On the Robustness and Provenance of the Gambler’s Fallacy

The gambler’s fallacy is typically defined as the false belief that a random event is less likely to occur if it has occurred recently. Although forms of this fallacy have been documented numerous times, past work either has not actually measured probabilistic predictions but rather point predictions or used sequences that were not independent. To address these problems, we conducted a series of high-powered, preregistered studies in which we asked 750 adult Amazon Mechanical Turk workers from the United States to report probabilistic predictions for truly independent sequences. In contrast to point predictions, which generated a significant gambler’s fallacy, probabilistic predictions were not found to lead to a gambler’s fallacy. Moreover, the point predictions could not be reconstructed by sampling from the probability judgments. This suggests that the gambler’s fallacy originates at the decision stage rather than in probabilistic reasoning, as posited by several leading theories. New theories of the gambler’s fallacy may be needed to explain these findings.