Gambling terms, explained straight

Not to be confused with the Monte Carlo method (a numerical simulation technique) or the hot-hand fallacy (the opposite bias that expects a streak to continue).

Odds, Probability & Bankroll

Monte Carlo fallacy

The Monte Carlo fallacy is the mistaken belief that after a run of the same result in an independent game of chance, the opposite outcome is now due, even though the odds stay the same.

Also called
Gambler's fallacy; fallacy of the maturity of chances1
Famous example
Monte Carlo Casino, 1913: roulette ball landed black 26 times in a row24
Core error
Treating independent trials as if they had negative serial correlation14

Key points

  • The fallacy arises when people infer that outcomes must "even out" after a streak, even though each trial remains independent.34
  • It applies to games of chance such as roulette and dice, where past results do not affect future probabilities.13
  • The opposite bias is the hot-hand fallacy, where a streak is expected to continue rather than reverse.15

Where this term is used

Odds & probability Gambler's fallacy Another name for the Monte Carlo fallacy, the belief that past outcomes affect future independent trials. Odds & probability Hot hand fallacy meaning The opposite bias, where a streak is expected to continue rather than reverse. Odds & probability Kelly betting A bankroll management formula that uses edge and odds, unrelated to streak-based fallacies. Odds & probability Roulette payouts The fixed odds and payouts for roulette bets, where the Monte Carlo fallacy often misleads players. Odds & probability Martingale strategy A betting system that doubles after a loss, often mistakenly justified by the Monte Carlo fallacy. Odds & probability Kelly criterion A mathematical formula for optimal bet sizing, independent of streak-based reasoning.

Sources

  1. Gambler's fallacy en.wikipedia.org Provides the definition, alternative names, and the core error of the fallacy.
  2. Monte Carlo Casino en.wikipedia.org Documents the 1913 Monte Carlo Casino roulette streak that illustrates the fallacy.
  3. Having a Positive Attitude or Doing Good Deeds? An ... - Cronfa cronfa.swan.ac.uk Supports the explanation of how people infer outcomes must even out after a streak.
  4. The number of available sample observations modulates gambler ... pmc.ncbi.nlm.nih.gov Confirms the famous example and the error of treating independent trials as correlated.
  5. Introduction To Monte Carlo Simulation - PMC - NIH pmc.ncbi.nlm.nih.gov Distinguishes the Monte Carlo fallacy from the hot-hand 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.

Written and maintained by Ellis Warrender, writer and maintainer.

Last updated 28 July 2026. Spotted an error? Tell me and it gets fixed and logged on the corrections page.