The modern form of roulette seems to have first appeared in Paris in 1796. It became the favored high-stakes game of the rich and the royal, enshrined in Monte Carlo in the nineteenth century, and celebrated in story and song. With its high stakes, splendid settings, and runs of extreme luck, which were sometimes good but more often bad, it was a target for those with systems attempting to overcome the casino’s advantage. These systems were too complex for gamblers to analyze precisely, but they had plausible features that inspired hope.
A favorite was the Labouchère, or cancellation, system. This was used in roulette for bets that paid even money, where you win or lose an amount equal to your bet. Among the even-money bets in roulette are wagers on red or on black, each of which has eighteen chances in thirty-eight of winning. To start the Labouchère, write down a string of numbers, such as 3, 5, and 7. The total of these, 15, is what you try to win. Your first bet is the total of the first and last numbers in the string, 3 + 7, or 10. If you win, cross off the first and last numbers, leaving only 5. Your next bet is 5, and if you win you have reached your goal. If you lose, add 10 to the string so it becomes, 3, 5, 7, 10 and then bet 3 + 10 or 13. In any case, each time you lose you add one number to the string, and each time you win you cross off two numbers. Therefore, you need to win only a little over a third of the time to reach your goal. What can go wrong? Gamblers, trying systems like the Labouchère, were baffled when they never seemed to prevail.
However, using the mathematical theory of probability, it was proven that if all roulette numbers were equally likely to come up, and they appeared in random order, it was impossible for any betting system to succeed. Despite this, hope flared briefly at the end of the nineteenth century when the great statistician Karl Pearson (1857–1936) discovered that the roulette numbers being reported daily in a French newspaper showed exploitable patterns. The mystery was resolved when it was discovered that rather than spend hours watching the wheels, the people recording the numbers simply made them up at the end of each day. The statistical patterns Pearson detected simply reflected the failure of the reporters to invent perfectly random numbers.
If betting systems don’t work, what about defective wheels where, in the long run, some numbers will come up more than others? In 1947, two graduate students at the University of Chicago, Albert Hibbs (1924–2003) and Roy Walford (1924–2004), found a roulette wheel in Reno that seemed to favor the number 9. They increased an initial stake of $200 to $12,000. The next year they found a wheel at the Palace Club in Las Vegas on which they made $30,000. They took a year off and sailed the Caribbean, then went on to distinguished careers in science. Among many accomplishments, Hibbs became director of space science for Caltech’s Jet Propulsion Laboratory, and Walford became a UCLA medical researcher who showed that caloric restriction in mice could more than double their maximum life span. Hibbs later wrote, “I wanted to conquer space, and my roommate, Roy Walford, decided that he would conquer death.”
Feynman must have known about biased wheels when he told me there was no way to beat the game, because Hibbs got his PhD in physics under Feynman at Caltech the previous year. In any case, biased wheels at big casinos were likely a thing of the past, as gambling houses took better care of their equipment.
So this was the setting when Claude Shannon and I, in September 1960, set to work to build a computer to beat roulette. So far as we knew, everyone else thought physical prediction was impossible.
As it was the last year of my two-year appointment at MIT, we had to complete the task in nine months. We spent twenty hours a week at the Shannons’ three-story wooden house. Dating from 1858, it was sited on one of the Mystic Lakes, a few miles from Cambridge. The basement was a gadgeteer’s paradise, with perhaps $100,000 worth of electronic, electrical, and mechanical items. There were thousands of mechanical and electrical components—motors, transistors, switches, pulleys, gears, condensers, transformers, and on and on. As someone who had spent much of his boyhood building and experimenting in electronics, physics, and chemistry, I was now happily working with the ultimate gadgeteer.
We purchased a reconditioned regulation roulette wheel from a company in Reno for $1,500. From the labs at MIT we borrowed a strobe light, and a large clock with a second hand that made one revolution per second, the latter recapitulating the role the stopwatch had in my earlier movie experiments. The dial was divided into hundredths of a second and we could interpolate still-finer time divisions. We set up shop in the billiard room, where a massive old slate table made a solid base on which to mount the wheel.
