A gambler’s fallacy for probability judgments when event sequences are truly random: A reanalysis of Xiang, Dorst, and Gershman’s (2025) data

Abstract

In a recent article on the gambler’s fallacy, Xiang, Dorst, and Gershman (2025, Psychological Science 36(6), 451–464) concluded that when event sequences are truly random, the fallacy is observed for binary predictions but not probability judgments and that binary predictions cannot be easily predicted from probability judgments. They suggested that the gambler’s fallacy does not arise from probabilistic reasoning, calling for new theories despite having not tested any existing theory directly. However, in the present article, we show that a more thorough reanalysis of Xiang et al.’s data yields strong evidence for a gambler’s fallacy for probability judgments and undermines the claimed disconnection between probability judgments and binary predictions. We find that an improved version of their representativeness model and a version of Rabin and Vayanos’s (2010, The Review of Economic Studies 77(2), 730–778) model account for both response types reasonably well, suggesting that probabilistic theories are not seriously threatened. Finally, we propose stratified random sampling as a more efficient method for presenting participants with representative event sequences.