2020/08/22 by Fangqi Li, Li, Fangqi
Computer Science · #Bayesian Modeling and Causal Inference #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #FOS: Mathematics #Logic, Reasoning, and Knowledge #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2008.09796
openalex publication_date 2020/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.