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.

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