Our wheel was typical, carefully machined with an elegant design and beauty that added to the appeal of the game. It consisted of a large stationary piece, or stator, with a circular track around the top, where the croupier starts each play of the game by launching a small white ball. As the ball orbits, it gradually slows until finally it falls down the sloped conelike inside of the stator and crosses onto a circular centerpiece, or rotor, with numbered pockets that the croupier previously set spinning in a direction opposite to that in which he spun the ball.
The motion of the ball is complicated by having several different phases, making it so daunting as to discourage analysis. We followed my original plan, which was to divide the motion of ball and rotor into stages and analyze each separately.
We began by predicting when and where the orbiting ball would leave the outer track. We did this by measuring the time it took for the ball to make one revolution. If the time was short, the ball was moving fast and would go relatively far. If the time was longer, the ball was traveling slower and would soon fall from the track.
To measure the speed of the ball, we hit a microswitch as the ball passed a reference mark on the stator. This started the clock. When the ball passed the same spot the second time we hit the switch again, stopping the clock, which then showed how long it took for the ball to go around once.
Simultaneous with starting and stopping the clock, the switch triggered the flash of a strobe whose very short pulses of light were like those in a disco. We dimmed the lights in the room so the strobe flashes “stopped” the ball each time the switch was hit, allowing us to see how much the ball was ahead or behind the reference mark. This showed us how much we were off in hitting the timing switch. From this we corrected the times recorded by the clock for one revolution of the ball, making the data more accurate. We also got from this a numerical measure of our errors in hitting the switch as well as direct visual feedback. As a result we learned to become much better at timing. With practice, our errors fell from values of about 0.03 second to about 0.01 second. We were able to retain this level of accuracy later when we concealed everything for casino play, having trained our big toes to operate switches hidden in our shoes.
We found that we could predict, with a high degree of accuracy, when and where the ball would slow enough to fall from the circular track. So far so good. Our next step was to determine the time the ball would take and the distance it would travel as it spiraled down the conical inside of the stator to reach the spinning rotor. Most wheels had vanes or deflectors in this region—typically eight—that the ball would frequently hit. The effect was to randomize the ball’s behavior. Its path could be shortened or lengthened, depending on whether and how it hit one of these deflectors. We found that the uncertainty this introduced into our prediction was too small to ruin our advantage. The deflectors also gave us a handy choice of reference points for timing the ball and rotor.
Finally, after the ball crossed onto the moving rotor, it would bounce around among the individual numbered pockets, introducing yet another uncertainty into our forecast.
The total prediction error was the sum of many effects, including our imperfect timing, the spattering of the ball on the rotor pocket dividers (frets), the deflection of the ball by metal obstacles as it spiraled down the stator, and the possible tilt of the wheel. Assuming the total error was approximately normally distributed (the Gaussian or bell-shaped curve), we needed the standard deviation (a measure of uncertainty) for the error of prediction around the actual outcome to be sixteen pockets (0.42 revolution) or less to get an edge. We achieved the tighter estimate of ten pockets, or 0.26 revolution. This gave us the enormous average profit of 44 percent of the amount we bet on the forecast number. If we spread our bet over the two closest numbers on each side, for a total of five numbers in all, we cut risk and still had a 43 percent advantage.
Using physics to win at roulette brings to mind the bizarre game of Russian roulette. You cannot win, but physics may help you survive. The name appears to have originated in a 1937 story by Georges Surdez:
“Did you ever hear of Russian Roulette?” […] With the Russian army in Romania, around 1917, some officer would suddenly pull out his revolver, put a single cartridge in the cylinder, spin the cylinder, snap it back in place, put it to his head and pull the trigger…
The spinning of the revolver’s cylinder is reminiscent of the roulette wheel’s whirling rotor. With six chambers, only one of which is loaded, the chance of firing the cartridge would seem to be one in six. But for a properly lubricated and maintained weapon held upright with the cylinder parallel to the ground, gravity and the weight of the cartridge will cause the full chamber to tend to end up near the bottom, provided the cylinder is allowed to stop on its own. If the cylinder is then relatched, the player has shifted the odds in his (women are too smart to play) favor. The effect of gravity on the final resting position of an unevenly weighted cylinder varies, depending on the orientation of the gun. My younger daughter, an assistant deputy district attorney for more than two decades, tells me that modern forensic scientists are aware of this.
