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.

翻译：在高级德州扑克AI系统的开发中，抽象技术因其在简化博弈复杂性方面的显著效果而受到广泛关注。本研究采用一个更具体的模型——有序信号博弈来描述德州扑克类游戏，并对该模型进行了优化，以简化其数学表示并拓宽其适用性。通过从宽泛的不完美信息博弈模型过渡到有序信号博弈模型，我们将先前交织在一起的信息集抽象与行动抽象分离为独立的信号抽象与行动抽象。重要的是，这种信号抽象为手牌抽象任务提供了一个数学框架，本文对此进行了重点讨论。此外，我们引入了一种新颖的公共细化原则，揭示了手牌抽象算法的极限性能。我们引入了潜在结果同构（POI），并指出其存在过度抽象的问题。进一步，我们证明了POI是领先的基于结果的手牌抽象算法（如E[HS]和PA&PAEMD）的一个公共细化。因此，过度抽象也固有地影响了这些算法，导致其性能欠佳。我们的研究表明，历史数据的遗漏是导致过度抽象的主要原因。为了弥补这一点，我们提出了K-回忆结果同构（KROI）以纳入缺失的信息。与POI相比，KROI更准确地反映了无损同构（LI）这一基本事实，从而提供了更高的信号抽象分辨率。在Numeral211 Hold'em中的实验结果表明，通过KROI开发的策略，其可剥削性比通过POI训练的策略更接近通过LI开发的策略。