This study examines how people deal with inherently stochastic cues when estimating a latent environmental property. Seven cues to a hidden location were presented one at a time in rapid succession. The seven cues were sampled from seven different Gaussian distributions that shared a common mean but differed in precision (the reciprocal of variance). The experimental task was to estimate the common mean of the Gaussians from which the cues were drawn. Observers ran in two conditions on separate days. In the “decreasing precision” condition the seven cues were ordered from most precise to least precise. In the “increasing precision” condition this ordering was reversed. For each condition, we estimated the weight that each cue in the sequence had on observers' estimates and compared human performance to that of an ideal observer who maximizes expected gain. We found that observers integrated information from more than one cue, and that they adaptively gave more weight to more precise cues and less weight to less precise cues. However, they did not assign weights that would maximize their expected gain, even over the course of several hundred trials with corrective feedback. The cost to observers of their suboptimal performance was on average 16% of their maximum possible winnings.