Superstitious responding and frequency matching in the positive bias and gambler’s fallacy effects

Abstract Three studies showed that success in predicting outcomes of a random binary series was associated with the positive bias effect, whereas failure was associated with the gambler’s fallacy effect. Moreover, success increased confidence and failure decreased it. Although explicit instructions that the source generated random output increased the likelihood of predicting an alternation in the series, these instructions had no effect on the relationships between success and the positive bias effect, and failure and the gambler’s fallacy effect. Importantly, intuitions about the randomness or nonrandomness of the source, assessed immediately prior to each trial, did not influence this interaction. These results suggest that people used a win-stay strategy, but that sensitivity to run length counteracted the corresponding lose-shift tendency. The data support a memory-based explanation of the gambler’s fallacy effect, consistent with the account from local representativeness, but the positive bias effect may be an instance of human superstitious responding.