Gambler's Fallacy
Monte Carlo Fallacy · Fallacy of the Maturity of Chances
The mistaken belief that, if something happens more frequently than normal during a given period, it will happen less frequently in the future (or vice versa).
Origin
The fallacy's most famous illustration occurred on August 18, 1913, at the Monte Carlo Casino, when a roulette ball landed on black 26 consecutive times. Gamblers lost millions of francs betting against the streak, convinced it had to end. The underlying psychology was formalized by Amos Tversky and Daniel Kahneman in their 1971 paper "Belief in the Law of Small Numbers," which showed that people erroneously expect short random sequences to mirror the statistical properties of the overall probability distribution.
Everyday Use
After flipping heads five times in a row, it feels like tails must be "due" — but the coin has no memory. You see this at roulette tables, in sports ("they're due for a win"), and even in everyday judgments about streaks of good or bad luck. Each independent event has the same odds regardless of what happened before.