Solving 7x7 Killall-Go with Seki Database

TL;DR

This paper enumerate all seki patterns up to a predetermined area size, then store these patterns into a seki table, which allows us to recognize seki during search, which significantly improves solving efficiency for the game of Killall-Go.

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.

Figures (3)

• Figure 1: An illustration of a 7x7 Killall-Go opening with two different winning conditions for White.
• Figure 2: Querying the seki database. The enclosed area is shaded in gray based on the last played move (marked with a cross).
• Figure 3: The collection of openings used to evaluate the seki database.