Checkers Move Prediction Algorithms David Johnson & Tyler Beatty

Introduction Checkers defined is “a game for two players using a checkerboard and 12 checkers each. The object is to jump over and capture the opponent's pieces”. Source dictionary.com

Problem Statement Create algorithms that will result in the display of the best move for the user with the lowest possible risk of being overtaken.

Formal Definition In a board containing a set number of spaces, S, in a game board, B, a value number will be assigned for { S ε B } based upon the following cases: A legal move is determined The risk of the move is evaluated The objective benefits from the movement

Offensive Algorithm Favours Captures Does not defend pieces Versus Test Case 42% Going First 56% Going Second

Defensive Algorithm Attempts to prevent capture Moves away when presented with interaction Versus Test Case 54% Going First 58% Going Second

Objective Algorithm Balanced Goals Attempts to Get Kings without losing pieces Versus Test Case 54% Going First 54% Going Second

Experimental Procedure Offensive vs. Defensive DEF wins going first OFF wins going first Defensive vs. Objective DEF wins going first and second Objective vs Offensive OFF wins going First DEF wins going First

Interpretation Against each other, going first is advantageous Using the test case, all have higher results going second Objective Balanced play had the most consistent win percentage

Conclusion Striking a Balanced gamestyle in Checkers Maximizing objectives while minimizing losses With more turns of predictive movement, the better the algorithm

Questions What does it mean for a game to be solved? What is heuristic layering? Is there an optimal conclusion to a checkers game method? Does changing the goal of a move prediction affect the likeliness of winning the game? Will going first or second in the checkers game affect the likeliness of winning the game?

Questions (cont.) A solved is a game whose outcome can be correctly predicted from any position, assuming that both players play perfectly. Heuristic Layers are projected outcomes based on possible changes to data, each layer contains options based on the options of the previous layer. The Offensive algorithm had the least varied win rate between going first and second, possibly indicating it as the most effective of the three. Examining the scatter plots for the three algorithms, the offensive algorithm appears the most consistent and with the least amount of deviation. There is no direct correlation between going first and going second in regards to win percentage.