What is the gambler’s fallacy?

The so-called gambler’s fallacy is a commonly-held, but mistaken, belief that in a game of chance, such as roulette, sequences of one binary outcome, such as the appearance of a red number, will be balanced by the opposite outcome, such as the appearance of a black number. Worse still, the longer the sequence, the stronger the belief becomes.

Of course, in reality, each spin of a roulette wheel is an independent, random event, which cannot be influenced, in any way, by past events. Indeed, the longest recorded sequence of one colour is 32, but even shorter sequences of one colour or the other can lead to a form of distorted thinking – technically known as ‘negative recency’ – that makes gamblers believe they have a higher-than-average chance of winning.

Notwithstanding the inherent house edge which, even in the European, single-zero version of roulette, stands at 2.7%, the probability of a red or a black number appearing on a single spin of the wheel is always approximately 50:50, regardless of previous results. The appearance of the green zero renders all ‘outside’ bets, including those on red or black, losers, so the actual probability of winning on red or black is 47.37%; the point is that that probability never changes, regardless of how counter-intuitive that may seem to the gambler. Of course, the gambler’s fallacy applies not just to roulette, but also to other games of chance, including blackjack, poker and slots, which operate on the same hard-and-fast laws of mathematical probability.