Designing an Artificial Neural Network for state evaluation in Arimaa : Using a Convolutional Neural Network

Abstract: Agents being able to play board games such as Tic Tac Toe, Chess, Go and Arimaa has been, and still is, a major difficulty in Artificial Intelligence. For the mentioned board games, there is a certain amount of legal moves a player can do in a specific board state. Tic Tac Toe have in average around 4-5 legal moves, with a total amount of 255168 possible games. Both Chess, Go and Arimaa have an increased amount of possible legal moves to do, and an almost infinite amount of possible games, making it impossible to have complete knowledge of the outcome. This thesis work have created various Neural Networks, with the purpose of evaluating the likelihood of winning a game given a certain board state. An improved evaluation function would compensate for the inability of doing a deeper tree search in Arimaa, and the anticipation is to compete on equal skills against another well-performing agent (meijin) having one less search depth. The results shows great potential. From a mere one hundred games against meijin, the network manages to separate good from bad positions, and after another one hundred games able to beat meijin with equal search depth. It seems promising that by improving the training and by testing different sizes for the neural network that a neural network could win even with one less search depth. The huge branching factor of Arimaa makes such an improvement of the evaluation beneficial, even if the evaluation would be 10 000 times more slow.