May 28, 2013. http://www.thelawpages.com/court-cases/Elliott-Sebastian-Short-11209–1.law.

  xAs its reputation spread: Ethier, Stewart. The Doctrine of Chances: Probabilistic Aspects of Gambling (New York: Springer, 2010), 115.

  xi“The martingale is as elusive”: Dumas, Alexandre. One Thousand and One Ghosts (London: Hesperus Classics, 2004).

  xiHaving frittered away his inheritance: O’Connor, J. J., and E. F. Robertson. “Girolamo Cardano.” June 1998. http://www-history.mcs.st-andrews.ac.uk/Biographies/Cardan.html.