Eight tennis players take part in an elimination tournament and are placed at random. The players are ranked 1, 2, ..., 8, so the player ranked 1 is first (best) and the player ranked 8 is last (worst). When two players play a game, the higher-ranked player always wins. Thus, the player ranked first always makes it to the final round. Find the expected value of the rank of the other player in the final round.

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15 September, 04:52

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Shaun Woodward · Answer 1

Averaging over all the possibilities, we see that the answer is 12/7.