The mistaken belief that a random event is more or less likely to occur based on past outcomes.

Past occurrences of an independent random event have no impact of future occurrences. For instance, the probability of getting heads in a coin toss is 1/2 regardless of the previous tosses. If we encounter a dozen heads in a row, we may feel that the next toss will be tails to balance things out. This is a mistaken belief--the probability of tails remains 1/2, the same as in previous tosses.

- A game of roulette at Monte Carlo Casino on August 18, 1913 is perhaps the most iconic example of the fallacy. The ball fell in the black 26 times in a row causing gamblers to lose millions in the mistaken belief that the probability of red was now higher.