Many classical models of food patch use under predation risk assume that predators impose patch-specific predation risks independent of prey behavior. These models predict that prey should leave a chosen patch only if and when the food depletes below some critical level. In nature, however, prey individuals may regularly move among food patches, even in the apparent absence of food depletion. We suggest that such prey movement is part of a predator-prey “shell game”, in which predators attempt to learn prey location, and the prey attempt to be unpredictable in space. We investigate this shell game using an individual-based model that allows predators to update information about prey location, and permits prey to move with some random component among patches, but with reduced energy intake. Our results show the best prey strategy depends on what the predator does. A non-learning (randomly moving) predator favors non-moving prey – moving prey suffer higher starvation and predation. However, a learning predator favors prey movement. In general, the best prey strategy involves movement biased toward, but not completely committed to, the richer food patch. The strategy of prey movement remains beneficial even in combination with other anti-predator defenses, such as prey vigilance.