The Optimal Strategy Of Multi-player Large Nim Game

This paper mainly studies the Large Nim game involving any n players,which can be described as:there are n players and N stacks of chips(x₁,x₂,…,x_N),where n?2 and N are any given positive integers,and x_i represents the amounts of chips in i.n players take turns in sequence,each player is required to remove any positive integer chips from the maximum pile in their decision round(at least one,or the whole stack of chip),the first players who cannot make a legal move winning.The full text is divided into four chapters:The first chapter mainly introduces the history and development of fair combination game,expounds the basic concept and research status.The second chapter studies the Large Nim game model involving any number of players,which is a generalized process from the Large Nim of two players to multiple players.Under the standard alliance matrix,we use recursive functions to obtain the corresponding game values and the optimal winning strategy respectively,aiming at the three relationships between the number of players n and the number of heaps N:n>N+1,n=N+1,n=N.At the same time,we also analyzed the reason why it is difficult to determine the game value when n?N-1.In the third chapter,we study the Large Nim game with a random player.Under the standard alliance matrix,we distinguish the two cases n=3 and n?4,and determine the value of a Large Nim game with n player that exactly contains a random player.We analyzed the effect of the presence of random players on the probability of winning and strategy of each play(including random players).By an example,it is difficult to determine the value of a game with n player N heap Large Nim and one random participant.In the fourth chapter,we continue to discuss how the existence of random players affect each player.In this chapter,we study the Chomp model,under the standard alliance matrix,we determine the game value and the optimal winning strategy of n player Chomp game with one random player in two cases.