Human belief in the Gambler’s Fallacy and the Hot Hand phenomenon has intrigued scientists and thinkers for centuries. New research suggests that these judgment patterns arise from mental models of how sequences are generated, influenced by the strength of prior beliefs. In a series of experiments, participants observed different mechanisms generating sequences of binary events and their beliefs about the base rate probabilities were manipulated. The results showed that participants often exhibited pragmatic belief updating, expecting streaks of identical outcomes to continue as the length of the streak increased. However, when a random mechanical device with a fixed base rate was involved, participants showed a bias towards expecting streak reversals. This bias was more pronounced when participants made dichotomous choices rather than numerical probability ratings. These findings challenge alternate explanations and support Rabin’s version of Tversky & Kahneman’s Law of Small Numbers. The study sheds light on how human beliefs can both adhere to patterns and deviate from them. For more details, read the full article!

Abstract
Beliefs like the Gambler’s Fallacy and the Hot Hand have interested cognitive scientists, economists, and philosophers for centuries. We propose that these judgment patterns arise from the observer’s mental models of the sequence-generating mechanism, moderated by the strength of belief in an a priori base rate. In six behavioral experiments, participants observed one of three mechanisms generating sequences of eight binary events: a random mechanical device, an intentional goal-directed actor, and a financial market. We systematically manipulated participants’ beliefs about the base rate probabilities at which different outcomes were generated by each mechanism. Participants judged 18 sequences of outcomes produced by a mechanism with either an unknown base rate, a specified distribution of three equiprobable base rates, or a precise, fixed base rate. Six target sequences ended in streaks of between two and seven identical outcomes. The most common predictions for subsequent events were best described as pragmatic belief updating, expressed as an increasingly strong expectation that a streak of identical signals would repeat as the length of that streak increased. The exception to this pattern was for sequences generated by a random mechanical device with a fixed base rate of .50. Under this specific condition, participants exhibited a bias toward reversal of streaks, and this bias was larger when participants were asked to make a dichotomous choice versus a numerical probability rating. We review alternate accounts for the anomalous judgments of sequences and conclude with our favored interpretation that is based on Rabin’s version of Tversky & Kahneman’s Law of Small Numbers.

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