Abstract: In this talk we introduce a game (a similar game was introduced independently by Rosendal) which plays a role for measure analogous to the Banach-Mazur game for category. We establish the basic connections between this game and measure, and then use the game to prove fundamental measure theoretical results such as Fubini's theorem, the Borel-Cantelli lemma, and a strong form of the Renyi-Lamperti Lemma. The proofs we give are all direct combinatorial arguments using the game, and do not depend on known measure theoretic arguments.