Large language models (LLMs) are increasingly deployed as economic agents in marketplaces, auctions, and bidding settings. Anticipating their behavior in any specific deployment is hard. Existing strategic-reasoning benchmarks evaluate models on fixed canonical games. These benchmarks may saturate as the frontier improves, and they do not allow evaluators to generalize with confidence from benchmark performance to the varied and messy strategic environments that actual deployments involve. We introduce GENSTRAT, which uses procedurally generated strategic environments to address these challenges. Concretely, we generate a distribution of two-player zero-sum imperfect-information card games. The generator can draw fresh games on demand, allowing for evergreen evaluation and resistance to contamination. We pair the game distribution with a capability-profile methodology that decomposes model competence across six axes (state space, temporal depth, information sensitivity, opponent modeling, risk, and brittleness). We also introduce a jaggedness measure of within-distribution smoothness that detects when a model's advantage jumps unpredictably between strategically similar games. We sample 50 benchmark games from a 2,000-game generated pool and evaluate nine frontier and open-weight LLMs in a head-to-head tournament with over 36,000 matches. Newer frontier-tier models score higher on average. Beyond that average, models with near-identical overall strength show qualitatively different capability profiles, and two of the top three leaderboard models (gpt-5 and claude) are noticeably more locally volatile than the third (gemini-3.1-pro), despite being close in overall strength. Together, the capability profile and the jaggedness measure give a deployment-relevant diagnostic that the overall ranking alone cannot provide.