The present work examines persistence in situations where delays are open-ended. From a normative standpoint, appropriate behavior in such situations depends on the statistical distribution of possible delay lengths. Depending on this distribution it may be appropriate either to persist indefinitely or to give up after a short period of time. In a behavioral experiment, human participants experienced reward timing statistics that implied it was productive to adopt either a high or low level of persistence. Human decision makers were highly responsive to these statistical cues. In a condition where timing statistics implied patience was productive, participants performed exceptionally well, and had little difficulty in waiting for delayed outcomes. In contrast, participants showed substantially lower willingness to wait when temporal statistics implied patience was an inappropriate strategy. The results demonstrate that seemingly impatient behavior can arise as an adaptive response to the perceived statistics of the environment.