Poker is a landmark challenge for artificial intelligence. The dominant approach relies on equilibrium solvers built on counterfactual regret minimization, requiring millions of core-hours of training. Large Language Models (LLMs) possess extensive poker knowledge but perform far below solver-based agents when asked to play directly. Traditional rule-based poker agents are interpretable and training-free, but their strategic ceiling remains far below equilibrium play. We introduce \textbf{PokerSkill}, a training-free and solver-free framework that bridges this gap by using detailed rule-based poker skills as a structured action-grounding interface for LLMs. A deterministic context engine analyzes the current state and retrieves only the relevant fragments from a layered skill library, which is entirely designed by human poker experts, constraining the LLM's choice to reasonable actions. Against GTOWizard, a state-of-the-art GTO benchmark, GPT-5.5 XHigh with PokerSkill achieves $-57 \pm 21$ mbb/hand, Claude Opus 4.6 achieves $-80 \pm 29$ mbb/hand and Claude Opus 4.7 achieves $-87\pm 64$ mbb/hand, reducing losses by 49--61\% compared to default-prompt baselines and outperforming the strong bot Slumbot. Our key finding is that rule-based skills alone do not constitute a strong strategy, and LLMs alone cannot play well, but their combination yields an agent that requires neither training nor solver access yet competes with systems built on millions of core-hours of computation. To our knowledge, this is the first demonstration of an LLM achieving competitive performance in a complex imperfect-information game without game-specific training or solver queries. Code is available at https://github.com/lbn187/PokerSkill.