Computational assessment of sparsity in board games

Abstract

Board games like chess, checkers and go all have squares or points on a matrix-like board and pieces that occupy them throughout the course of a game. The author proposes an evaluation function for the concept of sparsity in such games. Sparsity refers to the general lack of concentration of pieces on the board and is inversely proportional to the perceived density. Evaluating sparsity is important from a visual perspective and useful for computational aesthetics purposes since dense piece configurations can be confusing and less pleasing to the eye. The evaluation function was designed with aesthetics in mind and comparisons with possible alternatives were done, suggesting its advantages. Experiments involving over a thousand chess positions were carried out to validate the function with promising results. An alternative method was also tested using the same data and it was found that evaluating sparsity is not as straightforward as it may seem. The work presented in this paper could therefore be useful to other researchers interested in a viable computational approach to the concept in board games or other areas. © 2008 The University of Wolverhampton.