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Semi-Strongly solved: a New Definition Leading Computer to Perfect Gameplay

Hiroki Takizawa

TL;DR

This study introduces a novel definition called `semi-strongly solved' and proposes an algorithm to achieve this type of solution efficiently and derives the theoretical computational complexity of the algorithm under a simple condition, and applies it to the game of 6x6 Othello.

Abstract

Solving combinatorial games has been a classic research topic in artificial intelligence because solutions can offer essential information to improve gameplay. Several definitions exist for `solving the game,' but they are markedly different regarding computational cost and the detail of insights derived. In this study, we introduce a novel definition called `semi-strongly solved' and propose an algorithm to achieve this type of solution efficiently. This new definition addresses existing gaps because of its intermediate computational cost and the quality of the solution. To demonstrate the potential of our approach, we derive the theoretical computational complexity of our algorithm under a simple condition, and apply it to semi-strongly solve the game of 6x6 Othello. This study raises many new research goals in this research area.

Semi-Strongly solved: a New Definition Leading Computer to Perfect Gameplay

TL;DR

This study introduces a novel definition called `semi-strongly solved' and proposes an algorithm to achieve this type of solution efficiently and derives the theoretical computational complexity of the algorithm under a simple condition, and applies it to the game of 6x6 Othello.

Abstract

Solving combinatorial games has been a classic research topic in artificial intelligence because solutions can offer essential information to improve gameplay. Several definitions exist for `solving the game,' but they are markedly different regarding computational cost and the detail of insights derived. In this study, we introduce a novel definition called `semi-strongly solved' and propose an algorithm to achieve this type of solution efficiently. This new definition addresses existing gaps because of its intermediate computational cost and the quality of the solution. To demonstrate the potential of our approach, we derive the theoretical computational complexity of our algorithm under a simple condition, and apply it to semi-strongly solve the game of 6x6 Othello. This study raises many new research goals in this research area.

Paper Structure

This paper contains 16 sections, 1 figure, 3 tables.

Table of Contents

  1. Introduction
  2. Methods
  3. Definition of Semi-Strongly Solved
  4. Reopening Alpha-Beta Algorithm
  5. Kinds and Generation Rules of Nodes
  6. Intuitive Explanation of Each Nodes
  7. Complexity Analysis
  8. Algorithm Description
  9. Transposition Table
  10. Experimental Settings
  11. The Rules of the game of Othello
  12. Materials
  13. Experimental Results
  14. Numbers of Reachable Positions of the game of 6x6 Othello
  15. Discussion
  16. ...and 1 more sections

Figures (1)

  • Figure 1: The schematic diagram of semi-strong solving for the case where $b=3$. In the graph, nodes represent game positions, and edges represent moves. Nodes are color-coded based on whether the AI or the human can reach them. Edges labeled with "?" or "??" are either not the best move or are the same game-theoretic value as the best move but are not designated as the best move. Dashed edges indicate that subsequent graphs are omitted.