Role of simulation in developing game playing strategies

Abstract

Results are presented concerning the use of simulation in the analysis of finite games and the development of strategies for their solution. Programs were developed in the Scheme programming language to play large numbers of games pitting various strategies against each other. The games discussed range from the well-known tic-tac-toe, through versions of ConnectThree for various sized boards, to the commercial ConnectFour game. The ConnectThree game is based on ConnectFour, but was developed as a simplification that can be played within a reasonable time by perfect strategies that look ahead to the end of the game. The game is played on a vertical array with players alternately dropping disks of their color into the array. The first player to create a row, column, or diagonal of three disks of the player's own color wins. The ConnectFour game is similar, but requires completion of a line of four disks of one's own color to win. Conducting tournaments involving optimal strategies made it possible to predict for which board sizes the ConnectThree game is a first-player win and for which it is a draw. Using results from the simulation, it has been possible to prove these predictions in almost all cases.