Predation is a fundamental interaction between species, yet it is unclear what escape strategies are effective for prey survival. Classical theory proposes that prey should either escape in a direction that conforms to a performance optimum or that is random and therefore unpredictable. Here, we show that larval zebrafish (Danio rerio) instead use a mixed strategy that may be either random or directed. This was determined by testing classic theory with measurements of the escape direction in response to a predator robot. We found that prey consistently escaped in a direction contralateral to the robot when approached from the side of the prey's body. At such an orientation, the predator appeared in the prey's central visual field and the contralateral response was consistent with a model of strategy that maximizes the distance from the predator. By contrast, when the robot approached the rostral or caudal ends of the body, and appeared in the prey's peripheral vision, the escape showed an equal probability of a contralateral or ipsilateral direction. At this orientation, a contralateral response offered little strategic advantage. Therefore, zebrafish larvae adopt an escape strategy that maximizes distance from the threat when strategically beneficial and that is otherwise random. This sensory-mediated mixed strategy may be employed by a diversity of animals and offers a new paradigm for understanding the factors that govern prey survival.