Random Knockout Tournaments
研究了随机淘汰赛中选手的获胜概率，给出了最佳选手获胜概率的下界以及所有选手的上下界，并针对特殊情形分析了最佳赛制。
We consider a random knockout tournament among players 1,…, n, in which each match involves two players. The match format is specified by the number of matches played in each round, where the constitution of the matches in a round is random. Supposing that there are numbers v 1 ,…, v n such that a match between i and j will be won by i with probability v i /(v i + v j ), we obtain a lower bound on the tournament win probability for the best player, as well as upper and lower bounds for all of the players. We also obtain additional bounds by considering the best and worst formats for player 1 in the special case v 1 > v 2 = v 3 = … = v n .