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

Psychological science·2025

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Bayesians Commit the Gambler's Fallacy.

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

Cognitive Science

|January 27, 2026

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 updating Causal reasoning Gambler's fallacy Hot‐hand fallacy Memory limits Resource‐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.