Two models of how people predict the next outcome in a sequence of binary events were developed and compared on the basis of gambling data from a lab experiment using hierarchical Bayesian techniques. The results from a student sample (N = 39) indicated that a model that considers run length (“drift model”)—that is, how often the same event has previously occurred in a row—provided a better description of the data than did a stationary model taking only the immediately prior event into account. Both, expectation of negative and of positive recency was observed, and these tendencies mostly grew stronger with run length. For some individuals, however, the relationship was reversed, leading to a qualitative shift from expecting positive recency for short runs to expecting negative recency for long runs. Both patterns could be accounted for by the drift model but not the stationary model. The results highlight the importance of applying hierarchical analyses that provide both group- and individual-level estimates. Further extensions and applications of the approach in the context of the prediction literature are discussed.