Gambler’s Fallacy

The gambler’s fallacy is a belief that one event will affect the outcome of a future event, when in reality the two events are independent. People commit the gambler’s fallacy when they believe that the repeated occurrence of one thing must necessarily cause the repeated occurrence of something else.

Examples of Gambler’s Fallacy
The classic example of the gambler’s fallacy occurs when someone flips a coin. If the head lands face up, say, four or five times, most people will believe that the coin will land on the tails side next time, occasionally even arguing that the repeated “heads” coin increases the likelihood of a future “tails” coin. In reality, each time the coin is flipped, the probability that the coin will land on heads as opposed to tails is 50%. Previous coin flips do not affect the outcome.

The fallacy is also common surrounding childbirth. Parents might believe that, because they have three girls, they are more likely to give birth to a boy next. In previous generations, a person might believe that, if primarily girls had been born in the area that month, it was more likely that a boy’s birth would be next.

Gambler’s Fallacy Role in Psychology
The belief is a result of the belief in the law of small numbers. People who hold this belief believe that small collections of numbers have to be representative of the overall picture. So, for example, if the birth rate of girls and boys is 50 percent each, people believe that the number of boys and girls should be roughly 50/50 in a family, city or time span.

The gambler’s fallacy can be a source of false hope. For example, someone in an abusive relationship might believe that, because his/her partner has been abusive for a week, he/she is “due” for a nice streak.


  1. Colman, A. M. (2006). Oxford dictionary of psychology. New York, NY: Oxford University Press.

Last Updated: 08-7-2015

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