Gambler's Fallacy

The mistaken belief that past random events influence the probability of future independent events. The most famous real-world example is the Monte Carlo Fallacy of 1913: the roulette ball at Casino de Monte-Carlo landed on black 26 consecutive times. Gamblers lost millions betting on red, convinced a correction was "due." The ball had no memory. Each spin was independent. The gambler's fallacy underlies lottery number selection (players avoid "recent" numbers), sequential decision-making in courtrooms (judges grant fewer paroles after a run of approvals), and investment patterns (selling winners to "balance" a portfolio). Random sequences feel non-random to human brains wired to find patterns.