The Maths Behind Roulette

Roulette is a game of numbers and chance. You can sit around studying the odds in roulette and the outcomes of trying to predict where that little ball will next end up but unfortunately you will be wasting a great deal of your time.

Roulette is a game to be enjoyed. Sometimes you’ll win and sometimes you’ll lose. It’s a game that has been played for centuries and no-one yet has found a way to truly beat the game. The game has been used to help develop statistical theories and processes such as Karl Pearson´s Goodness of Fit test.

Could maths return the favour and help crack the code?

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Countless people through the ages have tried to crack the roulette code using mathematics. Some of the more famous roulette systems are beased on mathematical sequences, strategies like the Fibonacci System, for example.

Mathematics seems the most obvious way in which you can attempt to beat the dealer but predicting any result is simply a matter of probability. The entire game is based upon independent events, which therefore means that any event that occurs when the wheel spins and the ball lands has no affect or influence on any previous or future spin.

You should also check out our page that covers physics in roulette, by the way.

In European Roulette the payout on hitting any one of the 36 red or black numbers on the wheel is 35 to 1. It’s the highest payout you can achieve with a single bet and so of course means that the probability is the lowest (at just 2.7% in fact).

For a better chance of winning more frequently, many players will simply place an even-money bet on something like red or black, odds or evens or any one of the numbered groups. The probability is a massive 48.6% but the payout is just 1:1. But if the bet is pretty much a 50-50 chance then why is it only 48.6% and not 50%?

Well, don’t forget that the European table also includes the green zero pocket so this does mean that the odds will be slightly lower than 50/50. In fact, this little zero pocket is what gives the casino its roulette house edge, when combined with the payout structure.

British engineer Joseph Jagger did manage to use mathematics and predictability when he managed to win a significant sum of money on his visit to Monte Carlo in 1875.

Jagger has hired 6 clerks to visit the casino Beaux-Arts Casino in Monaco to record all the outcomes of 6 different roulette wheels over a period of time.

Using these findings he was able to discover a pattern of a group of numbers that kept coming in more frequently than others on just one of these wheels. He ended up placing his bets on this particular wheel using these numbers in question and was able to accumulate hundreds and thousands of pounds of winnings.

However, Jagger hadn’t uncovered an incredible flaw in the game itself. He had simply exposed the fact a roulette wheel in the world’s biggest gambling capital merely had a mechanical imbalance which gave the wheel a clear bias towards certain outcomes. And the problem with that discovery, was that the casino discovered it as well. And they fixed the wheel!