Solving games Dependence of applicable solving procedures M.J.H. Heule1? and L.J.M. Rothkrantz2 1 Department of Software Technology 2 Department of Mediamatica Faculty of Electrical Engineering, Mathematics and Computer Sciences Delft University of Technology
[email protected] [email protected] Abstract. We introduce an alternative concept to determine the solv- ability of two-player games with perfect information. This concept - based on games currently solved - claims that the applicable solving procedures have a significant influence on the solvability of games. This contrasts with current views that suggest that solvability is related to state-space and game-tree complexity. Twenty articles on this topic are discussed, including those that describe the currently obtained solutions. Results include a description of the available solving procedures as well as an overview of essential techniques from the past. Besides well-known classic games, the solvability of popular and recent games z`ertz, dvonn, and yinsh is analyzed. We conclude that our proposed concept could de- termine the solvability of games more accurately. Based on our concept, we expect that new solving techniques are required to obtain solutions for unsolved games. 1 Introduction Since the beginning of artificial intelligence, strategic games have captured the imagination of the professionals in this field. Two separate lines of thinking can be pointed out: Can artificial intelligence outperform the human masters in the game? Secondly, can it determine the game-theoretic value of a game when all participants play optimally? This value indicates whether a game is won or lost from the perspective of the player who makes the first move.