Construction, observation and knowledge abstraction for go endgames on small boards

Area of Science:

• Artificial Intelligence
• Game Theory
• Computational Complexity

Background:

• Go endgame databases are crucial for analyzing optimal strategies with limited pieces on an N by N board.
• Previous research has not fully explored the impact of board size parity and move repetition rules on endgame outcomes.

Purpose of the Study:

• To develop methods for constructing Go endgame databases for small board sizes (S <= 4).
• To investigate the influence of board size (even vs. odd N) and move repetition rules on game values and player advantage.
• To identify factors contributing to the difficulty of Go endgame positions.

Main Methods:

• Construction of Go endgame databases for N x N boards with S <= 4 pieces.
• Implementation of two rules for handling cycles of plies: one allowing and one disallowing repetition.
• Utilized the KataGo deep learning engine to solve positions and assess difficulty factors.

Main Results:

• Optimal game values differ significantly between even and odd N boards, irrespective of repetition rules.
• Player dominance shifts based on board parity and repetition rules: first player dominates odd N, players are equal on even N with repetition allowed.
• Identified distributions of optimal game values, cardinality, and values of true optimal moves as key difficulty indicators.

Conclusions:

• Board size parity and move repetition rules fundamentally alter Go endgame dynamics and player strengths.
• A simple formula can predict endgame difficulty with reasonable accuracy for a subset of positions.
• Findings provide insights into the fundamental properties of Go and offer tools for analyzing endgame complexity.