Odds, Probability & Bankroll
Gambler's fallacy
The gambler's fallacy is the false belief that a random event is more or less likely to happen because of what has happened before, even though each event is independent.
Key points
- The bias treats random sequences as if they should quickly 'balance out', so a run of the same outcome is expected to be followed by the opposite outcome.3
- For independent trials, earlier results do not alter the chance of the next result; a coin has no memory.7
- The hot-hand fallacy is the opposite error: believing a streak makes the same outcome more likely to continue.6
- The inverse gambler's fallacy infers many prior trials from an unlikely outcome, the reverse direction of inference.8
Example: roulette
After five red numbers in a row on a fair roulette wheel, a player bets on black because 'black is due'. The wheel has no memory: the chance of black on the next spin remains exactly the same as it was before the streak.4
Where this term is used
Not the same as
- Hot hand fallacy meaning — the mistaken belief that a streak makes the same outcome more likely to continue, not reverse
Related terms
Odds & probability
Monte Carlo fallacy
Another name for the gambler's fallacy, named after a famous 1913 roulette incident.
Odds & probability
Hot hand fallacy meaning
The opposite bias: believing a streak makes the same outcome more likely to continue.
Odds & probability
Odds
The ratio of probability of an event occurring to it not occurring.
Odds & probability
Roulette payouts
The fixed odds paid for different roulette bets, independent of past spins.
Odds & probability
Betting odds
How bookmakers express implied probability and potential returns.
Odds & probability
Kelly criterion
A formula for bet sizing that assumes independent probabilities, not streaks.
Sources
- The "Gambler's Fallacy" in Lottery Play nber.org Supports the definition and the concept of independence of trials.
- Gambler's fallacy en.wikipedia.org Provides the alternative names Monte Carlo fallacy and fallacy of the maturity of chances.
- [PDF] The Gambler's and Hot-Hand Fallacies: Theory and Applications - LSE personal.lse.ac.uk Supports that the fallacy applies to coin flips, roulette, and lottery, and explains the 'balancing out' bias.
- The gambler's fallacy in problem and non-problem gamblers pmc.ncbi.nlm.nih.gov Supports that the fallacy applies to roulette and lottery play.
- The Gambler's Fallacy: A Basic Inhibitory Process? - PMC pmc.ncbi.nlm.nih.gov Supports the definition and the independence of trials.
- Culture and gambling fallacies - PMC - NIH pmc.ncbi.nlm.nih.gov Distinguishes the gambler's fallacy from the hot-hand fallacy.
- Discussion pmc.ncbi.nlm.nih.gov Supports that earlier results do not alter the chance of the next result.
- Inverse gambler's fallacy en.wikipedia.org Defines the inverse gambler's fallacy.
Sources are drawn from regulators, universities and published research, and each one is labelled with what it actually is — a preprint is not called a paper. Bookmaker and affiliate pages are never cited here, because a page that sells betting is not a neutral authority on it.