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Gambler's Fallacy


Explanations > Theories > Gambler's Fallacy

Description | Example | So What? | See also | References 



The 'Gambler's Fallacy' (first noted by Laplace in 1796) occurs where people assume they can predict random events.

A number of descriptions define this solely in terms of reversals, where it is assumed that when one alternative happens it is less likely to happen in subsequent events. This is to misunderstand the law of large numbers, where a large number of random events, such as coin tossing, will closely approach the natural distribution (eg. 50% heads and 50% tails).

A critical element of the fallacy is that wins and losses will balance themselves out in the short term, rather than the long term, such that several losses means wins are more likely. The truth is when the driver is random chance, the probability of winning or losing is always the same each time.

This fallacy can appear as a contradiction to the Hot Hand Phenomenon, where a run of success is assumed to continue.

In the more general description of the gambler's fallacy, it includes the assumption of a run of luck or 'winning streak', where because I have won several times I feel I am more likely to continue winning.

Other false predictions around luck include assumptions of luck running out and being on a losing streak.

Generally we all need to explain our experiences (as in attribution theory) and gamblers are no different. They thus form theories about why they are winning or losing based on luck and their own skill. Recency and availability effects also have an impact on predictions.


I toss a coin and it comes down heads. I expect the next coin to be more likely to be tails than heads. It comes down heads. Now I am even more convinced that the subsequent coin will very likely be tails. If I am a betting person, I might double my bet each time, sure that I will walk away a winner.

So What?

Using it

Encourage people to take risks by telling them they (or your or the investment firm, etc.) are lucky or on a 'winning streak'.


Understand probability. Avoid depending on luck. Watch out for people who encourage otherwise.

See also

Gambler's Fallacy (argument), The Hot Hand Phenomenon, Attribution Theory, Representativeness Heuristic, Availability Heuristic, Recency Effect, Side-Bet Theory


Laplace (1796), Jarvik (1951), Clotfelter and Cook (1993), Roney and Trick (2003)



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