Abstract: The problem of Aiding the Poor Game put forward by Prof．Herbert Robbins at Columbia University of the USA was researched．In this problem‚the variance of the money provided for each individual needs to be calculated．In this research‚the problem was transformed into a non-homogeneous Markov chain model‚and the one-step transition prob-ability matrix was deduced‚thus proving that the variance approaches zero when the money approaches infinite．Moreover‚the accuracy solution of the problem‚when K＝3and N＝4‚was given．The Monte-Carlo simulation solution‚when N and K are both comparatively great‚was finally given and the coherence of the simulation solution and accurate solution was verified．

Key words:  Aiding the Poor Game, stochastic assigning model, variance, non-homogeneous, Markov chain