Gambler’s Fallacy

What is the Gambler’s Fallacy?

The gambler’s fallacy is the belief that a run of one outcome makes the opposite outcome due. It is a mistake when the events are independent and their probabilities have not changed.

Suppose a fair coin lands heads five times in a row. Tails can start to feel overdue. But the coin has no memory: the next flip still has a 50% chance of landing tails. The earlier flips have not created a debt that the next flip must repay.

Tversky and Kahneman described this misconception of chance: people expect even short random sequences to look balanced. Randomness is quite capable of producing a streak.

Why it matters

A gambler who thinks a win is overdue may keep betting after repeated losses. The feeling that things must turn around is not evidence that the odds have improved.

The qualification matters, though. Past outcomes can tell us something when a process is biased, changing, or dependent. A basketball player is not a coin. The hot-hand fallacy concerns expecting a run of success to continue; in a skill-based activity, whether that expectation is mistaken depends on evidence about the activity.