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A Study of Solving Life-and-Death Problems in Go Using Relevance-Zone Based Solvers

Chung-Chin Shih, Ti-Rong Wu, Ting Han Wei, Yu-Shan Hsu, Hung Guei, I-Chen Wu

TL;DR

The paper examines how Relevance-Zone Based Search (RZS) and Relevance-Zone Pattern Tables (RZPT) enable Go AIs to solve Life-and-Death (L&D) tsumego problems more efficiently. By evaluating two solvers, RZS-TT and RZS-PT, on 83 problems from Cho Chikun’s Life-and-Death Dictionary, the study demonstrates substantial speedups and the automated emergence of RZs and reusable patterns, while also revealing misalignments between AI objectives (e.g., unconditionally alive, faster wins) and human preferences (territory maximization). The findings highlight both the strengths of RZS-based search and the need for augmentations such as rare-pattern data and enhanced endgame features to align AI behavior with human pedagogy. The work also suggests that the RZ approach can generalize to other board games, offering a framework for analyzing planning and pattern reuse in game AI beyond Go.

Abstract

This paper analyzes the behavior of solving Life-and-Death (L&D) problems in the game of Go using current state-of-the-art computer Go solvers with two techniques: the Relevance-Zone Based Search (RZS) and the relevance-zone pattern table. We examined the solutions derived by relevance-zone based solvers on seven L&D problems from the renowned book "Life and Death Dictionary" written by Cho Chikun, a Go grandmaster, and found several interesting results. First, for each problem, the solvers identify a relevance-zone that highlights the critical areas for solving. Second, the solvers discover a series of patterns, including some that are rare. Finally, the solvers even find different answers compared to the given solutions for two problems. We also identified two issues with the solver: (a) it misjudges values of rare patterns, and (b) it tends to prioritize living directly rather than maximizing territory, which differs from the behavior of human Go players. We suggest possible approaches to address these issues in future work. Our code and data are available at https://rlg.iis.sinica.edu.tw/papers/study-LD-RZ.

A Study of Solving Life-and-Death Problems in Go Using Relevance-Zone Based Solvers

TL;DR

The paper examines how Relevance-Zone Based Search (RZS) and Relevance-Zone Pattern Tables (RZPT) enable Go AIs to solve Life-and-Death (L&D) tsumego problems more efficiently. By evaluating two solvers, RZS-TT and RZS-PT, on 83 problems from Cho Chikun’s Life-and-Death Dictionary, the study demonstrates substantial speedups and the automated emergence of RZs and reusable patterns, while also revealing misalignments between AI objectives (e.g., unconditionally alive, faster wins) and human preferences (territory maximization). The findings highlight both the strengths of RZS-based search and the need for augmentations such as rare-pattern data and enhanced endgame features to align AI behavior with human pedagogy. The work also suggests that the RZ approach can generalize to other board games, offering a framework for analyzing planning and pattern reuse in game AI beyond Go.

Abstract

This paper analyzes the behavior of solving Life-and-Death (L&D) problems in the game of Go using current state-of-the-art computer Go solvers with two techniques: the Relevance-Zone Based Search (RZS) and the relevance-zone pattern table. We examined the solutions derived by relevance-zone based solvers on seven L&D problems from the renowned book "Life and Death Dictionary" written by Cho Chikun, a Go grandmaster, and found several interesting results. First, for each problem, the solvers identify a relevance-zone that highlights the critical areas for solving. Second, the solvers discover a series of patterns, including some that are rare. Finally, the solvers even find different answers compared to the given solutions for two problems. We also identified two issues with the solver: (a) it misjudges values of rare patterns, and (b) it tends to prioritize living directly rather than maximizing territory, which differs from the behavior of human Go players. We suggest possible approaches to address these issues in future work. Our code and data are available at https://rlg.iis.sinica.edu.tw/papers/study-LD-RZ.
Paper Structure (16 sections, 9 figures)

This paper contains 16 sections, 9 figures.

Table of Contents

  1. Introduction
  2. Background
  3. Life-and-Death Problems
  4. Relevance-Zone Based Search
  5. Faster-to-Life Network
  6. Relevance-Zone Pattern Table
  7. The Solvers and Problem Sets
  8. Problem Analysis
  9. Problem 1
  10. Problem 2
  11. Problem 3
  12. Problem 4
  13. Problem 5
  14. Problem 6
  15. Problem 7
  16. ...and 1 more sections

Figures (9)

  • Figure 1: The problem is Black to play and live. (a) The minimum restricted area for both players to verify the solutions. (b) A position that might be encountered in the solutions.
  • Figure 2: An example to illustrate relevance-zones in Go, modified from shih_novel_2022.
  • Figure 3: Problem 1, from Volume 1, page 88 of the book.
  • Figure 4: Problem 2, from Volume 2, page 351 of the book.
  • Figure 5: Problem 3, from Volume 1, page 222 of the book.
  • ...and 4 more figures