Board Game:Dots -2

The aim of this project is to build a board game called “Dots.” Developing this game will enhance students’ ability to program using Visual Basic for Excel. The game is played with two players or a player and a computer. The student should implement the algorithms described below to generate computer moves when the game is played between a player and the computer. Below we describe how to play the game. The playing board for this game consists of an equal number of vertical and horizontal arrays of dots. Players take turns in playing the game. On the player’s turn, the player joins two horizontally or vertically adjacent dots with a line. When the player creates a box by closing its fourth side, the player gets one point, the corresponding box is filled in with the player’s color, and the player gets another turn to play. If the same move completes two boxes, the player gets two points and both boxes are filled in with the player’s color, but the player takes only one extra turn. The game ends when all boxes have been colored. The player who closed the maximum number of boxes wins. The following is a heuristic approach that the students can use to model the movements of the computer when this game is played between a player and a computer. Note that mathematical approaches have been used to model the movements of the computer when this game is played between a computer and a player. The branch of algebra and number theory called “Combinatorial Game Theory” provides relevant intelligence to program the “Dots” board game. If the students are interested in programming this game perfectly so that the computer almost always wins, we refer them to Berlekamp (2000).