Isaac Newton Vs. Las Vegas: How Physicists Used Science To Beat The Odds At Roulette
In every casino game, the house has an edge. Thanks to some very intrepid scientists, the rules had to be changed.
“I don’t always bet the same way I talk. Good advice is one thing, but smart gambling is quite another.” -Hunter S. Thompson
While Einstein famously attempted to forbid God from playing dice, his ordinance certainly did not apply to physicists. Indeed, scientists sometimes fall prey to the jangling siren song of clinking cash that lures so many people into casinos. After a long day applying the “Monte Carlo Method” (a simulation technique named after the Monaco gambling mecca), for example, some researchers might want to take a break and try their hands at the real thing.
Einstein’s dictum applied to his belief that quantum physics is fundamentally deterministic. On some level, he surmised, knowing the initial state of a quantum system with absolute precision, as well as all of its relevant forces, would enable calculation of all of its future states. On the contrary, untold experiments, drawing on the famous theorem of John Bell, have proven that quantum measurements possess a fundamental, built-in randomness that cannot be avoided. From a physical perspective, there’s no way to “beat the dealer” in guessing quantum outcomes.
Ironically, a dice roll itself is more deterministic than the typical quantum measurement. That is because tossing dice is largely a classical process, governed by Newton’s mechanistic laws of motion. Classically, if you could precisely record the position, orientation, and initial velocity of a pair of dice thrown in the air, and map out the environmental conditions acting on it such as air currents, you could tell before it hit the table if a particular roll would produce “snake eyes,” (a pair of ones) “double sixes,” or anything in between.
Roulette is another game of chance that is absolutely predictable, given sufficient knowledge of the initial conditions and forces involved. Surely, the moment that a roulette wheel is spun and a ball is set into motion along a track in the opposite direction, the fate of which slot the ball will land in is sealed. How the ball and wheel begin their trajectories clearly governs their rendezvous with destiny once the former leaves the track, bounces around, and ends up on one of the latter’s numbered spokes — rewarding those gamblers who bet on that outcome.
In practice, though, the game of roulette allows virtually no time to apply physics savvy for successful betting. Moreover, the very fact that a tiny variation in the initial conditions, such as the speed or trajectory of the ball, can dramatically alter the outcome, making predicting roulette outcomes a daunting task, in a practical sense. Some casinos forbid bets after the wheel starts spinning. Others — perhaps to build excitement — permit wagers for just a few rotations before the dealer calls no more bets. Tantalizingly, but not realistically, one might hope that a quick glance at the spinning rotor might spur a solid guess and an auspicious placement of chips.
In the late 1940s, two friends at the University of Chicago, mathematics graduate student Albert “Al” Hibbs and medical student Roy Walford, decided to take a break from their studies and attempt the beat the odds at casinos in the only state where gambling was then legal: Nevada. Hopping on their motorcycles, they scooted down to Reno, where they carefully studied the properties of roulette wheels to look for weaknesses to exploit. Later, they also frequented casinos in Las Vegas to do the same.
Early wheels were cruder than today’s and sometimes had defects. Such flaws, the students realized, offered the key to successful prediction. By studying the mechanical idiosyncrasies of various machines, they developed predictive models, carefully placed bets, and manage to win thousands of dollars. They used much of their earnings to buy a boat and sail around the world.
Once his gambling ventures were finished, Hibbs, who had received his undergraduate degree from Caltech, returned there as a graduate student in theoretical physics, where he completed his PhD work under Richard Feynman. He collaborated with Feynman on a co-authored textbook, Quantum Mechanics and Path Integrals. Hibbs and Feynman would remain close friends for life.
Hibbs and Walford were very open about their casino-beating methods. In December 1949, they were featured prominently in a Life Magazine story. Soon, and perhaps as a result, casinos began upgrading their equipment. Biased wheels were replaced with ones that ran far more smoothly. They wanted to make sure no one could repeat the two young scientists’ exploits.
In January 1959, Groucho Marx invited Hibbs on his popular television quiz show, “You Bet Your Life.” Millions of television viewers heard Hibbs speak about his casino-beating feats and plug his textbook. Groucho, with typical flair, wrung all the comic lines he could out of Hibbs’ dual role as quantum physicist and gambler.
