Roulette as we know it today seems to have first appeared in Paris in 1796. It was enshrined in Monte Carlo in the nineteenth century and celebrated in story and song as the preferred high-stakes game of the rich and royal. It was a target for those with systems attempting to overcome the casino's advantage because of its high stakes, stunning environments, and runs of extreme luck that were often successful but most often bad. These schemes were too complicated for gamblers to fully comprehend, but they did have plausible characteristics that gave them hope.
The Labouchère, or cancellation, method was a common option. This was used in roulette for bets that paid even money, where you won or lost the same amount you bet. Even-money bets in roulette include bets on red or black, which both have eighteen chances in thirty-eight of winning. Start the Labouchère by writing down a series of numbers, such as 3, 5, and 7. The number of these, 15, is what you are attempting to win. Your first wager is the sum of the first and last numbers in the string, which is 3 + 7, or 10. If you win, delete the first and last numbers, leaving only the number 5. Your next bet is $5, and if you win, you've met your target. If you lose, add 10 to the string, making it 3, 5, 7, 10, and then wager 3 + 10 or 13. In any case, each time you lose, one number is added to the string, and each time you win, two numbers are removed. As a result, you just need to win slightly more than one-third of the time to achieve your target. What could possibly go wrong? When gamblers tried systems like the Labouchère, they were perplexed because they never seemed to win.
However, using probability theory, it was shown that if all roulette numbers were equally likely to appear and appeared in random order, no betting scheme could succeed.
In September 1960, Claude Shannon and Edward O. Thorp started work on a machine to beat roulette. Everything else, as far as we understood, believed physical prediction was impossible.
We had nine months to complete the computer since it was the last year of Edward's two-year appointment at MIT. We worked twenty hours a week at the Shannons' three-story wooden home. It was built in 1858 on one of the Mystic Lakes, a few miles from Cambridge. The basement was a gadgeteer's dream, with items worth $100,000 or more in electronic, electrical, and mechanical components. Thousands of mechanical and electrical components were there, including motors, transistors, switches, pulleys, gears, condensers, transformers, and so on. I was now happily working with the ultimate gadgeteer, someone who had spent most of his childhood designing and playing in electronics, physics, and chemistry.
We paid $1,500 for a reconditioned regulation roulette wheel from a company in Reno. We borrowed a strobe light from MIT's laboratories, as well as a big clock with a second hand that rotated at one revolution per second, the latter mimicking the position of the stopwatch in my previous movie experiments. We could interpolate even finer time divisions because the dial was divided into hundredths of a second. We set up shop in the billiard room, where a huge old slate table provided a sturdy foundation for mounting the wheel. Our wheel was traditional, meticulously machined with an elegant style and elegance that added to the game's charm. It was made up of a large stationary piece, or stator, with a circular track around the top, where the croupier started each game play by launching a small white ball. The ball progressively slows as it orbits until it eventually falls down the sloped conelike inside of the stator and crosses onto a circular centerpiece, or rotor, with numbered pockets that the croupier had previously set spinning in the opposite direction that he spun the ball. The ball's motion is complicated by the fact that it goes through many stages, making analysis difficult. We stuck to my original idea of breaking down the motion of the ball and rotor into phases and analyzing each separately. We started by forecasting when and where the orbiting ball will depart from the outer track. We did this by timing how long it took the ball to complete one revolution. If the time was minimal, the ball would travel quickly and go a long way. If the time was longer, the ball would move slower and eventually fall off the track.
We used a microswitch to calculate the ball's speed as it passed a reference mark on the stator. This set the clock in motion. We hit the switch again as the ball reached the same spot the second time, stopping the clock, which then displayed how long it took for the ball to go around more.
The switch activated the flash of a strobe, whose very brief bursts of light were similar to those seen in a nightclub, at the same time as it started and stopped the clock. We dimmed the lights in the room so that when the switch was pressed, the strobe flashes “stopped” the ball, allowing us to see how far ahead or behind the reference mark it was. This revealed how far off we were on the timing turn. We were able to improve the accuracy of the data by correcting the times reported by the clock for one revolution of the ball. This provided us with a numerical measure of our switch-hitting errors as well as direct visual feedback. As a result, we improved our timing significantly. With practice, we were able to reduce our errors from 0.03 seconds to 0.01 seconds. After training our big toes to operate switches hidden in our shoes, we were able to preserve this degree of precision later when we concealed everything for casino play.
We discovered that we could accurately predict when and where the ball would slow enough to fall from the circular track. So far, all has gone well. The next move was to measure how long the ball would take to spiral down the conical inside of the stator to meet the spinning rotor, as well as how far it would fly. Most wheels had eight vanes or deflectors in this area, which the ball would frequently reach. The effect was to make the ball's conduct unpredictable. Depending on whether and how it collided with one of these deflectors, its course could be shortened or lengthened. We discovered that the amount of uncertainty this put into our prediction was insignificant enough to negate our benefit. The deflectors also provided us with a number of convenient reference points for timing the ball and rotor.
Finally, the ball will bounce around among the individual numbered pockets after crossing onto the moving rotor, adding yet another element of uncertainty to our forecast.
