Gambler's Fallacy

What is it?

The gambler's fallacy is the mistaken belief that past random events affect the probability of future random events. After a coin lands heads five times in a row, people believe tails is "due", but each flip remains 50/50. The fallacy stems from the representativeness heuristic: we expect short sequences to look like the long-run probability, so a streak seems unrepresentative and due for correction. This belief in a "balancing force" in random processes is deeply intuitive but mathematically false for independent events. In the often-told Monte Carlo casino story of 1913, black came up 26 times in a row at roulette and gamblers lost heavily betting on red, convinced it was overdue. In business, the fallacy shows up as expecting a run of bad results to reverse on its own without changing the underlying process. Its mirror image, the hot-hand fallacy, is expecting a run of successes to continue. Investment decisions are particularly vulnerable, for example assuming that a stock that has fallen must rebound. The antidote is understanding true randomness, distinguishing between independent events (each has the same probability) and dependent sequences (where history actually matters), and looking at base rates rather than patterns in small samples.