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We consider a best-of-three Tullock contest between two ex-ante symmetric players. An effort-maximizing designer commits to a vector of three biases (advantages or disadvantages), one per match. When the designer can choose victory-dependent biases (i.e., biases that depend on the record of matches won by players), the effort-maximizing biases eliminate the momentum effect, leaving players equally likely to win each match and the overall contest. Instead, when the designer can only choose victory-independent biases, the effort-maximizing biases alternate advantages in the first two matches and leave players not equally likely to win the overall contest. Therefore, in the victory-independent optimal contest, ex-ante symmetric players need not be treated identically, though a coin flip may restore ex-ante symmetry. We analyze several extensions of our basic model, including generalized Tullock contests, ex-ante asymmetric players, best-of-five contests, and winner's effort maximization.