Shannon, with his treasury of intriguing information and ingenious ideas, was a joy to work with. Discussing our need for secrecy, he mentioned that social network theorists studying the spread of rumors and secrets claimed that if you pick two people at random in, say, the United States, then they are usually connected by a chain of three or fewer acquaintances or “three degrees of separation.” An obvious way to test this when you meet strangers is to ask what famous people they know. It is likely that a famous person they know shares an acquaintance with a famous person you know. Then the steps are (1) you to your famous person, (2) your famous person to their famous person, and (3) their famous person to them. The two famous people connecting you give “two degrees of separation.”
As is my lifelong habit, I tested this claim, often with remarkable results. Once on a train from Manhattan to Princeton, New Jersey, I noticed that the pleasant, well-dressed, motherly-looking lady sitting beside me seemed agitated. She didn’t understand English, French, or Spanish but she responded to my elementary German, telling me her problem was knowing when to get off in Philadelphia. After I had helped her, I learned she was a Hungarian economic official from Budapest on her way to a meeting. I decided to play my “degrees of separation” game.
“Do you know anyone in Budapest named Sinetar?” I asked.
“Of course. They are a famous family,” she replied. “There’s Miklos, the film producer, as well as an engineer, and a psychologist.”
“Well,” I said, “they are relatives of my wife.”
Me, to Vivian, to a Budapest Sinetar, to my economist seatmate. Two degrees of separation. So far, I’ve never needed more than three to connect with a stranger.
The concept entered popular culture as “six degrees of separation” after John Guare’s 1990 play of that name. The notion of degrees of separation was well known as early as 1969 among mathematicians as the Erdös (ERR-dosh) number, linking them via other mathematicians to the prolific and peripatetic Hungarian mathematician Paul Erdös, using the relation “coauthored a paper with.” If you coauthored a paper with Erdös your Erdös number is one. If your number isn’t one but you coauthored with someone who had Erdös number one, then your number is two, and so forth.
The few steps that connect strangers explain how rumors spread rapidly and widely. If you have a good investment idea, you might want to keep it secret. In 1998 a New York Times Science Times article said that mathematicians had discovered how networks might “make a big world small” using the equivalent of the famous person idea, and attributed the concept of six degrees of separation to a sociologist in 1967. Yet all this was known to Claude Shannon in 1960.
He loved to build ingenious gadgets. One of these would flip a coin end over end a specified number of revolutions and have it land—at his choice—either heads or tails. He also ran a cable from his workshop (the “toy room”) to his kitchen. When Claude pulled on the cable, a finger, attached to it and set up in the kitchen, would silently and jokingly summon his wife, Betty.
During our work breaks, Claude taught me to juggle three balls, which he did while riding a unicycle. He also had a steel cable tied between two tree stumps and walked along it, encouraging me to learn with the aid of a balance bar. He could do any two of the three tricks together: juggle three balls, ride the unicycle, and balance on the tightrope, and his goal was to be able to do all three at once. One day I noticed two huge pieces of Styrofoam that looked as if they could be worn like snowshoes. Claude said they were water shoes that enabled him to “walketh upon the water,” in this case the Mystic Lake in front of his house. The neighbors had been astounded to see Claude moving upright above the surface of the lake. I tried the water shoes but found it difficult to keep from toppling over.
We got along so well because, from an early age, science was play for both of us. Tinkering and building things was part of the fun, as was letting our curiosity range freely.
In American roulette, the wheel has thirty-eight pockets for the ball to fall into. Thirty-six of these, numbered from 1 to 36, are either red or black, with eighteen of each. The green pockets, 0 and 00 (zero and double-zero), are opposite each other on the rotor and thus split the other thirty-six into two groups of eighteen. A winning bet on a single number pays 35:1, meaning you get back your stake plus a profit of thirty-five times the amount you bet. If there were no 0 or 00, this payoff would make the game even, because on average, for each $1 bet, the player wins $35 one time in thirty-six spins and loses $1 thirty-five times in thirty-six, for no net gain or loss. However, with the addition of 0 and 00, on average the bettor who has no ability to predict will win $35 one time in thirty-eight and lose $1 thirty-seven times in thirty-eight, for a net loss of $2 per thirty-eight bets. The casino edge for him on single-number bets then is $2 ÷ $38 or 5.26 percent. European roulette is typically more generous, having just the single zero.
