Gambler's Fallacy
The false belief that past independent outcomes change the odds of future ones — e.g. that a colour is 'due' after a run.
Definition
The gambler's fallacy is the mistaken belief that in a sequence of independent random events, past results influence what comes next — for instance, thinking red is 'due' after black has come up several times in a row on a roulette wheel. It is wrong because each spin, roll, or draw in a game of chance is statistically independent: the wheel has no memory, and the probability of each outcome is the same every time regardless of history. The fallacy can drive people to bet more heavily on an outcome they believe is overdue, deepening losses. It is essentially the mirror image of the illusion of control and a close cousin of the mistaken 'hot hand' belief that a streak will continue. Recognising that independent events do not self-correct in the short run is fundamental to understanding why no betting pattern can beat a fixed house edge.
Worked example
After black lands five times running, a player bets big on red because it 'must' come next — yet the odds of red on that spin are exactly what they always were, unchanged by the previous results.
Why it matters
Learners get a clear, memorable example of how probability really works versus how intuition misleads. Professionals use it to debunk 'due' thinking and to explain why streak-based betting strategies fail.