Expanding the Resolution Boundary of Outcome-Based Imperfect-Recall Abstraction in Games with Ordered Signals

In the development of advanced Texas Hold'em AI systems, abstraction technology has garnered widespread attention due to its significant effect in simplifying game complexity. This study adopts a more specific model, the games of ordered signal, to describe Texas Hold'em-style games and optimizes this model to streamline its mathematical representation and broaden its applicability. By transitioning from a broad imperfect information game model to a game with ordered signals model, we have separated the previously intertwined infoset abstraction and action abstraction into independent signal abstraction and action abstraction. Importantly, this signal abstraction provides a mathematical framework for the hand abstraction task, which is emphatically discussed in this paper. Additionally, a novel common refinement principle is introduced, revealing the limit performance of hand abstraction algorithms. We introduce potential outcome isomorphism (POI) and pinpoint that it suffers from the issue of excessive abstraction. Futher, We demonstrate that POI serves as a common refinement for leading outcome-based hand abstraction algorithms, such as E[HS] and PA\&PAEMD. Consequently, excessive abstraction also inherently affects these algorithms, leading to suboptimal performance. Our investigation reveals the omission of historical data as a primary contributor to excessive abstraction. To remedy this, we propose the K-Recall Outcome Isomorphism (KROI) to incorporate the missing information. Compared with POI, KROI more accurately mirrors lossless isomorphism (LI), the ground truth, offering enhanced signal abstraction resolution. Experimental results in the Numeral211 Hold'em indicate that strategies developed through KROI approximate the exploitability of those developed through LI more closely than those trained through POI.