Is the answer the same for a transitive "better" relation, as it is for an intransitive "better" relation? On Mon, Sep 5, 2011 at 2:00 PM, Erich Friedman <efriedma@stetson.edu> wrote:
suppose 16 tennis players enter an unseeded single-elimination tournament, and that the better player wins every match. after 4 stages and 15 matches, the best player (who we call W) wins.
on average, which of the two following players is better?
a) the player who loses to W in the first round,
or
b) the player who won the first match, but then was beaten by the player who was beaten by the player who lost to W in the final round?
the answer, obtained by a 16-fold integral, surprised me.
erich
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