Gambler’s fallacy

Etymology

Also called the Monte Carlo fallacy, after a night in 1913 when the roulette wheel at that casino landed black 26 times and bettors lost fortunes piling onto red. The underlying error — imagining that independent events keep a running balance — was noted by Laplace long before it got the gambler’s name.

noun phrase · /GAM-blurz FAL-uh-see/
The mistaken belief that a run of one outcome makes the opposite outcome "due" in a truly random process.
What it names
Why a coin that lands heads five times feels like it owes you tails — we expect chance to correct itself in the short run, and it doesn’t.
Example
Convinced by the gambler’s fallacy that the machine was overdue, he fed it another hour’s wages.
Related idea
Hot-hand fallacy is the mirror image: expecting a streak to continue rather than reverse. Both misread randomness — just in opposite directions.