Gambler’s fallacy in Craps

Other systems depend on the gambler’s fallacy, which in craps terms is the belief that past dice rolls influence the probabilities of future dice rolls. For example, the gambler’s fallacy indicates that a craps player should bet on eleven if an eleven has not appeared or has appeared too often in the last 20 rolls.

In reality, each roll of the dice is an independent event, so the probability of rolling an eleven is exactly 1/18 on every roll, even if eleven has not come up in the last 100 rolls, or if eleven has come up five times in the last five rolls. Even if the dice are actually biased toward particular results (”loaded”), each roll is still independent of all of the previous ones. The common term to describe this is “dice have no memory”.

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