Language is often used strategically, particularly in high-stakes, adversarial settings, yet most work on pragmatics and LLMs centers on cooperative settings. This leaves a gap in the systematic understanding of strategic communication in adversarial settings. To address this, we introduce SDA (Strategic Dialogue Assessment), a framework grounded in Gricean and game-theoretic pragmatics to assess strategic use of language. It adapts the ME Game jury function to make it empirically estimable for analyzing dialogue. Our approach incorporates two key adaptations: a commitment-based taxonomy of discourse moves, which provides a finer-grained account of strategic effects, and the use of estimable proxies grounded in Gricean maxims to operationalize abstract constructs such as credibility. Together, these adaptations build on discourse theory by treating discourse as the strategic management of commitments, enabling systematic evaluation of how conversational moves advance or undermine discourse goals. We further derive three interpretable metrics - Benefit at Turn (BAT), Penalty at Turn (PAT), and Normalized Relative Benefit at Turn (NRBAT) - to quantify the perceived strategic effects of discourse moves. We also present CPD (the Crooked Path Dataset), an annotated dataset of real courtroom cross-examinations, to demonstrate the framework’s effectiveness. Using these tools, we evaluate a range of LLMs and show that LLMs generally exhibit limited pragmatic understanding of strategic language. While model size shows an increase in performance on our metrics, reasoning ability does not help and largely hurts, introducing overcomplication and internal confusion.