Nonhuman animal models show that reinforcers control behavior through what they signal about the likelihood of future events, but such control is generally imperfect. Imperfect control by the relation between past and likely future events may result from imperfect detection of those events as they occur, which result in imperfect detection of the relation between events. Such an approach would suggest the involvement of more complex psychological processes like memory in simple operant learning. We extended a research paradigm previously examined with nonhuman animals to test the ability of a quantitative model that assumes imperfect control by the relation between events arises because of (a) occasional misallocation of reinforcers to the wrong response, causing imperfect control by the relation between events; and (b) a tendency to explore or exploit which is independent of the relation between events. Children played a game in which one of two different responses could produce a reinforcer. The likelihood of a reinforcer for the same response that produced the last one varied across three conditions (.1, .5, .9). As with nonhuman animal models, children's choices followed these probabilities closely but not perfectly, suggesting strong control by what one reinforcer signals about subsequent reinforcers. Choice was well described by the quantitative model. This same model also provides a good description of nonhuman animal-model data, suggesting fundamentally similar mechanisms of control across species. These findings suggest reinforcers control behavior to the extent the relation between reinforcers can be detected-that is, simple operant learning may be more complex than is typically assumed.