Gambler's fallacy

The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the belief that, if an event (whose occurrences are independent and identically distributed) has occurred less frequently than expected, it is more likely to happen again in the future (or vice versa). The fallacy is commonly associated with gambling, where it may be believed, for example, that the next dice roll is more than usually likely to be six because there have recently been fewer than the expected number of sixes.

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.^[1]