Signal Observation Models and Historical Information Integration in Poker Hand Abstraction

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.