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Signal Observation Models and Historical Information Integration in Poker Hand Abstraction

Yanchang Fu, Pei Xu, Dongdong Bai, Lingyun Zhao, Kaiqi Huang

TL;DR

The paper tackles the lack of theoretical foundations for hand abstraction in Hold'em by formulating the game as signal observation ordered games (SOOG) and introducing a resolution bound to quantify information retention. It shows that existing potential-aware abstraction algorithms (PAAs), which rely on future-only information, incur substantial information loss, and introduces the KrwEmd algorithm that leverages historical information through k-recall winrate features. The core contributions include the SOOG framework, a formal resolution bound, analysis of PAAs via Potential-Aware Outcome Isomorphism, and the KrwEmd method that empirically outperforms state-of-the-art abstractions in the Numeral211 Hold'em environment. The work offers a principled pathway to design more informative hand abstractions, with potential to enhance high-level Hold'em AI such as DeepStack, Libratus, and Pluribus.

Abstract

Hand abstraction has been instrumental in developing powerful AI for Texas Hold'em poker, a widely studied testbed for imperfect information games (IIGs). Despite its success, the hand abstraction task lacks robust theoretical tools, limiting both algorithmic innovation and theoretical progress. To address this, we extend the IIG framework with the \textbf{signal observation ordered game} model and introduce \textbf{signal observation abstraction} to formalize the hand abstraction task. We further propose a novel evaluation metric, the \textbf{resolution bound}, to assess the performance of signal observation abstraction algorithms. Using this metric, we uncover critical limitations in current state-of-the-art algorithms, particularly the significant information loss caused by the enforced omission of historical information. To resolve these issues, we present the \textbf{KrwEmd} algorithm, which effectively incorporates historical information into the abstraction process. Experiments in the Numeral211 hold'em environment demonstrate that KrwEmd addresses these limitations and significantly outperforms existing algorithms.

Signal Observation Models and Historical Information Integration in Poker Hand Abstraction

TL;DR

The paper tackles the lack of theoretical foundations for hand abstraction in Hold'em by formulating the game as signal observation ordered games (SOOG) and introducing a resolution bound to quantify information retention. It shows that existing potential-aware abstraction algorithms (PAAs), which rely on future-only information, incur substantial information loss, and introduces the KrwEmd algorithm that leverages historical information through k-recall winrate features. The core contributions include the SOOG framework, a formal resolution bound, analysis of PAAs via Potential-Aware Outcome Isomorphism, and the KrwEmd method that empirically outperforms state-of-the-art abstractions in the Numeral211 Hold'em environment. The work offers a principled pathway to design more informative hand abstractions, with potential to enhance high-level Hold'em AI such as DeepStack, Libratus, and Pluribus.

Abstract

Hand abstraction has been instrumental in developing powerful AI for Texas Hold'em poker, a widely studied testbed for imperfect information games (IIGs). Despite its success, the hand abstraction task lacks robust theoretical tools, limiting both algorithmic innovation and theoretical progress. To address this, we extend the IIG framework with the \textbf{signal observation ordered game} model and introduce \textbf{signal observation abstraction} to formalize the hand abstraction task. We further propose a novel evaluation metric, the \textbf{resolution bound}, to assess the performance of signal observation abstraction algorithms. Using this metric, we uncover critical limitations in current state-of-the-art algorithms, particularly the significant information loss caused by the enforced omission of historical information. To resolve these issues, we present the \textbf{KrwEmd} algorithm, which effectively incorporates historical information into the abstraction process. Experiments in the Numeral211 hold'em environment demonstrate that KrwEmd addresses these limitations and significantly outperforms existing algorithms.
Paper Structure (20 sections, 1 theorem, 16 equations, 4 figures, 3 tables)

This paper contains 20 sections, 1 theorem, 16 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Hold'em Games
  3. HULH and HUNL
  4. Numeral211 Hold'em
  5. Mathematical Modeling
  6. Signal Observation Ordered Games
  7. Signal Observation Abstraction
  8. Resolution Bound
  9. Potential-Aware Abstraction Algorithms and Their Resolution Bound
  10. Potential-Aware Abstraction Algorithms
  11. Potential-Aware Outcome Isomorphism
  12. Cluster Assignment Step:
  13. Centroid Update Step:
  14. The Issue of Excessive Abstraction in POI
  15. K-Recall Methods
  16. ...and 5 more sections

Key Result

Theorem 1

The POI serves as a resolution bound of algorithm PAAA and PAAEMD.

Figures (4)

  • Figure 1: The hand ranks of Numeral211 hold'em.
  • Figure 2: Two factors influencing the quantity of distinct abstracted signal observation infosets for future-consider-only approach.
  • Figure 3: Performance comparison of KRWI, POI, and LI, along with ablation study.
  • Figure 4: Performance comparison of PAAEMD, EHS, and KrwEmd with different parameters.

Theorems & Definitions (5)

  • Definition 1
  • Definition 2
  • Definition 3
  • Theorem 1
  • proof