A single elimination tournament is performed in rounds. In each round the teams each play exactly one game and the winners continue, and 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 find a second place winner?
What I don't understand is the transitivity rule, if A beats B wouldn't B be knocked out of the competition completely, how can he even have a change to beat C? Am I missing something. I started by creating a tree for 4 players A, B, C, and D when A beats B, I cross B which mean he can't play with anyone else anymore.