Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Deduction Game Framework and Information Set Entropy Search

Fandi Meng, Simon Lucas

TL;DR

The paper tackles efficient decision-making in single-player deduction games under limited computation time by introducing Information Set Entropy Search (ISES), a forward-search method that selects actions to maximize expected entropy reduction $E[\Delta H]$ across information sets. It presents a general framework for modeling these games, two representations of information sets, and an entropy-based analysis of game states to quantify uncertainty and strategic depth. Empirical results on eight games show that ISES consistently outperforms baselines like SO-ISMCTS, with a sampling-based variant achieving near-parity on smaller problems and exposing scalability limitations on larger spaces. The work provides a principled, explainable approach to deduction-game AI and offers a foundation for extending entropy-driven methods to multiplayer settings and game-design analysis.

Abstract

We present a game framework tailored for deduction games, enabling structured analysis from the perspective of Shannon entropy variations. Additionally, we introduce a new forward search algorithm, Information Set Entropy Search (ISES), which effectively solves many single-player deduction games. The ISES algorithm, augmented with sampling techniques, allows agents to make decisions within controlled computational resources and time constraints. Experimental results on eight games within our framework demonstrate the significant superiority of our method over the Single Observer Information Set Monte Carlo Tree Search(SO-ISMCTS) algorithm under limited decision time constraints. The entropy variation of game states in our framework enables explainable decision-making, which can also be used to analyze the appeal of deduction games and provide insights for game designers.

Deduction Game Framework and Information Set Entropy Search

TL;DR

The paper tackles efficient decision-making in single-player deduction games under limited computation time by introducing Information Set Entropy Search (ISES), a forward-search method that selects actions to maximize expected entropy reduction across information sets. It presents a general framework for modeling these games, two representations of information sets, and an entropy-based analysis of game states to quantify uncertainty and strategic depth. Empirical results on eight games show that ISES consistently outperforms baselines like SO-ISMCTS, with a sampling-based variant achieving near-parity on smaller problems and exposing scalability limitations on larger spaces. The work provides a principled, explainable approach to deduction-game AI and offers a foundation for extending entropy-driven methods to multiplayer settings and game-design analysis.

Abstract

We present a game framework tailored for deduction games, enabling structured analysis from the perspective of Shannon entropy variations. Additionally, we introduce a new forward search algorithm, Information Set Entropy Search (ISES), which effectively solves many single-player deduction games. The ISES algorithm, augmented with sampling techniques, allows agents to make decisions within controlled computational resources and time constraints. Experimental results on eight games within our framework demonstrate the significant superiority of our method over the Single Observer Information Set Monte Carlo Tree Search(SO-ISMCTS) algorithm under limited decision time constraints. The entropy variation of game states in our framework enables explainable decision-making, which can also be used to analyze the appeal of deduction games and provide insights for game designers.
Paper Structure (8 sections, 2 equations, 5 figures, 1 algorithm)

This paper contains 8 sections, 2 equations, 5 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. Deduction Game Framework
  4. Structure of Single-player Deduction Games
  5. Two representations of information sets
  6. Entropy analysis of games
  7. Information Set Entropy Search
  8. Results and Conclusions

Figures (5)

  • Figure 1: The structure of typical single player deduction games
  • Figure 2: The change in the information state matrix of the 4-coin fake coin game after a weighing result.
  • Figure 3: The impact of different actions on the entropy change of game state information in the initial state.
  • Figure 4: The variation of state information entropy of two games over 20 experiments with the use of the optimal average entropy reduction strategy.
  • Figure 5: The performance of four agents in different game sizes across 8 games.