Several different “hat games ” have recentlyreceived afair amount of attention. Typically, in a hat game, one or more players are required to correctly guess their hat colour when given some information about other players ’ hat colours. Some versions of these games have been motivated by research in complexity theory and have ties to well-known research problems in coding theory, and some variations have led to interesting new research. In this paper, we review Ebert’s Hat Game [5, 6] which garnered a considerable amount of publicity in the late 90’s and early 00’s , and the Hats-on-a-line Game [2, 3]. Then we introduce a new hat game which is a “hybrid ” of these two games and provide an optimal strategy for playing the new game. The optimal strategy is quite simple, but the proof involves an interesting combinatorial argument.