Gambler's Fallacy
Past random events are mistakenly believed to influence future independent random events.
Origin & History
The Gambler's Fallacy has been documented in gambling contexts for centuries, but its psychological explanation was formalized by Kahneman and Tversky in their 1971 paper on the 'law of small numbers' — the mistaken belief that small samples should represent the properties of the distribution they're drawn from. The fallacy is also known as the Monte Carlo Fallacy, after a famous 1913 incident at a Monte Carlo casino where black came up 26 consecutive times and gamblers lost millions betting on red, believing the 'overdue' outcome was increasingly likely.
Real-World Examples
A roulette wheel lands on red 11 times consecutively. A gambler bets heavily on black, reasoning 'it's due.' The probability of black on the next spin is identical to every other spin: 47.4%.
Commentators routinely claim that a player on a hot streak is 'due for a cold one' — and that a player in a slump is 'due for a hit.' Statistical analysis consistently shows these expectations are not predictive.
After 10 heads in a row, most people predict tails is more likely next. In reality, each flip is independent. The coin has no memory of previous flips.
Why It Matters
The Gambler's Fallacy is maintained by the mistaken intuition that randomness must look balanced over short sequences. True randomness has no obligation to balance. The fallacy is rational in non-random contexts: if a fair coin produces 95 heads in 100 flips, the coin is probably not fair — and it's rational to adjust your expectation. But for genuinely independent, random events, each outcome is fully independent of history. Recognizing which contexts are truly independent is the critical judgment the fallacy obscures.
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Play the Game — Free →Frequently Asked Questions
The mistaken belief that past random events influence future independent ones — that a coin 'due' to land tails is more likely to do so after a run of heads.
Another name for the Gambler's Fallacy, named after a 1913 incident at Monte Carlo where gamblers lost millions betting against a 26-time consecutive streak of black on roulette.
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