Roulette is likely to come to mind: the spinning of a doughnut wheel at a casino, complete with dinner jacketed croupiers and Bond movie montages. But at its most basic, this is pure chance. There are 38 equally sized slots that the ball can land in, and each time the wheel spins this counts as a fresh independent run.
Yet physics models show that, in principle, with enough information you can tell where on the wheel the ball will stop and gain some advantage over the house.
The Ball
Yet, mathematicians and scientists have been trying to figure out, from the time of the famous mathematician and gambler Blaise Pascal, to even today, how you can place a bet deliberately in order to win a game of roulette by predicting which number the ball will fall on. (This has been, of course, part of roulette’s appeal as a speedy avenue to making money!)
Some systems of gambling rely on mathematical formulas, and others on physical laws. The Martingale system of gambling, for example, says you should double your bet after each loss. Eventually, you will win enough times to make up all your losses and turn a profit.
Casino makers are consistentlyseeking to perfect the performance of the roulette wheel. The technology Random Rotor Speed (RSS) for example, varies the rotor speed after every spin, utilising contactless methods, making it impossible for expert players to predict its mechanical behaviour by exploit the mechanical performance.
The Wheel
From sweaty tension in the casino pits of Las Vegas to James Bond at the baccarat table cashing in his winnings, roulette wheels have become an iconic symbol of randomness. After all, with a zero slot, plus balls that can land in any of the 37 prize-paying slots at random and with no predictable pattern, these wheels truly appear to spin up a chaotic result every time.
However, reality can be more nuanced: the wheel itself can be tweaked; even a tiny bias will favour certain numbers over others.
A typical European roulette wheel has 38 pockets numbered ball-by-ball from 0 to 36 plus one extra pocket labelled ‘00’. It is widely recognised that every one of these pockets has an equal probability of appearing on every spin.
It could rotate over and over again on the wheel before it loses momentum and rolls on to the rotor (the part with the pockets), where it rolls down and perhaps hits metal frets on the rotor or rides over them; perhaps it is bigger, heavier or lighter, or made of tin or wood; perhaps it is easier or harder to predict where it should or will fall; its trajectory could be affected by the friction of the metal fret Depending on the coin, the random element may come earlier or later.
The Odds of Winning
Perhaps the most useful approach to understanding roulette’s odds (which are, after all, vastly different depending on the bets you make) is simply to look at fractional values and at the numbers that are associated with them: the proportion of times any given number or kind of number should appear (this is the easiest approach where fractions are used) and use those fractions to help keep track of its ratios or percentages.
Initially perhaps it was purely about maintaining 100 per cent odds against winning, but over time players might have devised predictive systems to gain an edge over the casino. And they would do this by working out the mechanical performance of the wheel.
However, implementing the process can be daunting, and several failed attempts have been transished both by shortcomings in the calculation of odds figures, and also by glitches that could electrocuted the wearer in his back. Odds figures do not reflect, in the short term, the chance of winning in practice.
The Payouts
Roulette is a fundamentally random game. When you play at the Las Vegas casino or see it in James Bond movies or just at your best online casino, each slot on the wheel has an equal chance of appearing on each spin – and that’s what makes the game so fun and unpredictable!
Casinos exploit certain aspects of the mechanism whereby the ball lands in one of the 36 red or black numbers or in a green zero or double-zero notch. These minor flaws boost the role of luck to some degree, making it easier for them to win and draw players in, and allow one to bet on certain subgroups of numbers, increasing your chances of winning, sometimes with major paybacks. It is for these reasons that this type of gambling has so much suspense attached to it.
Edward Thorp, on the other hand, is the entire reason casinos were forced into the netherworld of sports betting if they wanted to keep roulette. Thorp was the first to devise an objective method of beating casinos at roulette based on physical defects which allowed him to pick up on inconsistencies in the wheel and ball. By contrast, Small employed his knowledge of physics, and the very motion that sets the ball on its trajectory, to increase the odds he could predict. He dubbed this method Eudaemonic Pie, after the dessert to which it often led. He explains his roulette strategy in his introduction to the anthology The Newtonian Casino (also published internationally under the title The Newtonian Gamble).