We believe luck "evens out" in the short run, even though each event is independent.
If a coin lands heads five times in a row, many people feel tails is "due" to come up. The gambler's fallacy is believing a random event becomes less likely to repeat just because it already happened several times in a row, when in truly independent events the probability never changes at all.
At the Monte Carlo casino in 1913, the ball on a roulette table landed on black 26 times in a row. As the streak stretched on, more and more players bet increasingly heavily on red, convinced it was "due". They lost millions of francs. The probability of red on each following spin stayed exactly the same as always, the roulette wheel has no memory of its previous spins.
We expect short random sequences to look "balanced", the way we believe long sequences look. A streak of identical results feels statistically rare to us, so we anticipate a correction, even though each event is, in fact, completely independent of the one before it.
Source: Croson, R. & Sundali, J. (2005). The Gambler's Fallacy and the Hot Hand: Empirical Data from Casinos. Journal of Risk and Uncertainty, 30(3), 195-209.
In investment or credit decisions, a streak of results, good or bad, doesn't change the probability of the next event if the events are truly independent. Mistaking a streak for a real signal is a costly and common error.
Related concepts
