Human and mouse subjects tried to anticipate at which of 2 locations a reward would appear. On a randomly scheduled fraction of the trials, it appeared with a short latency at one location; on the complementary fraction, it appeared after a longer latency at the other location. Subjects of both species accurately assessed the exogenous uncertainty (the probability of a short versus a long trial) and the endogenous uncertainty (from the scalar variability in their estimates of an elapsed duration) to compute the optimal target latency for a switch from the short- to the long-latency location. The optimal latency was arrived at so rapidly that there was no reliably discernible improvement over trials. Under these nonverbal conditions, humans and mice accurately assess risks and behave nearly optimally. That this capacity is well-developed in the mouse opens up the possibility of a genetic approach to the neurobiological mechanisms underlying risk assessment.