Evaluating embodied systems on real dexterous hardware requires more than isolated primitive skills: an agent must perceive a changing tabletop scene, choose a context-appropriate action, execute it with a dexterous hand, and leave the scene usable for later decisions. We introduce DexHoldem, a real-world system-level benchmark built around Texas Hold'em dexterous manipulation with a ShadowHand. DexHoldem provides 1,470 teleoperated demonstrations across 14 Texas Hold'em manipulation primitives, a standardized physical policy benchmark, and an agentic perception benchmark that tests whether agents can recover the structured game state needed for embodied decision making. On primitive execution, π_{0.5} obtains the highest task completion rate (61.2%), while π_{0.5} and π_0 tie on scene-preserving success rate (47.5%). On agentic perception, Opus 4.7 obtains the best strict problem-level accuracy (34.3%), while GPT 5.5 obtains the best average field-wise accuracy (66.8%), exposing a gap between isolated visual sub-capabilities and complete routing-relevant state recovery. Finally, we instantiate the full embodied-agent loop in three case studies, where waiting, recovery dispatches, human-help requests, and repeated primitive execution reveal how perception and policy errors accumulate during closed-loop deployment. DexHoldem therefore evaluates dexterous tabletop execution, agentic perception, and embodied decision routing in a shared physical setting. Project page: https://dexholdem.github.io/Dexholdem/.