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You and an opponent each split 4 units of funds over 3 districts, and the larger share wins a district. Against a uniformly random opponent, which split is best and which is worst?

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There are 3 districts. You and an opponent each have 4 units of funds to split over the districts in whole units, and in each district the larger allocation wins it (equal is a tie). Whoever wins more districts wins the election. The opponent picks uniformly at random among all allocations. How many allocations does the opponent have, which type of allocation maximises your win probability, and which type minimises it?

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The opponent spreads 9 units over 8 districts as evenly as possible, in positions unknown to you. What is the least funding with which some allocation of yours could win?

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