This analysis considers a search problem in which the search is directed against a conscious evader or an object controlled by a conscious evader. It is a two-person, zero-sum game called a search evasion game. Although the searcher cannot observe any of the evaders actions, the evader can observe the searchers and can capitalize on errors that he makes. At the beginning of the game, the evader hides in one of several boxes. The search process consists of a sequence of looks into the various boxes until the evader is found. Each look into a given box takes a fixed amount of time. If the searcher looks into the box in which the evader is located, he will find the evader with a certain probability--the detection probability associated with the box in question. A particular evasion device is assumed the evader can move from one box to another between looks. A cost is usually associated with such a move.