Briefly Explore the Combinatorial Game

Abstract

The paper talks about a series of games called combinatorial games. Combinatorial games are two-person games with perfect information, no chance moves, and a win-or-lose outcome. To be precise, a combinatorial game is a game that satisfies the following conditions. The paper also talks about the rules of the combinatorial game, such as how many players the game has and the rules of the game specify for both players and each position that moves to other positions a legal move. Then, the meaning of the P-positions and N-positions were introduced. After that, the paper talks about the typical combinatorial game- the game of Nim, another example of the combinatorial game, to illustrate the paper’s point of view. The paper talks about the whole rules of this example game, such as the number of players and the initial configuration of the piles/heaps. The author gives several strategies and talks about why these strategies can help the players win combinatorial games. The paper gives two cases to illustrate the game rules and give a better understanding after all. In the end, the paper gives a Python3 program for combinatorial games, making the ideas of combinatorial games more comprehensive.