A Subjective Theory of Belief in the Gambler’s Fallacy

• Authors: Jawwad Noor and Fernando Payró Chew
• BSE Working Paper: 1588 | July 2026
• Keywords: belief biases, gambler’s fallacy, mean reversion
• JEL codes: D01, D9

Studies suggest that people often believe that random processes exhibit reversion to the mean, regardless of the size of the sample. In a canonical coin-tossing environment, a belief in mean reversion towards some bias θ∗ is straightforward to define if it is assumed that the tosses are objectively i.i.d. with bias θ ∗ . In this paper we define and represent a belief in mean reversion without assuming the existence of an objective random process. This decouples the notion of a belief in mean reversion from the notion of misspecified beliefs that is predominantly used in the literature.