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Probability puzzle 2 SOLUTION and EXPLANATION

Posted By: Bob Koca
Date: Sunday, 28 April 2019, at 3:17 p.m.

In Response To: Probability puzzle 2 (Ray Kershaw)

In a single elimination tourney with N players there will be N - 1 games played (since each game played eliminates one player).

In any particular game the probability it involves those two players is (2/N)(1/N-1). Multiplying by the (N-1) games gives 2/N.

Even though the probabilities are dependent they can be added N-1 times since for a 0 - 1 variable the probabilities can be seen as expected values which do add.

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Note that the 2/N value applies to any single elimination formats with a random draw. Maybe it is a playoff round coming from a Swiss (like has been done before). One player is slotted into the round of 4, 2 others are given a round of 8 position, and then 16 other players are given a round of 32 position. Or maybe it is like bowling tournaments are sometimes done: The finalists are ranked from 1 to N. The first match is between N and N-1, the winner goes on to play N-2, that winner goes on to play N -3, until someone plays player 1 for the championship.

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