The predator-prey shell game predicts random movement of prey across the landscape, whereas the behavioral response race and landscape of fear models predict that there should be a negative relationship between the spatial distribution of a predator and its behaviorally active prey. Additionally, prey have imperfect information on the whereabouts of their predator, which the predator should incorporate in its patch use strategy. I used a one-predator-one-prey system, puma (Puma concolor)-mule deer (Odocoileus hemionus) to test the following predictions regarding predator-prey distribution and patch use by the predator. (1) Pumas will spend more time in high prey risk/low prey use habitat types, while deer will spend their time in low-risk habitats. Pumas should (2) select large forage patches more often, (3) remain in large patches longer, and (4) revisit individual large patches more often than individual smaller ones. I tested these predictions with an extensive telemetry data set collected over 16 years in a study area of patchy forested habitat. When active, pumas spent significantly less time in open areas of low intrinsic predation risk than did deer. Pumas used large patches more than expected, revisited individual large patches significantly more often than smaller ones, and stayed significantly longer in larger patches than in smaller ones. The results supported the prediction of a negative relationship in the spatial distribution of a predator and its prey and indicated that the predator is incorporating the prey's imperfect information about its presence. These results indicate a behavioral complexity on the landscape scale that can have far-reaching impacts on predator-prey interactions.