For bet sizing in favorable games, Shannon suggested I look at a 1956 paper by John Kelly. I adapted it as the guide for bets in blackjack and roulette, and later in other favorable games, sports betting, and the stock market. For roulette, the Kelly strategy showed that it was worth trading a little expected gain for a large reduction in risk by betting on several (neighboring) numbers, rather than a single number.
The croupier begins play by spinning the rotor. With our roulette computer, we then time one revolution of the rotor, after which our device knows where it is in the future, until the time comes when the croupier once again gives it a push. Our computer then sends out a repeating sequence of eight increasing pitched numerical tones, do, re, mi…Think of it as a piano scale: (middle) C, D, E…C (next octave) and repeat. We chose to time the ball when it had between three and four revolutions remaining. The closer to the end we made our measurements, the more accurate our predictions, and three revolutions to go still gave us enough time to place our bets. The computer’s timing switch was hit when the orbiting ball first passed a reference mark on the wheel. When this happened, the tone sequence shifted and played faster. When the timing switch clocked the ball as it passed the reference mark again, after having made one revolution, the tones stopped. The last tone heard named the group of numbers on which to bet. If the person doing the timing misjudged the number of ball revolutions that were left, the tones did not stop and we placed no bets, except for camouflage. When the prediction was sent, it was simultaneous with the last input. The compute time was zero!
Claude and I were doing this work while I went to Nevada with Manny and Eddie to test my blackjack system, which gave me the opportunity to check roulette wheels and confirm that they behaved like our lab wheel. I saw that many were tilted, which we had already discovered could further improve prediction because it tended to limit the zones of the track from which the ball could fall. I reported to Claude that half-chip and even one-chip tilts were common. In our lab we had experimented by putting a coin half the thickness of a casino chip (a “half-chip tilt”) under one of the three feet of the wheel and found that this amount of tilt gave us a nice boost in advantage.
Months of experiments with a wide range of designs led us to a final version of the system. We split our equipment into parts, requiring a team of two. One of us wore the computer, which had twelve transistors and was the size of a pack of cigarettes. Data was input with switches hidden in the wearer’s shoes and operated by his big toes. The computer’s forecast was transmitted by radio, using a modification of the inexpensive, widely available equipment ordinarily used to remotely control model airplanes. The other person, the bettor, would wear a radio receiver, which played the musical tones telling him on which group of numbers to bet. We two confederates would act like strangers.
The person placing the bets heard musical output through a tiny loudspeaker pushed into one ear canal and connected by very thin wires to the radio receiver, which was concealed under his clothing. So the wires wouldn’t be noticed, we stuck them on with transparent spirit gum and painted them to match the wearer’s skin and hair. The fragile copper wires, only the diameter of a hair, broke constantly. Claude suggested that we find ultrathin steel wires to replace the copper. After an hour of telephoning we located a supplier in Worcester, Massachusetts, that had what we needed.
We worked feverishly through April and May 1961 to complete the computer because I would be leaving MIT the following month for Los Angeles with Vivian and our not-quite-two-year-old daughter, Raun, and then on to New Mexico State University in the fall. As we hadn’t quite finished when Vivian, Raun, and I left, a couple of weeks later I took a red-eye back from Los Angeles to Boston, showing up on the Shannons’ country doorstep about 7 A.M. on a sunny summer morning. I lived there for three weeks while Claude and I worked furiously to finish the project. Finally, after more tuning and testing, we were ready. The wearable version of the computer was operational at the end of June 1961.
Returning to Los Angeles, I told Vivian that the roulette computer was ready, and Claude and I wanted to test it. Vivian and I met Betty and Claude in Las Vegas in August. After we settled in adjoining hotel rooms with our equipment, we headed out to locate suitable wheels. Our machine could beat all the wheels we saw, so we chose one for the next day where we liked the casino ambience. Then it was on to dinner and plans for the morrow.
The next morning we wired ourselves up. Claude wore the computer and the radio transmitter and would use his big toes to operate switches hidden in his shoes. I wore the radio receiver with the new steel wires going up my neck to the speaker in my right ear canal. As I stood ready to leave for the casino, Claude cocked his head and with an elfish smile asked, “What makes you tick?”
