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In this paper, we consider how to search for a mobile evader in a large heterogeneous region when sensors are used for detection. Sensors are modeled using probability of detection. Due to environmental effects, this probability will not be constant over the entire region. We map this problem to a graph-search problem, and even though deterministic graph search is NP-complete, we derive a tractable optimal probabilistic search strategy. We do this by defining the problem as a dynamic game played on a Markov chain. We prove that this strategy is optimal in the sense of Nash. Simulations of an example problem illustrate our approach and verify our claims.