让扑克AI从不输转向真赚钱，靠的是先稳扎稳打再动态抓对手漏洞。
Beyond Game Theory Optimal: Profit-Maximizing Poker Agents for No-Limit Holdem
- 先用自对弈逼近博弈论最优策略，构建防御基石。
- 再实时观察对手行为，针对性调整策略多赚收益。
- 在两人和多人局中均优于纯博弈论最优，适合实战对抗。
博弈论在近几十年发展迅速，扑克一直是其关键研究案例。博弈论最优（GTO）能确保不亏损，但无法最大化盈利。为此，本文旨在开发一种在单挑（两人）和多人局（三名及以上）中均能超越GTO、实现利润最大化的德州扑克智能体。该模型首先通过自对弈模拟大量牌局，持续调整决策直至无动作可稳定击败自身，形成接近理论最优的强基准策略。随后，模型根据对手行为实时调整策略以捕获额外价值。实验表明，在单挑场景下，蒙特卡洛反事实遗憾最小化（Monte-Carlo Counterfactual Regret Minimization, CFR）表现最佳；在多数多人场景中，CFR仍是最强方法。本方法融合了GTO的防守优势与实时剥削能力，展示了扑克智能体如何从避免亏损转向持续赢利。
原文摘要 · Abstract (English)
Game theory has grown into a major field over the past few decades, and poker has long served as one of its key case studies. Game-Theory-Optimal (GTO) provides strategies to avoid loss in poker, but pure GTO does not guarantee maximum profit. To this end, we aim to develop a model that outperforms GTO strategies to maximize profit in No Limit Holdem, in heads-up (two-player) and multi-way (more than two-player) situations. Our model finds the GTO foundation and goes further to exploit opponents. The model first navigates toward many simulated poker hands against itself and keeps adjusting its decisions until no action can reliably beat it, creating a strong baseline that is close to the theoretical best strategy. Then, it adapts by observing opponent behavior and adjusting its strategy to capture extra value accordingly. Our results indicate that Monte-Carlo Counterfactual Regret Minimization (CFR) performs best in heads-up situations and CFR remains the strongest method in most multi-way situations. By combining the defensive strength of GTO with real-time exploitation, our approach aims to show how poker agents can move from merely not losing to consistently winning against diverse opponents.
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