Locally Informed Global Search for Sums of Combinatorial Games

Abstract

There are two complementary approaches to playing sums of combinatorial games. They can be characterized as local analysis and global search. Algorithms from combinatorial game theory such as Hotstrat and Thermostrat [2] exploit summary information about each subgame such as its temperature or its thermograph. These algorithms can achieve good play, with a bounded error. Their runtime depends mainly on the complexity of analyzing individual subgames. Most importantly, it is not exponential in global parameters such as the branching factor and the number of moves in the sum game. One problem of these classic combinatorial game algorithms is that they cannot exploit extra available computation time.

A global minimax search method such as αβ can determine the optimal result of a sum game. However, the solution cost grows exponentially with the total size of the sum game, even if each subgame by itself is simple. Such an approach does not exploit the independence of subgames.

This paper explores combinations of both local and global-level analysis in order to develop locally informed global search algorithms for sum games. The algorithms utilize the subgame structure in order to reduce the runtime of a global αβ search by orders of magnitude. In contrast to methods such as Hotstrat and Thermostrat, the new algorithms exhibit improving solution quality with increasing time limits.