A Gambler’s Fallacy for Probability Judgments when Event Sequences Are Truly Random: A Reanalysis of Xiang, Dorst, and Gershman’s (2025) Data

Xiang, Dorst, and Gershman (2025) recently challenged previous research and theory regarding the gambler’s fallacy. They concluded that when sequences of events are truly random, the fallacy is observed for binary predictions but not probability judgments and that binary predictions cannot be reconstructed from probability judgments, in contrast to most theoretical accounts. This “disconnection” implies that new theories may be needed. However, a reanalysis of Xiang et al.’s data using their methods and very similar methods yields strong evidence for a gambler’s fallacy for probability judgments (although not for all participants) and indicates that the gap between probability judgments and binary predictions was overstated. A version of Rabin and Vayanos’s (2010) model accounts for responses to both question types reasonably well, suggesting that such theories are not seriously threatened. Finally, we propose stratified random sampling of sequences as a more efficient method for presenting participants with representative sequences of events.