Sorted Bucket Hash and Combinatorial Game Algorithms: Two Efficient Solvers for the Game of NoGo

Abstract

NoGo is a variant of the popular game of Go. NoGo shares the same mechanisms as Go, but it requires stones, once played, to be not removed from the board. Strong computer players have been created for NoGo, yet the game properties and optimal play strategies are not well studied. This thesis describes our recent contributions to solving and understanding NoGo. Two solvers were developed for this purpose: SBHSolver and CGTSolver. SBHSolver uses a newly proposed Sorted Bucket Hash hashing method and its general data structure to build the transposition table. It is capable of weakly solving games on memory-limited machines efficiently. CGTSolver equips Negamax search algorithm with enhancements derived from combinatorial game theory to solve Linear NoGo which is NoGo played on a one-dimensional board. SBHSolver weakly solved all NoGo positions of sizes up to 27 points, and CGTSolver pushed beyond and ultra-weakly solved Linear NoGo up to 39 points. Those achievements were made possible by the improved efficiency of these solvers. Statistical observations of game-playing strategies, rigorous proofs of combinatorial game properties, and detailed experimental results are provided in this thesis