A knockout tournament, such as the NCAA March Madness Basketball Championship (i

Question

A knockout tournament, such as the NCAA March Madness Basketball Championship (in the U.S.) is performed in rounds. In each round the teams each play exactly one game and the winners progress, while the losers are knocked out of the competition. So, in each round, exactly half of the teams are eliminated. At the completion of the tournament, there is one winner who is undefeated. Assuming that when two teams play each other the outcome is always the same and assuming transitivity (i.e. A beats B and B beats C implies A would beat C), how many more games would have to be played to always find a second place winner? We need the exact number, not an asymptotic bound!

Explanation / Answer

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