Research and Implementation of Dots-and-Boxes Chessboard Based on the Game Strings-and-Coins

Abstract

The model of computer game system is important for us to make careful analyses of games; generally this model includes description of the board, rules of the game, searching method and estimation value. Dots-and-Boxes is a familiar paper and pencil game for two players, while Strings-and-Coins is a game invented by Elwin Berlekamp to generalize Dots-and-Coins to general graphs. In this paper we made a detailed analysis trying to talk about if the two games are equivalent and to discuss how to describe the Dots-and-Coins chessboard by generalizing Strings-and-Coins graphs. Because of the advantage of Stings-and-Coins that it can be played on any graph, it can simplify certain Dots-and-Boxes observations and is convenient to recognize the chain or cycle formed in the process of playing game, compared with other descriptions of board, this way is effective in improving the efficiency of programs.