Roulette: the mathematics of the game

Roulette, like most gambling games, is a game of chance. That being said many will insist upon wasting hours trying to work out the odds of the little ball stopping on a particular color and number, instead of just having fun playing. The very nature of gambling means that you will win sometimes and lose others, and roulette is no different. People have been trying to figure out how to beat the game for centuries, all to no avail. Is it possible that using mathematics there could finally be a way to win consistently at roulette?


Mathematics has been the basis of many systems designed to beat the odds of roulette with one particularly famous system being the Fibonacci System. While mathematics may seem the way to work out a system that lets you win consistently the truth is that predicting the result of any roulette spin comes down to probability. Each spin of the wheel is completely independent of any previous spin and so is not impacted. Where the ball stops is dependent solely on that particular spin of the wheel and no others.

European Roulette has very low odds (2.7%) of the ball stopping on any particular color or number, but the payout on a single bet is the highest possible at 35 to 1. For anyone who doesn’t like those odds they can choose to place even-money bets or their choice of black or red, or even or odd numbers. While the probability is much greater at 48.6% naturally the payout is very small at 1:1.

You are probably thinking that the probability should be 50% when you have a 50 – 50 chance of winning but you may be forgetting the green zero pocket that is typical of a European roulette table, which makes the odds that little bit lower. The zero pocket and the payout structure are what give the casino its edge at the roulette table.

In 1875 Joseph Jagger, an engineer from Britain visited the Beaux-Arts Casino in Monte Carlo and by using mathematics to predict a win managed to be successful at the roulette table, winning a large amount of money. Jagger paid 6 clerks to observe and make note of the results of 6 roulette wheels. The statistics were recorded over a significant enough time period that allowed for the findings to be used to discover that a pattern existed. On one specific wheel the ball stopped on a specific group of numbers more often than the other wheels. By using these statistics he was able to play roulette on that specific wheel and place bets on those particular numbers until he amassed a significant amount of money.

Source: Monte Carlo Casino – Wikipedia

While it seemed that Jagger had managed to figure out a system to win at roulette it turned out that the reason he could win at that particular wheel as often as he did was simply because the wheel itself was out of balance, causing the ball to stop on those numbers more often than it should have. Naturally Jagger’s supposed mathematical ‘streak of luck’ ran out when the casino fixed the roulette wheel, thereby putting paid to his mathematical theory.