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

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 abstraction algorithm. 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 a hold'em game benchmark confirm that FROI consistently outperforms outcome-based imperfect-recall baselines. Our research provides practical guidance for further designing higher-resolution abstraction algorithms in IIGs.