Beyond Tracking or Shortcut: Composition-Bounded Predictive States in Poker Autoregressive Models

Hidden-state probes often recover latent labels in imperfect-information sequence models, but this alone does not establish that a model maintains a posterior belief distribution over hidden states. This paper studies this ambiguity in a no-range Limit Hold'em autoregressive model trained only on action and value targets, not on an opponent's hand or range. Opponent-range probes are positive after action/value controls in two of three seeds, and the behavior head predicts held-out actions about five percentage points above a baseline using only observable public history. However, visible public betting composition explains more opponent-range signal than residual hidden states, suggesting that most recoverable information comes from betting summaries. Action/value+composition baselines reach 16.5-16.7% top-10 accuracy while composition-residual hidden probes fall to 11.4-12.2%, and matched-composition comparisons are negative in every seed. We call this evidence pattern composition-bounded predictive support: hidden states remain behavior-predictive and opponent-range correlated, but most recoverable range information is explained by visible betting composition rather than residual hidden-state structure. This is a case-study claim about opponent-range representational evidence, not exact Bayesian posterior tracking or a causal belief mechanism. Synthetic control and oracle validations show that the same diagnostics accept posterior-sensitive states and reject raw composition states under matched controls. Thus positive belief probes should be interpreted through targeted alternatives before being treated as evidence of belief tracking.