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Minibal: Balanced Game-Playing Without Opponent Modeling

Quentin Cohen-Solal, Tristan Cazenave

Abstract

Recent advances in game AI, such as AlphaZero and Athénan, have achieved superhuman performance across a wide range of board games. While highly powerful, these agents are ill-suited for human-AI interaction, as they consistently overwhelm human players, offering little enjoyment and limited educational value. This paper addresses the problem of balanced play, in which an agent challenges its opponent without either dominating or conceding. We introduce Minibal (Minimize & Balance), a variant of Minimax specifically designed for balanced play. Building on this concept, we propose several modifications of the Unbounded Minimax algorithm explicitly aimed at discovering balanced strategies. Experiments conducted across seven board games demonstrate that one variant consistently achieves the most balanced play, with average outcomes close to perfect balance. These results establish Minibal as a promising foundation for designing AI agents that are both challenging and engaging, suitable for both entertainment and serious games.

Minibal: Balanced Game-Playing Without Opponent Modeling

Abstract

Recent advances in game AI, such as AlphaZero and Athénan, have achieved superhuman performance across a wide range of board games. While highly powerful, these agents are ill-suited for human-AI interaction, as they consistently overwhelm human players, offering little enjoyment and limited educational value. This paper addresses the problem of balanced play, in which an agent challenges its opponent without either dominating or conceding. We introduce Minibal (Minimize & Balance), a variant of Minimax specifically designed for balanced play. Building on this concept, we propose several modifications of the Unbounded Minimax algorithm explicitly aimed at discovering balanced strategies. Experiments conducted across seven board games demonstrate that one variant consistently achieves the most balanced play, with average outcomes close to perfect balance. These results establish Minibal as a promising foundation for designing AI agents that are both challenging and engaging, suitable for both entertainment and serious games.
Paper Structure (31 sections, 3 equations, 4 figures, 4 tables, 4 algorithms)

This paper contains 31 sections, 3 equations, 4 figures, 4 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Games as Trees for Best Action Searching
  4. Classical Adversarial Search
  5. Monte-Carlo Tree Search
  6. AlphaZero
  7. Athénan: Unbounded and Descent Minimax
  8. Dynamic Difficulty Adjustment
  9. AlphaDDA
  10. Contribution: Modeling the Balanced Player
  11. First Modeling
  12. Second Modeling
  13. Experiments
  14. Evaluation Protocol
  15. Technical Details
  16. ...and 16 more sections

Figures (4)

  • Figure 1: Average binary gain (left) and average scores (right) as a function of search time (in seconds) for $\mathrm{Minibal_{n}}$ (dotted green curve), $\mathrm{Minibal_{+}}$ (dashed cyan curve), and Unbounded Minimax (black line) across the studied games (in percentage).
  • Figure 2: Average binary gains as a function of search time (in seconds) for $\mathrm{Minibal_{n}}$ (dotted green curve), $\mathrm{Minibal_{+}}$ (dashed cyan curve), and Unbounded Minimax (black line) across the studied games (C.R.: confidence radius).
  • Figure 3: Average scores as a function of search time (in seconds) for $\mathrm{Minibal_{n}}$ (dotted green curve), $\mathrm{Minibal_{+}}$ (dashed cyan curve), and Unbounded Minimax (black line) across all studied games.
  • Figure 4: Average binary gain (left) and average scores (right) as a function of search time (in seconds) for $\mathrm{Minibal_{n}}$ (dotted green curve), $\mathrm{Minibal_{+}}$ (dashed cyan curve), and Unbounded Minimax (black line) across the studied games against MCTS (in percentage).