Judgment & BeliefMedium Impact

Gambler's Fallacy

Edited by Paweł Raja, PhD · Published 8 Oct 2026

Definition

Gambler's Fallacy is the gambler's fallacy is the mistaken belief that after a run of one outcome in a random process, the opposite outcome becomes more likely — for example, that tails is 'due' after several heads.

Also known as:: Monte Carlo fallacy, Fallacy of the maturity of chances
Category:: Judgment & Belief
Impact:: Medium
Landmark study:: Tversky & Kahneman (1971)
Evidence here:: 5 cited studies

Why it happens: the psychology of gambler's fallacy

The gambler's fallacy is a belief in negative autocorrelation where there is none: people expect an independent random sequence to reverse itself. A fair coin has no memory, so the chance of heads on the next flip is 50% however many heads came before.

Tversky and Kahneman (1971) traced the error to a 'law of small numbers': people expect even short sequences to look like the long-run population, so a run of heads feels like an imbalance that must be corrected. This is the representativeness heuristic applied to randomness — a sequence such as H-T-T-H-T-H looks more random, and therefore more likely, than H-H-H-H-H-H, although both are equally probable.

Rabin (2002) formalized this idea, modeling believers in the law of small numbers as people who treat random draws as if they were taken without replacement from a small urn, so that each head 'uses up' a head and makes tails more likely.

The fallacy is not confined to gamblers. Chen, Moskowitz and Shue (2016) found that asylum judges, loan officers and baseball umpires made decisions that were negatively correlated with their previous decisions, independent of the merits — consistent with decision-makers believing that a streak of similar outcomes is unlikely to be right.

Gambler's Fallacy examples

Video recordings of roulette play in a casino showed that after the same type of outcome came up six or more times in a row, 85% of the bets that took a side on the streak went against it — even though every spin is independent.

Money: a roulette player bets heavily on black after a long run of red, believing black is 'due'.
Money: lottery players avoid a number that won yesterday, as if it were less likely to come up again.
Family: parents with three boys believe their next child is more likely to be a girl.
Investing: an investor sells a stock after several up days because it 'can't keep going up', with no new information about its value.
Work: a loan officer who has approved several applications in a row becomes stricter with the next one, regardless of its merits.

Gambler's fallacy vs hot-hand fallacy

The two errors point in opposite directions. The gambler's fallacy expects a streak to reverse ('red is due to stop'); the hot-hand fallacy expects it to continue ('she's on fire, keep giving her the ball'). Both misread random sequences, and Croson and Sundali (2005) observed both in the same roulette players: they bet against streaks of outcomes, yet bet on more numbers after a win than after a loss.

A common way to reconcile them is the source of the outcome. When results come from a mechanical device such as a roulette wheel or coin, people tend to expect reversals. When results seem to come from a person's skill, they tend to expect streaks to continue.

The hot hand itself has been re-examined. Gilovich, Vallone and Tversky (1985) found no evidence for it in basketball shooting data and called the belief a fallacy. Miller and Sanjurjo (2018) later showed that the standard way of measuring streaks contains a subtle selection bias; correcting for it reversed the original conclusion and pointed to a real, if modest, hot hand. The gambler's fallacy about genuinely independent events, such as roulette spins, remains an error.

How to avoid the gambler's fallacy

Ask whether the events are truly independent. If each trial is a fresh spin, draw or flip, past results carry no information about the next one.
Restate the odds for the next trial only. 'What is the chance of black on this spin?' has the same answer whatever happened on the last ten spins.
Expect streaks. Long runs are a normal feature of random sequences; seeing one is not evidence that a correction is coming.
In repeated professional decisions, judge each case on its own merits and check your decisions for streak patterns — for example, whether approvals become rarer after a run of approvals.
Hide or ignore history boards and 'hot/cold number' displays designed to suggest patterns that do not exist.

How to design for it (nudge strategy)

Make independence visible: show that the odds on the next trial are unchanged, avoid displaying recent-history boards that invite pattern-seeking, and in professional settings review decisions in randomized order and audit for streak effects.

Ethical use: design for choices people would endorse on reflection — a nudge, not sludge. Be transparent and keep opting out easy.

Key studies

Showed that people, including trained researchers, expect small samples to be highly representative of the population — the intuition behind the gambler's fallacy.
Tversky, A., & Kahneman, D. (1971). Belief in the law of small numbers. Psychological Bulletin, 76(2), 105–110. DOI →
In the Maryland daily numbers game, money bet on a number fell sharply right after it was drawn and recovered only gradually over several months.
Clotfelter, C. T., & Cook, P. J. (1993). The 'gambler's fallacy' in lottery play. Management Science, 39(12), 1521–1525. DOI →
In 18 hours of videotaped casino roulette (139 players), bets increasingly went against streaks of five or more; after streaks of six or more, 85% of such bets followed the gambler's fallacy.
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. DOI →
Found negatively autocorrelated decisions unrelated to case merits in all three settings, stronger among less experienced decision-makers, after longer streaks and when incentives for accuracy were weaker.
Chen, D. L., Moskowitz, T. J., & Shue, K. (2016). Decision making under the gambler's fallacy: Evidence from asylum judges, loan officers, and baseball umpires. Quarterly Journal of Economics, 131(3), 1181–1242. DOI →

Key research

Errors in Probabilistic Reasoning and Judgment BiasesDaniel J. Benjamin · Handbook of Behavioral Economics: Applications and Foundations 1 (2019)

Gambler's Fallacy: frequently asked questions

What is the gambler's fallacy in simple terms?

It is believing that a random outcome is 'due' because it has not happened for a while — for example, expecting tails after a string of heads.

Why is it called the Monte Carlo fallacy?

The name refers to the famous casino in Monte Carlo, where roulette players have long bet on the belief that a color or number is due after a streak.

What is the difference between the gambler's fallacy and the hot-hand fallacy?

The gambler's fallacy expects a streak to end; the hot-hand fallacy expects it to continue. Both read patterns into independent events, but in opposite directions.

Does the gambler's fallacy affect professionals?

Yes. Chen, Moskowitz and Shue (2016) found decision patterns consistent with it among asylum judges, loan officers and Major League Baseball umpires.

Is the gambler's fallacy ever correct?

Only when events are not independent. Drawing cards without replacing them does change the odds of what comes next; spinning a fair roulette wheel or flipping a fair coin does not.

Cite this page

Raja, P. (Ed.). (2026, 8 Oct 2026). Gambler's Fallacy. Behavioral Economics Lab. https://www.behavioraleconomicslab.com/biases/gamblers-fallacy

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