Isaac Newton vs. Las Vegas: how physicists used science to beat roulette

Roulette wheel is a traditional symbol of the system, whose results are completely random. But not all roulettes were created the same.

When Einstein tested his famous impulse to forbid God to play dice, his ban, of course, did not apply to physicists. Scientists are sometimes the victims of the insistent call of sirens, heard in the ringing of coins, luring so many people to the casino. After a long day using the “Monte-Carlo method” (simulation technique, named after the game Mecca in Monaco), some researchers may want to take a break and start a real game.


Simulation "Monte Carlo" allows you to calculate an approximate answer in principle to any task, simulating possible options that obey a certain rule. In the picture, hundreds of simulations together calculate the value of the number π

Einstein's maxim related to his belief that quantum physics is fundamentally deterministic. He assumed that at some level, knowing the initial state of a quantum system with absolute accuracy and all the corresponding interactions, it would be possible to calculate all its future states. However, countless experiments based on the famous John Bell theorem proved the opposite - in quantum measurements there is a fundamental inherent in them an accident, which is impossible to avoid. From the point of view of physics, guessing about the variants of quantum outcomes, one cannot “defeat the casino”.


Even quantum entanglement will not give you anything better than random guesses about what is in the hand of the dealer

Ironically, the results of the dice fallout are more deterministic than the typical quantum measurement. A die roll is a classic process, depending on the mechanistic laws of Newton's motion. Classically, if you accurately record the location, orientation and initial speed of a pair of dice thrown into the air, as well as mark all environmental conditions - air flow, for example - you can predict in advance whether a throw will cause a pair of “snake eyes” to drop sixes or something else between these two options.


After a random throw of two dice, 11 different results may fall out - while the seven falls 1 time out of 6, and a deuce or 12 - 1 time out of 36.

Roulette is another randomness game that can be predicted with enough knowledge of the initial conditions and the forces involved in its work. Obviously, when the roulette wheel is untwisted and the ball is sent in its movement towards it, the ball hit in a certain slot is predetermined. The way the ball and the roulette wheel started moving predetermines their meeting when the ball leaves the track, jumps on the roulette wheel and falls into one of the numbered pockets - rewarding the players who put on this result.


Guests play roulette at the 2016 Guys Choice award ceremony on Spike TV channel

In practice, the game of roulette practically does not give time to apply physics for the successful placement of bets. Moreover, the fact that a small change in the initial conditions, such as the speed or trajectory of the ball, can drastically affect the result, which makes the task of predicting the roulette results extremely difficult. Some casinos prohibit betting after the start of wheel spin. Others, in order to increase the excitement, are allowed to wait a few turns, after which the croupier declares that there are no more bets. There is an unrealistic temptation to hope that a quick glance at a spinning wheel can lead to an exact guess, followed by a favorable placement of chips.


It is believed that Al Hibbs won about $ 12,000 in Nevada casinos during his tour of 1947. He later appeared on the “You Bet Your Life” show [Life as a Bet]

In the late 1940s, two friends from the University of Chicago, graduate mathematician Albert "El" Hibbs and medical student Roy Walford decided to take a break from school and try to beat the casino in the only state where gambling was allowed: in Nevada. He jumped on his motorcycles and went to Reno, where they carefully studied the properties of roulettes to find weak spots in them. Later, they often went to a Las Vegas casino for the same purpose.


Al Hibbs and Roy Walford pose with a roulette wheel, winning an unprecedentedly large amount

Earlier wheels were made more rough, and could have defects. These defects, as students understood, offered the key to successful prediction of results. Studying the mechanical deviations of various machines, they developed predictive models, a carefully calibrated rate system, and were able to win several thousand dollars. They spent most of the winnings buying a boat and going on a world tour.

At the end of the gambling games, Hibbs, who received a diploma from Caltech, returned there as a graduate student in theoretical physics, where he received his doctoral degree under the guidance of Richard Feynman. He worked with Feynman on the textbook " Quantum Mechanics and Path Integrals ". Hibbs and Feynman remained close friends throughout their lives.


Their joint book taught an approach to quantum mechanics through integrals over the trajectories of a whole generation of physics students.

Hibbs and Walford actively shared their methods of playing with casinos. In December 1949, they became the subject of an article in the journal Life. Soon, as a result of their activities, casinos began to upgrade their equipment. The wheels with distortion were replaced with more smoothly working ones. The casinos wanted to make sure that no one could repeat the feat of two scientists.

In January 1959, Groucho Marx invited Hibbs to his popular game show "You Bet Your Life". Millions of viewers heard Hibbs talking about his winnings in a casino and promoting his textbook. Groucho used every opportunity to build jokes based on the fact that Hibbs was both a quantum physicist and a player in a casino.


