What is the gambler’s fallacy?

The mistaken belief that past independent random outcomes affect future ones — e.g. that black is "due" after a run of reds. The odds actually reset every spin.

Why is it called the Monte Carlo fallacy?

After a 1913 Monte Carlo casino night when roulette landed on black 26 times in a row; gamblers lost fortunes betting on red, certain it was "due."

How is it different from regression to the mean?

Regression to the mean is real — extremes tend to be followed by averages. The gambler’s fallacy is false — it wrongly assumes independent events "balance out" in the short run.

The gambler’s fallacy

Also known as the Monte Carlo fallacy · Probability & judgement

The gambler’s fallacy is the belief that past random events change the odds of future ones — that after a run of reds, black is "due." For independent events the probability resets every time; the coin has no memory.

By the ReadGlobe Editors · Reviewed 2026-05-29

Why it happens

We expect even short sequences to look "representative" of randomness, so a streak feels like it must balance out soon. But independence means each trial is unaffected by the last.

The coin has no memory — a streak is a story imposed on noise that has none.

Examples

Betting on black after five reds on roulette — the odds are still about 50/50.
Assuming a couple with four daughters is "due" a son.
Thinking a slot machine that hasn’t paid out is "about to."

How to counter it

For independent events, ignore the streak — the odds reset every trial.
Ask whether the outcome actually depends on the previous one. Often it doesn’t.
Don’t confuse "an unlikely sequence" with "an unlikely next event."

The deeper point

The gambler’s fallacy and the hot-hand fallacy are mirror errors from one root: the gambler thinks a streak must break, the hot-hand believer thinks it must continue. Both impose a story on noise that has none.

Frequently asked

What is the gambler’s fallacy?: The mistaken belief that past independent random outcomes affect future ones — e.g. that black is "due" after a run of reds. The odds actually reset every spin.
Why is it called the Monte Carlo fallacy?: After a 1913 Monte Carlo casino night when roulette landed on black 26 times in a row; gamblers lost fortunes betting on red, certain it was "due."
How is it different from regression to the mean?: Regression to the mean is real — extremes tend to be followed by averages. The gambler’s fallacy is false — it wrongly assumes independent events "balance out" in the short run.

Base-rate neglect Recency bias Availability heuristic Bayesian thinking Regression to the mean

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The books behind better thinking

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Prefer to read? The canonical picks:

Thinking, Fast and Slow — Daniel Kahneman
The Art of Thinking Clearly — Rolf Dobelli
The Great Mental Models, Volume 1 — Shane Parrish
Poor Charlie’s Almanack — Charlie Munger
Super Thinking — Gabriel Weinberg & Lauren McCann
Seeking Wisdom — Peter Bevelin

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APA

ReadGlobe. (2026). The gambler’s fallacy. https://readglobe.com/bias/gamblers-fallacy/

MLA

"The gambler’s fallacy." ReadGlobe, 29 May 2026, readglobe.com/bias/gamblers-fallacy/.

Primary source: Wikipedia

Editorial synthesis © ReadGlobe 2026, drawing on Kahneman’s Thinking, Fast and Slow, the Tversky–Kahneman research program, and the primary cognitive-science literature. · Last reviewed 2026-05-29.