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The Counterfactual Regret Minimization (CFR) algorithm and its variants have enabled the development of pokerbots capable of beating the best human players in heads-up (1v1) cash games and competing with them in six-player formats. However,…

Machine Learning · Computer Science 2026-02-24 Narada Maugin , Tristan Cazenave

We introduce PokerBench - a benchmark for evaluating the poker-playing abilities of large language models (LLMs). As LLMs excel in traditional NLP tasks, their application to complex, strategic games like poker poses a new challenge. Poker,…

Computation and Language · Computer Science 2025-01-28 Richard Zhuang , Akshat Gupta , Richard Yang , Aniket Rahane , Zhengyu Li , Gopala Anumanchipalli

An imperfect-information game is a type of game with asymmetric information. It is more common in life than perfect-information game. Artificial intelligence (AI) in imperfect-information games, such like poker, has made considerable…

Artificial Intelligence · Computer Science 2024-05-29 Qibin Zhou , Dongdong Bai , Junge Zhang , Fuqing Duan , Kaiqi Huang

High-quality information set abstraction remains a core challenge in solving large-scale imperfect-information extensive-form games (IIEFGs)--such as no-limit Texas Hold'em--where the finite nature of spatial resources hinders solving…

Artificial Intelligence · Computer Science 2025-12-10 Yanchang Fu , Shengda Liu , Pei Xu , Kaiqi Huang

Counterfactual Regret Minimization (CFR) is the dominant algorithmic family for solving large imperfect-information games, underpinning breakthroughs such as Libratus and Pluribus in No-Limit Texas Hold'em poker. In real-time game-playing…

Computer Science and Game Theory · Computer Science 2026-05-20 Boning Li , Longbo Huang

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…

Artificial Intelligence · Computer Science 2026-05-29 Boning Li , Baoxiang Wang , Longbo Huang

Artificial intelligence has seen several breakthroughs in recent years, with games often serving as milestones. A common feature of these games is that players have perfect information. Poker is the quintessential game of imperfect…

Transformer-based large language models (LLMs) have demonstrated strong reasoning abilities across diverse fields, from solving programming challenges to competing in strategy-intensive games such as chess. Prior work has shown that LLMs…

Computation and Language · Computer Science 2026-01-01 Adam Kamel , Tanish Rastogi , Michael Ma , Kailash Ranganathan , Kevin Zhu

Owning to the unremitting efforts by a few institutes, significant progress has recently been made in designing superhuman AIs in No-limit Texas Hold'em (NLTH), the primary testbed for large-scale imperfect-information game research.…

Machine Learning · Computer Science 2021-12-15 Kai Li , Hang Xu , Enmin Zhao , Zhe Wu , Junliang Xing

As Large Language Models (LLMs) are increasingly applied in high-stakes domains, their ability to reason strategically under uncertainty becomes critical. Poker provides a rigorous testbed, requiring not only strong actions but also…

Artificial Intelligence · Computer Science 2026-02-03 Minhua Lin , Enyan Dai , Hui Liu , Xianfeng Tang , Yuliang Yan , Zhenwei Dai , Jingying Zeng , Zhiwei Zhang , Fali Wang , Hongcheng Gao , Chen Luo , Xiang Zhang , Qi He , Suhang Wang

A fundamental challenge in imperfect-information games is that states do not have well-defined values. As a result, depth-limited search algorithms used in single-agent settings and perfect-information games do not apply. This paper…

Computer Science and Game Theory · Computer Science 2018-05-23 Noam Brown , Tuomas Sandholm , Brandon Amos

Counterfactual Regret Minimization(CFR) has shown its success in Texas Hold'em poker. We apply this algorithm to another popular incomplete information game, Mahjong. Compared to the poker game, Mahjong is much more complex with many…

Artificial Intelligence · Computer Science 2023-07-25 Shiheng Wang

Counterfactual Regret Minimization and variants (e.g. Public Chance Sampling CFR and Pure CFR) have been known as the best approaches for creating approximate Nash equilibrium solutions for imperfect information games such as poker. This…

Computer Science and Game Theory · Computer Science 2014-07-21 Oskari Tammelin

In two-player zero-sum games, if both players minimize their average external regret, then the average of the strategy profiles converges to a Nash equilibrium. For n-player general-sum games, however, theoretical guarantees for regret…

Computer Science and Game Theory · Computer Science 2013-05-02 Richard Gibson

Computational equilibrium finding in large zero-sum extensive-form imperfect-information games has led to significant recent AI breakthroughs. The fastest algorithms for the problem are new forms of counterfactual regret minimization [Brown…

Computer Science and Game Theory · Computer Science 2020-07-01 Brian Hu Zhang , Tuomas Sandholm

Poker is a large complex game of imperfect information, which has been singled out as a major AI challenge problem. Recently there has been a series of breakthroughs culminating in agents that have successfully defeated the strongest human…

Artificial Intelligence · Computer Science 2022-06-28 Sam Ganzfried , Max Chiswick

Artificial intelligence (AI) has surpassed top human players in a variety of games. In imperfect information games, these achievements have primarily been driven by Counterfactual Regret Minimization (CFR) and its variants for computing…

Computer Science and Game Theory · Computer Science 2025-05-29 Qi Ju , Thomas Tellier , Meng Sun , Zhemei Fang , Yunfeng Luo

Poker is a challenging problem for artificial intelligence, with non-deterministic dynamics, partial observability, and the added difficulty of unknown adversaries. Modelling all of the uncertainties in this domain is not an easy task. In…

Computer Science and Game Theory · Computer Science 2012-07-09 Finnegan Southey , Michael P. Bowling , Bryce Larson , Carmelo Piccione , Neil Burch , Darse Billings , Chris Rayner

Adversarial board games, as a paradigmatic domain of strategic reasoning and intelligence, have long served as both a popular competitive activity and a benchmark for evaluating artificial intelligence (AI) systems. Building on this…

Artificial Intelligence · Computer Science 2025-08-08 Yingjie Zhou , Jiezhang Cao , Farong Wen , Li Xu , Yanwei Jiang , Jun Jia , Ronghui Li , Xiaohong Liu , Yu Zhou , Xiongkuo Min , Jie Guo , Zicheng Zhang , Guangtao Zhai

Evaluating agent performance when outcomes are stochastic and agents use randomized strategies can be challenging when there is limited data available. The variance of sampled outcomes may make the simple approach of Monte Carlo sampling…

Artificial Intelligence · Computer Science 2017-01-23 Neil Burch , Martin Schmid , Matej Moravčík , Michael Bowling
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