  In this paper we solve the three-player-game question. A three-player-game
consists of a series of rounds. There are altogether three players. Two players
participate in each round, at the end of the round the loser quits and the
third player enters the ring and another round starts. The game terminates if
all six win-lose relationships appear. During each round, two players win with
equal probability. One is asked to calculate the expectation of the number of
rounds. It turns out to be an exemplary question that involves probabiltiy
theory and dynamic programming. It can serve as an instance or exercise in the
chapter of conditional expectation of any elementary or advanced textbook on
probability.
