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On the Robustness and Provenance of the Gambler's Fallacy.

Psychological science·2025
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Related Experiment Video

Updated: Jul 7, 2026

A Tactile Automated Passive-Finger Stimulator (TAPS)
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Bayesians Commit the Gambler's Fallacy.

Kevin Dorst1

  • 1Department of Linguistics and Philosophy, Massachusetts Institute of Technology.

Cognitive Science
|January 27, 2026
PubMed
Summary

The gambler's fallacy, the belief that random events will correct themselves, may not be irrational. It can be a rational response to uncertainty and limited data, even with large datasets.

Keywords:
Bayesian updatingCausal reasoningGambler's fallacyHot‐hand fallacyMemory limitsResource‐rational analysis

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Area of Science:

  • Cognitive Science
  • Behavioral Economics
  • Probability Theory

Background:

  • The gambler's fallacy is commonly viewed as a cognitive bias indicating irrationality.
  • This fallacy involves expecting random processes to self-correct, such as predicting a different outcome after a streak.

Purpose of the Study:

  • To investigate whether the gambler's fallacy can be explained as a rational response.
  • To model Bayesian agents with causal uncertainty and limited memory encountering random data.

Main Methods:

  • Simulating Bayesian agents with varying degrees of causal uncertainty.
  • Observing agent responses to statistically independent random processes.
  • Analyzing agent predictions after different sequences of outcomes.

Main Results:

  • Bayesian agents with initial causal uncertainty exhibited the gambler's fallacy.
  • Agents ruled out 'streaky' hypotheses faster than 'switchy' ones, leading to asymmetric confidence.
  • Limited memory exacerbated the fallacy, persisting even with large amounts of data.

Conclusions:

  • The gambler's fallacy can arise from rational Bayesian inference under conditions of uncertainty and limited memory.
  • Observed empirical trends in gambler's fallacy studies align with these rational, albeit limited, Bayesian responses.
  • This suggests that apparent irrationality may stem from adaptive strategies to incomplete information.