How effective is incidental learning of the shape of probability distributions?

The idea that people learn detailed probabilistic generative models of the environments they interact with is intuitively appealing, and has received support from recent studies of implicit knowledge acquired in daily life. The goal of this study was to see whether people efficiently induce a probability distribution based upon incidental exposure to an unknown generative process. Subjects played a 'whack-a-mole' game in which they attempted to click on objects appearing briefly, one at a time on the screen. Horizontal positions of the objects were generated from a bimodal distribution. After 180 plays of the game, subjects were unexpectedly asked to generate another 180 target positions of their own from the same distribution. Their responses did not even show a bimodal distribution, much less an accurate one (Experiment 1). The same was true for a pre-announced test (Experiment 2). On the other hand, a more extreme bimodality with zero density in a middle region did produce some distributional learning (Experiment 3), perhaps reflecting conscious hypothesis testing. We discuss the challenge this poses to the idea of efficient accurate distributional learning.