The gambler's fallacy is the mistaken belief that independent chance events are influenced by previous outcomes. For example, if a fair coin has landed heads several times in a row, one might mistakenly believe that tails is now 'due' to occur. This fallacy assumes that past random events can affect the probabilities of future random events, despite each event being independent of previous ones.
A well-known instance of the gambler's fallacy occurred at the Monte Carlo Casino in 1913 when a roulette wheel landed on black 26 times in a row, leading many gamblers to believe that red was 'due' to occur, despite the fact that each spin is independent.
To overcome the gambler's fallacy, it's crucial to understand that each event in a series of independent trials has an unchanged probability. Remind yourself that past outcomes do not affect future probabilities.