Albert Hibbs (second from left) on the “You Bet Your Life” show in 1959

Careers Hibbs and Walford have developed perfectly. After graduation, Hibbs settled at NASA's Jet Propulsion Laboratory (JPL), where he became known as the man who announced new missions: he was called the “JPL voice”. In addition, he himself participated in the development of many missions. In particular, he played an important role in the launch of the Explorer 1 satellite, the first American artificial satellite launched into orbit on January 31, 1958, six weeks after the launch of Sputnik in the USSR. He was training for the role of an astronaut for the Apollo mission, but he was not chosen for flights, and then the program was canceled in the early 1970s.


The launch of the satellite "Explorer-1" marked the inclusion of the United States in the space race

Doctor Walford became famous for advertising a low-calorie diet as the key to longevity. He worked for many years at the faculty of the University of California at Los Angeles, and was a member of the team of the mission " Biosphere-2 ", which created a closed ecological system.

In 1955, as a graduate student at the University of California at Los Angeles, Edward Thorpe learned about the exploits of Hibbs and Walford and decided to try to beat the casino on his own . He realized that since the roulettes had no defects anymore, he needed to develop a new strategy. He decided that the key for her would be a small portable computer that is available to a person who watches the rotation of the roulette and the throw of the ball. The computer must be fast enough and powerful enough to be able to calculate their trajectories and make a prediction. The observer, pretending to be a simple onlooker, will broadcast this forecast by radio to another participant, who should also bid.


Ed Thorp was a famous gambling enthusiast - in the photo he poses with the rules and strategy for playing blackjack

Having built a prototype and tested his methods in the late 1950s, Thorp got a job at MIT, where he became friends with the mathematician Claude Shannon . Shannon, known for his contribution to the theory of information due to the unique definition of " information entropy ", became interested in the work of Thorp in connection with a related project that used computational methods to win blackjack. When Thorp told him about his ideas on predicting roulette, Shannon set about creating roulette models in the laboratory and small computers to track them.


Mathematician Claude Shannon, who worked with Thorp on creating roulette models hoping to beat the casino

By 1961, Thorpe and Shannon had designed and tested the world's first portable computer: it was about the size of a pack of cigarettes and fit in the sole of a specially made shoe. Switches under the toes activated the computer when the roulette wheel and ball were started, and information about them was collected. By counting the most likely result, the computer transmitted this value using musical notes through a tiny speaker located in the ear. The wires were hidden to the maximum.

For several years, Thorpe and Shannon, together with their wives, tried several times to apply their technology in Las Vegas. They were faced with the problem that if they only made late bets, they would stand out very much among the players. Therefore, they had to mix the optimal bets made after the wheel started spinning and the movement of the ball could be predicted with random ones placed before the start of rotation. Such a mixture made it difficult to make a profit. Finally, in 1966, Thorpe decided to share information with the world and published these methods.

By that time Thorp had become a professor of mathematics at the University of California, Irvine, where he had worked for many years. He continued to write books and articles in mathematics and the science of gambling.


In almost every random game, there is an optimal strategy for maximizing winnings and minimizing losses, in terms of mathematical statistics.

The next generation of scientific roulette winners - a group of representatives of the counterculture, hippie graduate students from the University of California at Santa Cruz in the 1970s - were even more cunning. The group was led by astrophysicist J. Doin Farmer and Norman Packard statistics. They called themselves the “Rosetta Stone Project”, or simply “the Project” or “ Eudaemonists ” (in honor of the Greek ethical system, Eudemonism, which proclaimed the human desire for happiness as the criterion of morality). Thomas Bass, another team member, documented their antics in the popular eudemonist book.

In an effort to improve the methods of Thorp, Farmer has developed an even more compact computer, located in the shoe, with the most modern processor and convenient switches for toes. To eliminate the wires, the computer sent the results of the predictions by means of vibration right on the foot - it was something like a vibrating alert on modern phones. They managed to secretly use their casino system with a result of 44% of the profits from each dollar delivered. Earnings were divided equally in the group.


The infamous boot-in computer used by eudemonists to win casinos

Farmer and Packard, having finished their studies, became interested in the emerging area of dynamic chaos . Together with two other Santa Cruz graduates, Robert Shaw and James Crutchfield, they founded the Dynamic Systems Team, who studied dynamic systems of chaotic behavior. The group became known as the “chaotic clique” and released many important works.

By the mid-1980s, casinos had upgraded their equipment and banned the use of computers. Although in theory today it would have been more difficult for students to win on the basis of their knowledge of mathematics and physics, the so-called “blackjack team from MIT” in the 1990s developed the extremely successful system described in the book “ Playing the Casino ” [the book was drafted under the title “21 " / Approx. trans. ]

From Hibbs and Walford, through Thorpe and Shannon, to Farmer and Pacard, we see how the interest in winning over the chance led scientists to successful scientific careers. On the roulette of fate, their bets were excellent.