gambler's fallacy

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The false belief that the probability of an event in a random sequence is dependent on preceding events, its probability increasing with each successive occasion on which it fails to occur. Thus if black has come up many times in succession at a roulette table, a false belief may develop that red is increasingly likely on each subsequent spin of the wheel, to even out the sequence in the long run; or if a fair coin is tossed repeatedly and tails comes up many times in a row, a gambler may believe that heads is more likely on the following toss; or if a mother gives birth to several girls in succession, she may come to believe that the probability of a boy is greater than 1/2 for her next baby. See also sample size fallacy.

Subjects: Psychology — Philosophy.

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