Gambler's fallacy

Mistakenly drawing statistical inference from independent events

The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the belief that an independent and equally probable outcome which happened less frequently than expected is more likely to happen in the future (or vice versa). The fallacy is commonly associated with gambling, where it may be mistakenly believed, for example, that the next dice roll is more likely to give '4' because there have recently been fewer '4's than expected, when in reality the probability of the next outcome being '4' is always 1/6, for each dice roll is an independent event. The term Monte Carlo fallacy originates from an example of the phenomenon, in which the roulette wheel spun black 26 times in succession at the Monte Carlo Casino in 1913.

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