Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Beyond Outcome-Based Imperfect-Recall: Higher-Resolution Abstractions for Imperfect-Information Games

Yanchang Fu, Qiyue Yin, Shengda Liu, Pei Xu, Kaiqi Huang

TL;DR

The paper tackles scaling imperfect-information games through hand abstraction by introducing Signal Observation Ordered Games (SOOGs) as a formal task model. It defines a resolution-bound evaluation (PAOI) and shows that outcome-based access discards historical information, impairing performance. It then proposes Full-Recall Outcome Isomorphism (FROI) to inject historical information, with monotonicity-based arguments and experiments demonstrating its superiority over PAOI. The work provides a unified formal framework for hand abstraction and practical guidance for designing higher-resolution abstractions in imperfect-information games.

Abstract

Hand abstraction is crucial for scaling imperfect-information games (IIGs) such as Texas Hold'em, yet progress is limited by the lack of a formal task model and by evaluations that require resource-intensive strategy solving. We introduce signal observation ordered games (SOOGs), a subclass of IIGs tailored to hold'em-style games that cleanly separates signal from player action sequences, providing a precise mathematical foundation for hand abstraction. Within this framework, we define a resolution bound-an information-theoretic upper bound on achievable performance under a given signal abstraction. Using the bound, we show that mainstream outcome-based imperfect-recall algorithms suffer substantial losses by arbitrarily discarding historical information; we formalize this behavior via potential-aware outcome Isomorphism (PAOI) and prove that PAOI characterizes their resolution bound. To overcome this limitation, we propose full-recall outcome isomorphism (FROI), which integrates historical information to raise the bound and improve policy quality. Experiments on hold'em-style benchmarks confirm that FROI consistently outperforms outcome-based imperfect-recall baselines. Our results provide a unified formal treatment of hand abstraction and practical guidance for designing higher-resolution abstractions in IIGs.

Beyond Outcome-Based Imperfect-Recall: Higher-Resolution Abstractions for Imperfect-Information Games

TL;DR

The paper tackles scaling imperfect-information games through hand abstraction by introducing Signal Observation Ordered Games (SOOGs) as a formal task model. It defines a resolution-bound evaluation (PAOI) and shows that outcome-based access discards historical information, impairing performance. It then proposes Full-Recall Outcome Isomorphism (FROI) to inject historical information, with monotonicity-based arguments and experiments demonstrating its superiority over PAOI. The work provides a unified formal framework for hand abstraction and practical guidance for designing higher-resolution abstractions in imperfect-information games.

Abstract

Hand abstraction is crucial for scaling imperfect-information games (IIGs) such as Texas Hold'em, yet progress is limited by the lack of a formal task model and by evaluations that require resource-intensive strategy solving. We introduce signal observation ordered games (SOOGs), a subclass of IIGs tailored to hold'em-style games that cleanly separates signal from player action sequences, providing a precise mathematical foundation for hand abstraction. Within this framework, we define a resolution bound-an information-theoretic upper bound on achievable performance under a given signal abstraction. Using the bound, we show that mainstream outcome-based imperfect-recall algorithms suffer substantial losses by arbitrarily discarding historical information; we formalize this behavior via potential-aware outcome Isomorphism (PAOI) and prove that PAOI characterizes their resolution bound. To overcome this limitation, we propose full-recall outcome isomorphism (FROI), which integrates historical information to raise the bound and improve policy quality. Experiments on hold'em-style benchmarks confirm that FROI consistently outperforms outcome-based imperfect-recall baselines. Our results provide a unified formal treatment of hand abstraction and practical guidance for designing higher-resolution abstractions in IIGs.
Paper Structure (25 sections, 3 theorems, 8 equations, 4 figures, 5 tables)

This paper contains 25 sections, 3 theorems, 8 equations, 4 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Related Works
  3. Background
  4. Hold'em Games
  5. Imperfect-Information Games
  6. Strategies and Solution Concepts for IIGs
  7. Modeling for Hand Abstraction
  8. Signal Observation Ordered games
  9. Signal Observation Abstraction
  10. Evaluation for Hand Abstraction Algorithms
  11. Resolution Bound
  12. Potential-Aware Outcome Isomorphism
  13. Full-Recall Outcome Isomorphism
  14. Experiment
  15. Conclusion
  16. ...and 10 more sections

Key Result

theorem 1

Let $\alpha_i$ and $\beta_i$ be signal observation abstractions for player $i\in \{1, 2\}$ in a 2-player zero-sum perfect-recall SOOG $\mathcal{G}$. Let $\alpha = (\alpha_i, \vartheta_{-i})$ and $\beta = (\beta_i, \vartheta_{-i})$ be perfect-recall signal observation abstraction profiles, with $\mat

Figures (4)

  • Figure 1: The process of constructing potential-aware outcome isomorphism in Leduc Hold'em.
  • Figure 2: Two factors influencing the quantity of distinct abstracted signal observation infosets for algorithms that only use current and future information.
  • Figure 3: The process of constructing full-recall outcome isomorphism in Leduc Hold'em.
  • Figure 4: Experimental results on Numeral211 Hold'em.

Theorems & Definitions (7)

  • definition 1: Imperfect-Information Game (IIG)
  • definition 2: Signal Observation Ordered Games (SOOG)
  • definition 3
  • definition 4
  • theorem 1: Adapted to SOOG from Theorem 3 in waugh2009abstraction
  • proposition 1
  • proposition 2