Claude was jokingly referring to the strange sounds (actually these were musical tones) he would be sending from the computer he was wearing to my ear canal, once we went into action at the roulette table. As I look back now from the future, seeing myself wired up with our equipment, I stop that moment in time and I think about a deeper meaning to the question of what makes me tick.
I was at a point then in life when I could choose between two very different futures. I could roam the world as a professional gambler winning millions per year. Switching between blackjack and roulette, I could spend some of the winnings as perfect camouflage by also betting on other games offering a small casino edge, like craps or baccarat.
My other choice was to continue my academic life. The path I would take was determined by my character, namely, What makes me tick? As the Greek philosopher Heraclitus said, “Character is destiny.” I unfreeze time and watch us head for the roulette tables.
The four of us arrive in the casino, with Vivian and Betty Shannon strolling and chatting, while Claude and I are strangers to them and each other. Lacking my casino experience, the others are nervous but fortunately don’t show it. Claude stands by the wheel and times the ball and rotor; as misdirection for what he is really doing, he writes down the winning number after each roll of the ball, looking like just another doomed-to-fail system player. Meanwhile, I take my seat at the far end of the layout, some distance from both Claude and the wheel.
Claude waits for the croupier to give the rotor a push to keep it spinning. As the green zero on the rotor goes by a reference point on the stator, which Claude has chosen to be one of the ball-deflecting vanes, his big toe hits one of the silent mercury switches hidden in his shoe. Contact. The soundless equivalent of a click! When the green 0 comes around again, click. The elapsed time is the duration of one rotation. After the second click, an eight-tone musical scale—do, re, mi, and so on—begins to play in my ear, repeating each time the rotor turns once. Now the computer knows not only how fast the rotor is turning but also where it is in relation to the stator. The rotor will gradually slow down even though it is suspended on a very low-friction jeweled bearing. The computer also corrects for that. Claude will have to retime the rotor every few minutes when the croupier gives it another push to offset its gradual loss of speed.
I get ready to bet. The croupier launches the ball. As it speeds around the track inside the top of the stator, Claude watches each time it passes the reference point. When he thinks it has more than three but less than four revolutions left, he clicks with the other big toe. The pace of the repeating musical scale speeds up. Finally, as the ball completes the next revolution, Claude’s toe hits the switch again. Click! The musical tones stop. The last tone I hear tells me the group of numbers on which to bet. As it is only a test, I bet 10-cent chips. Within a few spins, the computer works its magic, turning a few dimes into a heap as yet another bet scores. I bet each time on a group of five numbers that are adjacent on the rotor. This is common in Europe, where the French call a group like this a voisinage, or “neighborhood.”
We have divided the numbers on the wheel into eight such groups of five, with 0 and 00 appearing twice, as our groups included forty numbers and the wheel has only thirty-eight. We’ve called these groups of five “octants.” The average player who bets $1 on each of five numbers will win about five times in thirty-eight or just over one-eighth of the time and lose all five bets otherwise, with an overall rate of loss that turns out to be $2 for each $38 worth of bets, a 5.3 percent disadvantage. However, using our computer, our bet on five numbers won a fifth of the time, giving us a 44 percent edge.
But we had issues. Well into one winning session, a lady next to me looked over in horror. Knowing I should leave, but not why, I raced to the restroom and there in the mirror saw the speaker peeking out from my ear canal like an alien insect. More seriously, though we frequently turned small piles of dime chips into large ones, we had a problem that prevented us on this trip from moving to large-scale betting. This had to do with the wires to the ear speaker. Even though they were steel, they were so fine that they broke frequently, leading to long interruptions while we returned to our rooms and went through the tedious process of doing the repairs and then rewiring me.
But when it was up and running, the computer was a success. We knew we could solve the wire problem by using larger wires and growing hair to cover both our ears and the wire running up our neck. We also considered persuading our reluctant wives to “wire up,” concealing everything under their fashionable longer hair.
