What is the Gambler’s Fallacy?

The Gambler’s Fallacy is a very common misconception when it comes to predicting an outcome, which fools many happy players into wasting the contents of their wallet. It’s an idea that feels logical, but in fact is entirely false. The Gambler’s Fallacy assumes that a certain outcome is ‘due’ because what has occurred previously is not what would be expected on average in the long term. The most common way that this mistake is made is when there are two events whose probabilities of occurring are entirely independent of one another.

Tossing a Coin

If you imagine that a fair, two sided coin is tossed, there is a 50% chance of it landing on Heads, and a 50% chance of it landing on Tails. Statistically in the long term, you would therefore expect it to land on either side an equal number of times. A person tosses the coin 6 times in a row, and each time it lands on Heads. He might then conclude that because it is statistically improbably to get 6 Heads in a row, let alone 7, that a Tails must be ‘due’. However in making this assumption he has committed the Gambler’s Fallacy. With each individual coin toss there is always a 50% chance of it landing on Heads and a 50% chance of it landing on Tails. Each coin toss is independent of the last one and so has absolutely no impact on the outcome of the next.

Roulette

It is very easy to fall into this trap when playing Roulette. After observing a long run of red, for example, it is very common for players to bet increasingly large amounts of money on black, as they are sure it must be ‘due’. However a long term average of 50/50 is by no means automatically represented in the short term, so any players who believe a streak like this must necessarily end the longer it continues are falling victim to the Gambler’s Fallacy.