Combining Combinatorial Game Theory with an α-β Solver for Domineering

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 NegaScout search with many possible enhancements. This technique is applicable to every game, mainly limited to 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 we show that the methods can be combined in a fruitful way by using endgame databases filled with CGT values.

We apply this technique to the game of Domineering, a well-known partisan type of combinatorial game. Our test suite consisted of all 36 non-trivial boards with dimensions from 2 to 7. Endgame databases were created for all subgames of size 15 and less. The CGT values were calculated using the CGSUITE package. We show how CGT values of subgames can be used in several ways as refinements of a basic NegaScout solver. Experiments reveal up to 99% reduction in number of nodes investigated.