In a search game, a seeker searches for a hider in some space. The seeker wishes to find the hider as quickly as possible, and the hider wishes to avoid capture as long as possible. In this paper, I will focus on the case where the search space is a star, and the only information the seeker has is the speed of the hider. I will provide algorithms for some cases where the seeker is guaranteed to find the hider and prove optimality for some of these cases. Also, I will look at some cases where the hider can avoid capture indefinitely. I will also present some results for searching on trees.