Both Hibbs and Walford went on to illustrious careers. After graduate school, Hibbs moved on to a position at NASA’s Jet Propulsion Laboratory (JPL) where he became famous as its mission announcer: “the voice of JPL.” Behind the scenes, he was involved in many missions. Notably, he played a major role in the launch of Explorer 1, the first American satellite to orbit the earth, on January 31, 1958, six weeks after Sputnik was launched by the Soviets. He also trained to be an astronaut in the Apollo mission, but was never selected to fly before the program was cancelled in the early 1970s.
Walford, as a physician, became known for his advocacy of a severely calorie-restricted diet as the key to longevity. He served for many years on the faculty of UCLA, and was also crew-member in the Biosphere II mission to create a sustainable, livable environment disconnected from Earth’s resources.
In 1955, while a second-year physics graduate student at UCLA, Edward Thorp learned about Hibbs and Walford’s exploits and decided to try to beat the casinos himself. Given that roulette wheels no longer had discernible defects, he realized he would need to develop a new strategy. The key, he decided, would be a small computer, worn by someone observing how the wheel was spun and the ball was launched, that was fast and powerful enough to calculate their trajectories and make a prediction. Pretending just to be a casual onlooker, that observer would transmit the forecast by radio to a second participant charged with placing bets.
After building a prototype, and testing his methods in the late 1950s, Thorp took on a position at MIT where he became acquainted with mathematician Claude Shannon. Shannon, who was widely known for his contributions to information theory through his unique definition of “information entropy,” became interested in Thorp’s work through a related project on using computational methods to master the card game “blackjack.” When Thorp told him about his roulette prediction ideas, Shannon went right to work on constructing roulette wheel models and tiny computers to track them.
By 1961, Thorp and Shannon had built and tested the world’s first wearable computer: it was merely the size of a cigarette pack and able to fit into the bottom of a specially-designed shoe. Toe switches would activate the computer once the wheel and ball were set into motion, collecting timing data for both. Once the computer calculated the most likely result, it would transmit that value as musical tones to a tiny speaker lodged in an earpiece. The wires were camouflaged as much as possible.
For several years, on various occasions, Thorp and Shannon, along with their wives, tried out their methods in Las Vegas. They ran into the snag that they didn’t want to be too obvious in always placing late bets. Therefore, they had to mix their optimal bets, made after the wheel had revolved a few times and could be tracked, with random ones, placed before the spinning began. That mixture made it hard for them to profit. Finally, in 1966, Thorp decided to let the cat out of the bag and publish their methods.
By then, Thorp had became a professor of mathematics at U.C. Irvine, a position he held for many years. He continued to write books and articles about the mathematics and science of gambling.
The next generation of scientific roulette masters — a group of hip, counterculture graduate students studying at UC Santa Cruz in the 1970s — were even savvier. Led by astrophysics major J. Doyne Farmer and statistics major Norman Packard (a recent graduate of Reed College), they called themselves “Project Rosetta Stone,” alternatively known as “The Project” and “The Eudaemons” (after a Greek ethical system based on listening to the “good voice” inside your head, known as “eudaimonism.”). Thomas Bass, another group member, would document their antics in a popular book called The Eudaemonic Pie.
Keen on upgrading Thorp’s methods, Farmer designed an even more compact shoe computer, with a state-of-the-art processor, and easy to operate toe switches. To eliminate the need for extra wiring, the computer would send its prediction as a direct signal to part of the foot, a bit like the vibrating mechanisms of modern phones. They managed to use their system discretely at casinos, estimating a 44% profit on each dollar bet. All earnings were pooled by the group.
Once Farmer and Packard completed their degrees they became attracted to the nascent field of chaotic dynamics. Along with two other Santa Cruz students — Robert Shaw and Californian James Crutchfield — they founded the “Dynamical Systems Collective,” to study dynamical systems that behaved chaotically. The group soon became known as the “Chaos Cabal,” and produced a number of important papers.
By the mid-1980s, casinos upgraded their equipment once more and prohibited the use of computers. Although, in theory, it would now be harder for students today to gain an advantage through their knowledge of mathematics and physics, the so-called MIT Blackjack Team implemented a system to great success in the 1990s, as detailed in the book, Bringing Down The House.
From Hibbs and Walford, to Thorp and Shannon, and finally to Farmer and Packard, we see how an interest in beating the odds would lead to successful scientific careers. On the roulette wheel of life, their gambles paid off splendidly.
Paul Halpern is the author of fifteen popular science books, including The Quantum Labyrinth: How Richard Feynman and John Wheeler Revolutionized Time and Reality.