While I was betting, no one watching had any idea that what Claude and I were doing was in any way unusual, nor did they realize the connections among the four of us. Even so, I realized that if the casinos figured out what we were doing, they had an easy way to stop us. All they had to do was say “No more bets” before the ball was spun, instead of waiting as they customarily did until the ball had almost completed its rotations around its track. To prevent them from catching on and doing this, we would need to put on an act to divert attention from our winning. I already knew how much effort this would take, based on my experience with blackjack. Neither I nor Vivian, Claude, and Betty would want to go through the rehearsed theatrics, disguises, and misdirection needed, and with all the blackjack publicity I was becoming too conspicuous to go unrecognized for long. It also wasn’t the way any of the four of us wanted to spend what would inevitably involve a very large amount of our time. So, with some ambivalence, we put the project aside. I have always thought it was a good decision.
The MIT Media Lab lists our device as the first of what would later be called wearable computers, namely, computers that are worn on the body as part of their function. In late 1961 I built the second wearable computer, a knockoff to predict the wheel of fortune or money wheel. As in the roulette computer, my device used the toe-operated switch for input, the speaker for output, and just a single unijunction transistor; it required only one person. Matchbox-sized, it worked well in the casinos, but the game had too little action to conceal the spectacular consequences of my late bets. Several times when I placed bets on 40:1 as the wheel was spinning, the croupier would give the wheel an extra push.
Finally in 1966, I publicly announced our roulette system because it was clear by then that we weren’t going to exploit it. I published the details later. When a mathematician from UC–Santa Cruz phoned me, I explained the method to him. UCSC was where the Eudaemonic Pie group of physicists would use the more advanced technology of the next decade to build their own roulette computer. Like us they found a 44 percent advantage and, like us, were frustrated by hardware problems. Later, groups using roulette computers reportedly won large amounts.
Shannon and I had also discussed building a wearable blackjack computer. Using the program I had used to analyze blackjack, such a computer could count the cards and play a perfect game, winning at up to double the rate of the best human card counters. This was an early instance, perhaps the first, of a computer that could outplay any human at a game. Later, computers went on to play perfect checkers and to beat the world’s best at chess, Go, and Jeopardy. Subsequently, others built and marketed wearable blackjack computers. At the time, Nevada law, in particular the statutes on cheating, did not forbid their use. However, as hidden computers in blackjack and roulette increasingly cut into casino profits, the Nevada devices law was passed as an emergency measure on May 30, 1985. It banned use or possession of any device to predict outcomes, analyze probabilities of occurrence, analyze strategy for playing or betting, or keep track of cards played. The penalty: fines and imprisonment. This broadly drawn legislation even seems to outlaw the palm-sized strategy cards that are part of every copy of Beat the Dealer. When, in 2009, an entrepreneur wrote a popular iPhone application to count cards and recommend plays for blackjack, casinos reminded users that it was a crime to do so at the tables.
Claude and I corresponded at intervals for a few years, initially about roulette, until it became more and more clear that we didn’t want to take it further. The last letter I remember writing was in late 1965 or early 1966, where I recalled our discussions about the stock market triggered by my seeing on his blackboard the figure 211, which equals 2048, representing the amount $1 becomes if it is doubled eleven successive times, an investing goal he was contemplating. I told him in my letter that I had found an extraordinary method for investing in a small niche in the stock market, which I thought could make 30 percent per year. Given time, I could surpass the 211 figure. He never said what he thought of this hubris. And hubris it was, as the actual rate of profit would turn out to be closer to 20 percent.
We met for the last time in 1968, at a math meeting in San Francisco. His poignant last words to me were, “Let’s get together again before we’re both six feet under.”
After Claude’s death in 2001, Betty donated many of his papers and devices to the MIT museum, including the roulette computer. It was lent by the museum to the Heinz Nixdorf Computer Museum in Paderborn, Germany, for an exhibit in the spring of 2008 where thirty-five thousand people viewed it in the first eight weeks.
When Claude walked up to the Las Vegas roulette wheel in August 1961, he was using something no one but the four of us had ever seen before. This was the world’s first wearable computer. To me, a wearable computer is just what the name indicates: a computer that is worn by a person in order to fulfill its intended function. Though our device had little impact on later developments, wearable computers, such as my Apple Watch, are everywhere today.
After blackjack and roulette, I wondered: Could other casino games be beaten?