gambler's fallacy

Meaning: The gambler's fallacy is a cognitive bias in which a person believes that after a streak of one outcome in independent random events, the opposite outcome is now "due." Past results are treated as if the process corrects itself. A fair coin has no memory, so the chance of tails stays 0.5 after any number of heads. It is usually explained by the representativeness heuristic: people expect even short sequences to look like the random process that produced them, with a balanced mix of outcomes.

On the MCAT: A passage describes a person who bets on red after black has come up many times in a row on roulette, or parents with several sons who feel a daughter is due next. You are asked to name the bias or to say what the true probability is. Look for independent events plus a predicted reversal.

Common confusion: The law of large numbers says observed proportions approach the expected value over many trials, but that happens because early streaks are swamped by later trials, not because later outcomes compensate. Do not mix it up with the hot-hand fallacy, the belief that a streak will continue.