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, even when the probability of the event is known to be independent across trials. While forms of this fallacy have been documented numerous times, past work suffers from two problems. First, most studies have not actually measured probabilistic predictions (“60% likely to be heads”), but rather point predictions (“Heads”). Second, the few studies that did measure probabilistic beliefs used sequences that were not independent, and therefore not a strong test of the fallacy. To address these problems, we conducted a series of high-powered, preregistered studies. We asked participants to report probabilistic predictions for truly independent sequences. In contrast to point predictions, which (as in previous research) generated a significant gambler’s fallacy, we found no evidence for a gambler’s fallacy in probabilistic predictions. 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. In a separate experiment, we replicate the results of a previous study showing a small gambler’s fallacy for probabilistic predictions with non-independent sequences. However, to the extent that the gambler’s fallacy manifests for probabilistic predictions, it seems to be driven by a small proportion of the participants. Taken together, these findings demonstrate that the gambler’s fallacy is real and robust for point predictions, but not for probabilistic predictions with independent sequences. New theories of the gambler’s fallacy may be needed to explain these findings.