The overall prediction error was the result of a variety of factors, including our sloppy timing, the ball spattering on the rotor pocket dividers (frets), the ball being deflected by metal obstacles as it spiraled down the stator, and the wheel's potential tilt. To gain an advantage, we required 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, assuming the total error was roughly normally distributed (the Gaussian or bell-shaped curve). The tighter estimate of ten pockets, or 0.26 revolution, was achieved. This resulted in a massive average profit of 44% of the sum bet on the forecast number. We could minimize risk by betting on the two closest numbers on each side, for a total of five numbers, and still have a 43 percent advantage.
The game is started by the croupier spinning the rotor. We then time one revolution of the rotor with our roulette machine, after which our system knows where it is in the future before the croupier gives it another push. Our machine then emits a series of eight increasing-pitched numerical tones, do, re, mi... Consider it a piano scale: (middle) C, D, E...C (next octave) and so on. We decided to time the ball while it was still rotating between three and four times. The closer we got to the end, the more correct our forecasts were, and three revolutions left gave us plenty of time to place our bets. When the orbiting ball first reached a reference mark on the wheel, the computer's timing switch was activated. The tone sequence changed and became quicker as a result of this. The tones came to a halt when the timing switch clocked the ball when it crossed the reference mark for the second time after one revolution. The last tone defined the group of numbers to bet on. The tones did not stop if the person doing the timing miscalculated the number of ball revolutions left, and we made no bets except for camouflage. The prediction was sent at the same time as the previous input. The computation time was zero!
We ended at the final version of the device after months of experimentation with a variety of designs. We divided our equipment into sections, which required a two-person team. One of us wore the computer, which was the size of a pack of cigarettes and had twelve transistors. Data was entered using switches concealed in the wearer's shoes, which were controlled by his big toes. The computer's forecast was broadcast over the radio, using a modification of the cheap, widely available equipment usually used to run model airplanes remotely. The bettor, on the other hand, would wear a radio receiver that would play musical tones instructing him on which group of numbers to bet on. We'd behave as though we were strangers to each other.
The person placing the bets could hear music through a tiny loudspeaker inserted into one ear canal and connected to a radio receiver hidden under his clothing by very thin wires. We used clear spirit gum to adhere the wires and painted them to match the wearer's skin and hair so they wouldn't be seen. The thin copper wires, which were just a hair's width, were continuously breaking. Claude recommended that we replace the copper with ultrathin steel wires. We found a supplier in Worcester, Massachusetts, who had everything we wanted after an hour of calling.
We arrive at the casino, with Vivian (Thorp's wife) and Betty Shannon (Claude's wife) strolling and talking, while Claude and I are total strangers to them and each other. The others are anxious because they lack my casino experience, but they don't show it. Claude stands by the wheel, timing the ball and rotor, he writes down the winning number after each roll of the ball, giving the impression that he is just another doomed-to-fail machine player. In the meantime, I take a seat at the far end of the layout, away from both Claude and the wheel. To keep the rotor turning, Claude waits for the croupier to give it a drive. His big toe hits one of the silent mercury switches concealed in his shoe as the green zero on the rotor moves by a reference point on the stator that Claude has selected to be one of the ball-deflecting vanes. Make touch. It's the acoustic equivalent of a click! Select when the green 0 appears again. The elapsed time is the time it takes for one rotation to complete. An eighttone musical scale—do, re, mi, and so on—begins to play in my ear after the second click, and it repeats every time the rotor turns once. The machine now knows not just how fast the rotor is spinning, but also how far away it is from the stator.
Since our classes had forty numbers and the wheel only has thirty-eight, we split the numbers on the wheel into eight such groups of five, with 0 and 00 appearing twice. We call these five-person groups "octants." The average player who bets $1 on each of five numbers will win about five times out of thirty-eight times, or just over one-eighth of the time, and lose all five bets the rest of the time, resulting in an overall rate of loss of $2 for every $38 worth of bets, a 5.3 percent disadvantage. Using our machine, however, our five-number bet won a fifth of the time, giving us a 44 percent advantage.
However, we encountered difficulties. A lady sitting next to me glanced over in horror as we were well into one of our winning sessions. I dashed to the toilet, knowing I should leave but not why, and saw the speaker peering out from my ear canal like an alien bug in the mirror. More seriously, we had a problem that prevented us from switching to large-scale betting on this trip, despite the fact that we often converted small piles of dime chips into large ones. It had everything to do with the wires leading to the ear speaker. Even though they were steel, they were so fine that they cracked all the time, forcing us to return to our rooms and go through the boring process of making repairs and then rewiring me.
The machine, however, was a success once it was up and running. We knew that by using larger wires and rising hair to cover both our ears and the wire running up our neck, we could solve the wire issue. We also considered persuading our hesitant wives to "wire up," hiding all behind their trendy longer hair.
Finally, in 1966, Edward Thorp made our roulette device public because it was obvious that we weren't going to use it. Later, I made the information public. I demonstrated the process to a mathematician from UC–Santa Cruz when he called. The Eudaemonic Pie group of physicists will use the next decade's more sophisticated technologies to develop their own roulette machine at UCSC. They, like us, discovered a 44 percent advantage and were irritated by hardware issues. Later, it was claimed that groups using roulette computers earned large sums of money.
Betty donated many of Claude's papers and devices to the MIT museum after his death in 2001, including the roulette machine. In the spring of 2008, the museum loaned it to the Heinz Nixdorf Computer Museum in Paderborn, Germany, for an exhibit that attracted 35 thousand visitors in the first eight weeks. In August 1961, as Claude walked up to the Las Vegas roulette wheel, he was using something that none of us had ever seen before. This was the first wearable computer in the world.