Gambler’s fallacy

The mistaken belief that an independent random event becomes more or less likely because of earlier outcomes. It often appears as an expectation that a run of results must soon reverse.

Independence (probability theory): Two events are independent when the occurrence of either does not change the probability of the other. The fallacy mistakes a sequence of independent outcomes for one that must compensate for its past.
Roulette: A casino wheel game in which a ball lands in one of several numbered pockets, with bets determined by the result. A long run of red does not alter the chance of red on a fair roulette spin.
Pierre-Simon Laplace: A French mathematician and astronomer who made foundational contributions to probability and celestial mechanics. Laplace described the tendency to expect reversals in sequences of chance outcomes.
Behavioral economics: The study of how psychological, social, and emotional factors shape economic decisions. The fallacy is a documented bias that can influence decisions under uncertainty.
Law of large numbers: A theorem stating that sample averages tend to approach expected values as the number of observations grows. Long-run convergence is wrongly treated as a force that corrects short-run imbalances immediately.
Coin flipping: A random experiment in which a coin lands heads or tails, often used to illustrate probability. A run of heads provides a simple example of independent outcomes that need not reverse.
Monte Carlo Casino: A casino in Monaco that opened in 1863 and became a major European gambling destination. A roulette streak there gave the fallacy one of its best-known historical examples.
Gambling disorder: A behavioral addiction involving persistent gambling despite significant harm or distress. Believing losses make a win due can encourage continued betting and escalating losses.
Probability matching: A choice strategy that selects options in proportion to their estimated probabilities rather than always choosing the most likely option. It helps distinguish adapting choices to estimated patterns from expecting independent outcomes to self-correct.
Lottery: A game of chance in which prizes are awarded according to randomly selected numbers or tickets. Past winning numbers do not make an unselected number more likely in a fair independent draw.

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