Adding possibilities can reduce the Gambler's Fallacy: A naïve-probability paradox

This paper reports a novel paradox of intuitive probabilistic reasoning detected in naïve reasoners’ responses in two separate experiments where we manipulated the number of sets (or possibilities) of the problem keeping constant the probability of the critical set. Experiment 1 showed that the incidence of the Gambler's Fallacy (GF) was reduced when the number of sets was increased. In Experiment 2, a reduction of the GF also occurred but, more importantly, the percentage of correct responses of the participants increased when three sets of possibilities instead of two were used. Therefore, both Experiments 1 and 2 demonstrated that an increase in the extensional complexity of a problem can, under certain circumstances, lead to facilitation. These results support the importance of the extensional features in solving chance problems and are consistent with the model theory of reasoning.