Consider a group of players playing a sequence of games. There are k players, having arbitrary initial fortunes. Each game consists of each remaining player putting 1 in a pot, which is then won (with equal probability) by one of them. Players whose fortunes drop to 0 are eliminated. Let T(i) be the number of games played by i, and let T=max iT(i). For the case k=3, martingale stopping theory can be used to derive E[T] and E[T(i)]. When k>3, we obtain upper bounds on E[T] and, in the case in which all players have the same initial fortune, on E[T(i)]. Efficient simulation methods for estimating E[T] and E[T(i)] are discussed.