Learning the generative model of the world based on limited data is an important problem faced by both human and artificial intelligence. How should one choose among multiple generative models that all well fit the existing data? Occam's razor suggests that one should select the simplest one. Here we asked whether Occam’s razor applies to human learning of probability distribution models. On each trial, participants saw 20~160 samples of spatial locations from a Gaussian mixture model and were asked to choose among four different Gaussian mixture models the one that had generated the samples. In three experiments, we found participants did not, as Occam’s razor would suggest, prefer the one-cluster option that appears to be simplest, other things being the same. Instead, they showed preference for options with two or three clusters. Such violation of Occam’s razor sheds light on distinction between complexity-based and experience-based priors for model selection.

Superstitions are false beliefs about causality, closely related to the illusory control of luck. Previous research often focused on their influencing factors, whereas the cognitive processes underlying the formation and persistence of superstitions were understudied. Here we designed a behavioral task to track the evolution of superstitious beliefs over time. In a series of trials participants attempted to produce rewardable keypress patterns, but unbeknown to them the outcomes were independent of their actions. Similarity analysis of keypress patterns revealed that participants adopted the win-stay, lose-shift strategy, a heuristic to maximize rewards, and those under high reward rates converged to a few patterns. Similarly, participants’ perception of controllability were higher under high reward rates but increased with their perceived instead of the actual reward rate across conditions. Our findings suggest that the formation of superstitious beliefs is motivated by reward maximization but associated with distorted perception of reward rate.

People are known for their ability to learn probabilistic rewarding rules of the environment. However, the rules tested in most studies consisted of one feature dimension or a linear combination of multiple features. It is unclear how well people can learn non-linear combinatory rules where each single dimension is noninformative. In an adapted matching-pennies game, we asked participants to predict whether their opponent would choose head or tail next trial. Though the feature space for possible rules was small, including only two binary dimensions (i.e., the two players’ current choices), participants had striking failures in learning the probabilistic XOR rules (e.g., the opponent would have a probability of 0.8 to choose head if the two players had matching pennies and tail for unmatching pennies). The failure persisted in a series of experiments, even when the feature space was made explicit, after 320 trials of learning, and for different cover stories.