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. The famous Monte Carlo casino incident of 1913, where black came up 26 times in a row at roulette, saw gamblers lose millions betting on red, convinced it was overdue. In business, the fallacy manifests as expecting a string of successes to continue (hot hand fallacy—the inverse) or expecting failure to reverse without changing the underlying process. Investment decisions are particularly vulnerable: assuming a stock that dropped must rebound, or that a fund's recent performance predicts future returns. The antidote is understanding true randomness, distinguishing between independent events (each has the same probability) and dependent sequences (where history actually matters), and evaluating base rates rather than patterns in small samples.