We present a methodology for finding globally optimal knockout tournament designs when partial information is known about the strengths of the players. Our approach involves maximizing an expected utility through a Bayesian optimal design framework. Given the prohibitive computational barriers connected with direct computation, we compute a Monte Carlo estimate of the expected utility for a fixed tournament bracket, and optimize the expected utility through simulated annealing. We demonstrate our method by optimizing the probability that the best player wins the tournament. We compare our approach to other knockout tournament designs, including brackets following the standard seeding. We also demonstrate how our approach can be applied to a variety of other utility functions, including whether the best two players meet in the final, the consistency between the number of wins and the player strengths, and whether the players are matched up according to the standard seeding.
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