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.

The Monte Carlo Casino

One of the biggest gambler’s fallacies ever recorded in the history of gambling occurred way back in 1913 in the Monte Carlo Casino.  On the 18th of August of that year in a game of roulette, the ball landed on black 26 times in a row. This rarity in the history of gambling is not just notable for the consistency of one colour but for the tremendous amount of money lost. Due to the laws that govern the gamblers fallacy, everyone around the table just assumed that the colour red would eventually avail itself, as it was ‘due’ and thus many players bet massive amounts against black expecting a long streak of red.

Other instances of the Gambler’s Fallacy

The gambler’s fallacy is not exclusive to gambling. It’s also reared its head in childbirth as far back as 1796 when Pier-Simon Laplace published his paper called ‘A Philosophical Essay on Probabilities’. In it he wrote essays about soon to be fathers who could calculate their probabilities of having sons.  Laplace observed that soon to be fathers assumed that if more sons were being born in the community, that their likelihood of having daughters increased. In other cases expecting parents would believe that after having had same sex children consistently, that they would be due one of the opposite sex.

Gambler’s Fallacy Variations

According to researchers, there are actually two kinds of gambler’s fallacy – type 1 and type 2.  Type 1 refers to the belief that a certain outcome is due after a long streak of the opposite outcome or a different outcome. Type 2, expounded upon by Charles Lewis and Gideon Keren, refers to the observation of a certain amount of outcomes which then leads to the incorrect estimation of a certain number or outcome. A prime example is when a player watches a roulette wheel for a length of time and then elects to bet on numbers that have occurred often.