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Life sciences · Preprint
arXiv · August 7, 2026
Raises a question worth testing. It does not answer one.
This preprint proposes Mixed-Strategy Decision Tree (MDT), a method to improve large language model reasoning in game-theoretic equilibrium play by conditioning on solver output rather than human demonstrations. The approach reduces ℓ₁ distance to equilibrium by 52.6% across eight LLM configurations in No-Limit Texas Hold'em, but the work is unpublished, domain-specific to games, and does not demonstrate clinical or practical relevance.
Algorithmic comparison study with ablation testing. Intervention: Mixed-Strategy Decision Tree (MDT), a method to articulate equilibrium optimality into sparse strategic rules for LLM conditioning, using solver output. Compared with: LLM reasoning conditioned on human demonstration data (implied baseline).
MDT reduces ℓ₁ distance to equilibrium by 52.6% across 8 different LLM configurations Study queried solver oracle for over 250 million mixed-strategy decisions in No-Limit Texas Hold'em Route-only ablation evaluated incremental contribution of shadow-based contrast
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This is a computer science methods paper presenting a novel algorithmic approach to improve LLM reasoning in game theory; it demonstrates a proof-of-concept with a specific metric reduction but lacks clinical or real-world application and is not peer reviewed.
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Reasoning in large language models (LLMs) is often grounded in human text, human demonstrations, and human-generated rationales. For equilibrium reasoning in complex games, however, relying on human data can be suboptimal. In fact, human play is often guided by intuition and heuristics and can deviate substantially from game equilibrium. This discrepancy is amplified in games with mixed-strategy equilibria, where human data is heavily biased toward pure strategies. Consequently, conditioning LLMs on this data yields weak game strategies. To grant LLMs the reasoning capacity in games, in this work, we study how to elicit equilibrium play using solver output. We propose Mixed-Strategy Decision Tree (MDT), which articulates the silent optimality of the equilibrium into sparse strategic rules that both humans and LLMs could understand. Using solver output rather than human annotation allows us to extend the input to arbitrarily new states and continuations. We instantiate this study on No-Limit Texas Hold'em by querying a solver oracle for over \textbf{250 million mixed-strategy decisions}; MDT together with other techniques \textbf{reduces the $\ell_1$ distance to the equilibrium by $52.6\%$} across $8$ different LLM configurations. A Route-only ablation tests the incremental contribution of the shadow-based contrast, while complete River-endgame and Liar's Dice experiments evaluate strategic fidelity and portability beyond the original NLH communication setting.
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