Gambler's Fallacy

Gambler's Fallacy is a term that describes the mistaken automatic notion that many people experience in relation to the odds of a random event having any relation to past occurrences for the same random event.

Gambler's Fallacy is also known as The Doctrine of the Maturity of Chances or Monte Carlo Fallacy, named so after the famous case that occurred in 1913 in a Monte Carlo casino. During a game of Roulette the roulette ball landed on Black several times in succession. After the fifteenth time the ball landed on Black there was an alarming rush by gamblers to bet on Red. After the twentieth time the ball landed on Black most gamblers doubled and tripled their bets on Red and many claimed that there isn't a chance in a million that the ball will land again on Black.

This case is a perfect example of Gambler's Fallacy. The gamblers kept betting huge amounts of money on Red believing that the outcome of previous rounds had any bearing on the outcome of subsequent events.

This fallacy played directly into the hands of the casino owners that pocketed that night several million Francs more than on average nights.

The reason this fallacy works on most people is due to the fact that people have a cognitive bias that makes them expect that a run of random outcomes would have shared properties for the long run. They believe that any deviations from average must find a way of balancing out eventually.

Ask yourself this; if a coin was tossed nine times and came up Heads every time. What are the chances of it coming up Heads the tenth time? If your answer is that there is a greater chance that the coin toss for the tenth time would result in Tails as Heads came up already nine times in a row, then you are afflicted by the Gambler's Fallacy.

In fact the odds are the same for each coin toss, no matter how many times before the coin was tossed previously and the outcome of those tosses. Coins have no memory and each coin toss is a random event that carries fixed odds of 50/50.