Gambler's fallacy

The error that, in a series of independent chance events, future events can be predicted from past ones. For example, the idea that if, say, ten (fair) coin tosses have resulted in successive heads that there is an increased probability of a ‘tails’ being thrown on the next toss, when the probability remains 50/50 – an almost compulsive tendency by actors to believe that some particular outcome, in this case ‘tails’, will become more likely in the face of a well-known and well-established statistical independence of the events.

(see also: Illusion of control, Representativeness heuristic, Conjunction fallacy, clustering illusion, Regression towards the mean, pattern-seeking)