Let p(¸≥0.5) denote the probability that team A beats team B in a single game. The series continues until either A or B wins n games. Assuming that these games are independent replications, we study some features of the distribution of Xn, the number of games played in the series. It is shown that Xn is unimodal, has an IFRA distribution, and is stochastically decreasing in p. Close approximations to its mode, mean, and variance are given. Finally, it is shown that the maximum-likelihood estimator of p based on Xn is unique.
