Combining combinatorial game theory with an α-β Solver for Clobber: Theory and Experiments

Abstract

Combinatorial games are a special category of games sharing the property that the winner is by definition the last player able to move. To solve such games two main methods are being applied. The first is a general α-β search with many possible enhancements. This technique is applicable to every game, mainly limited by the size of the game due to the exponential explosion of the solution tree. The second way is to use techniques from Combinatorial Game Theory (CGT), with very precise CGT values for (subgames of) combinatorial games. This method is only applicable to relatively small (sub)games. In this paper, which is an extended version of [7], we show that the methods can be combined in a fruitful way by incorporating an endgame database filled with CGT values into an α-β solver. We apply this technique to the game of Clobber, a well-known all-small combinatorial game. Our test suite consists of 20 boards with sizes up to 18 squares. An endgame database was created for all subgames of size 8 and less. The CGT values were calculated using the CGSUITE package. Experiments reveal reductions of at least 75% in number of nodes investigated.