There are N players in a tennis tournament. Assuming the initial pairings are done randomly, what are the odds that a certain pair will play each other?

Simulations suggest the odds of a given pair playing in a N-player tournament is 2/N.
Assuming that all players are equally matched and that the first round games and byes are all randomly constructed, then every tournament is equally likely to occur. Any given tournament consists of N-1 pairings (this number coming from another rather famous puzzle), out of a total of N choose 2 possible pairs. Thus, all things being equally likely, the probability that a stated pairing actually occurs in a tournament is (N-1)/C(N,2)=2/N.

Posted by owl on 2005-08-18 14:56:32