How to Beat the House: the Science Behind Gamblers’ Hot Streaks

From the MIT card counters to the Irish lottery schemers to Hong Kong’s racetracks, how a few brains spotted the loopholes, beat the house, and cashed in.


For as long as games of chance have existed, people have tried to find an edge. Some have relied on superstition, while others have hunted for quick-and-easy schemes. The top gamblers, however, have often turned to science. By combining academic theory with ambition and focus—plus a good dose of audacity—they have managed to exploit loopholes that nobody even knew existed. But how did they do it?

One tactic is to use sheer brute-force effort. In this respect, few could rival the wager Stefan Klincewicz and 27 collaborators carried out in May 1992. Their target was the Irish National Lottery, and their motivation was a simple mathematical calculation. They’d noticed it would cost about £1 million to buy up every possible combination of lottery numbers, which would by definition include the winning ticket. So if the jackpot was big enough—as it was in the £1.7 million May rollover—they could in theory buy their way to victory.

Unfortunately, reality proved a little trickier. To carry out their plan, the team needed to make more than a million ticket purchases, with each one filled out by hand. Plus, they had to win a cat-and-mouse game with lottery officials, who were trying to stop them. Still, it was worth the effort: When the draw was made, they netted a £300,000 profit. They were not the first to win this way. In 1729, Voltaire made his fortune by taking advantage in a similar flaw in a Parisian lottery.

Lotteries aren’t the only game to have been tackled with science. An early pioneer of scientific betting was Gerolamo Cardano, a physician in Renaissance Italy. As a doctor, he’d been one of the first to describe typhoid fever; as a gambler, he was the first to tackle games of chance mathematically. At a time when there was no real grasp of probability, he wrote a gamblers’ manual outlining how chance could be measured, and game strategies could be evaluated.

One of Cardano’s main interests was what made a game “fair.” Roll a dice and there is a 1 in 6 chance of getting a particular number, so any bet should reflect this probability. Cardano extended this logic to more complicated bets, and used his superior gambling knowledge to fund his lifestyle. Others would later follow suit, using science to take on games that were thought to be unbeatable.

For a long time, blackjack was one such game. In the 1950s, a group of Army statisticians had shown that if you played the ideal strategy, you’d lose a mere 0.6 percent per hand on average. It wasn’t particularly good news for players, as it meant your money would still end up in the casino’s pocket eventually. Until physicist Edward Thorp worked out how to tip things back in the gamblers’ favor, that is.

Thorp’s crucial insight, published in 1961, was that card deals are not independent of one another. If you could keep track of what cards had come up previously—even in a fairly approximate way—you’d be able to spot potentially profitable situations, and adjust your bets accordingly. With his profitable strategy, Thorp soon became an unwanted guest in a house that was used to winning. Casinos would watch out for sudden changes in betting, and kick out anyone they thought was counting cards. For a while Thorp employed disguises to avoid casino security, but eventually he turned his attention to other endeavors, most notably in finance.

As with the lottery, teamwork would provide a solution to the card-counting problem. During the 1980s and 1990s, a group of students at the Massachusetts Institute of Technology took on casinos. Building on Thorp’s work, the now-infamous “MIT blackjack team” hid from security by playing up to stereotypes—girls acted dumb, foreign students pretended to be wealthy and spoiled—all the while working together to count cards and flag up favorable situations to teammates. It proved a lucrative tactic. After one of their most successful weekends, they left Las Vegas with almost $1 million in cash.

Teams have successfully taken on other casino games, too. Between 1977 and 1979, a group of physicists from the University of California—collectively known as the “Eudaemons”—took a hidden computer into Nevada casinos, and with it a massive advantage at roulette. People had tried to beat roulette before, by collecting data on spins and looking out for worn-out tables that had a bias toward certain numbers. In 1947, Albert Hibbs and Roy Walford, two students at the University of Chicago, headed to the casinos of Reno to search for biased roulette wheels. In one vacation, they made enough to buy a yacht and take it sailing around the Caribbean for the year.

Eventually casinos had latched on to the strategy and removed biased tables, so the Eudaemons decided to take a different approach. Rather than use statistics to find a profitable wheel, they gathered information on the roulette ball as it spun around the table, and used their computer to predict the ball’s trajectory with physics. By the time the croupier called “no more bets,” they on average had a 20 percent advantage over the house. The Eudaemons would later go into finance and academia, but their betting techniques lived on. In March 2004, a computer was reportedly used to win £1.2 million from a roulette table in London’s Ritz casino.

Yet the biggest profits from scientific betting have come outside traditional casino games. While the Eudaemons were placing bets in Las Vegas in the late 1970s, another gambler was also making his debut in the city. A mathematician by training, Michael Kent was using statistical models to make sports predictions. Focusing mostly on college matches, he collected together reams of data and used his models to identify which factors were important for performance. While Kent concentrated on the predictions, others looked after the betting. Between 1980 and 1985, Kent’s “Computer Group” made about $14 million in profits.

It didn’t take long for scientific gambling to take off in other regions, too. Tired of betting in casinos, blackjack players like Alan Woods and Bill Benter had abandoned the game, and instead turned their attention to the horse races of Hong Kong. From scientific point of view, the set-up there was ideal: There was a small pool of horses that raced against each other repeatedly, generating plenty of data to analyze. Using statistical models, syndicates estimated the “true” probability that a horse would win, and compared it with the betting odds displayed at the track. If the odds underestimated its chances, teams would place bets accordingly. It turned out to be a highly lucrative strategy. During the first half of the 1990s, Benter’s syndicate reportedly made a more than 3,000 percent return on their initial bankroll.

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Scientific betting has continued to expand. Some syndicates are even sharing their expertise with outsiders, and letting investors into what has long been an opaque, secretive industry. Firms like Priomha Capital in Australia and Strategem Technologies in Britain are pitching sports betting as an alternative type of financial asset. Rather than specialize in traditional investments such as stocks or commodities, sports funds could allow investors to capitalize on inefficiencies in betting markets.

The rise of such ideas demonstrates how much scientific betting has evolved in recent years. Where there were once solitary gamblers trying their luck in game rooms and casinos, there are now established businesses employing teams of mathematics and statistics Ph.Ds. Strategies are refined over time, powered by vast amounts of data and statistical models. Betting is quantitative, systematic, and on a big scale.

It’s gotten to the point where the top betting syndicates don’t even celebrate their wins. After all, if a profit is unexpected, that suggests it was a lucky wager. And the best bettors don’t want to leave their gambling to chance.