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We present a deterministic algorithm, solving discounted games with n nodes in n^O(1)· (2 + √(2))^n-time. For bipartite discounted games our algorithm runs in n^O(1)· 2^n-time. Prior to our work no deterministic algorithm running in time 2^o(nlog n) regardless of the discount factor was known. We call our approach polyhedral value iteration. We rely on a well-known fact that the values of a discounted game can be found from the so-called optimality equations. In the algorithm we consider aarXiv:2007.08575v2 fatcat:fdv66pzkbfhubdi7s34pajb3aq