Solving 7x7 Killall-Go with Seki Database

TL;DR

This paper introduces a seki pattern database for Killall-Go, which significantly reduces search space and improves solving efficiency by recognizing shared liberties and mutual life situations.

Contribution

The paper presents a novel seki pattern enumeration and storage method that enhances game solving efficiency for 7x7 Killall-Go.

Findings

Solved a complex position in 482 seconds using seki table

Achieved 10-20% reduction in search time and node count

Demonstrated effectiveness of seki recognition in game solving

Abstract

Game solving is the process of finding the theoretical outcome for a game, assuming that all player choices are optimal. This paper focuses on a technique that can reduce the heuristic search space significantly for 7x7 Killall-Go. In Go and Killall-Go, live patterns are stones that are protected from opponent capture. Mutual life, also referred to as seki, is when both players' stones achieve life by sharing liberties with their opponent. Whichever player attempts to capture the opponent first will leave their own stones vulnerable. Therefore, it is critical to recognize seki patterns to avoid putting oneself in jeopardy. Recognizing seki can reduce the search depth significantly. In this paper, we enumerate all seki patterns up to a predetermined area size, then store these patterns into a seki table. This allows us to recognize seki during search, which significantly improves solving efficiency for the game of Killall-Go. Experiments show that a day-long, unsolvable position can be solved in 482 seconds with the addition of a seki table. For general positions, a 10% to 20% improvement in wall clock time and node count is observed.