Heads-up limit hold’em poker is solved

By Michael H. Bowling, Neil Burch, Michael Bradley Johanson, Oskari Tammelin. 2015

554 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Economics and Econometrics, Sociology and Political Science, Game & Decision Theory

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Citations in the corpus

The Hanabi Challenge: A New Frontier for AI Research (2019, background): “In the competitive case, such as poker, strong play required new algorithmic foundations [71,72,14,13].”
Deep Reinforcement Learning from Self-Play in Imperfect-Information Games (2016, methodology): “domain expertise. 1 Introduction Games have a tradition of encouraging advances in artiﬁcial intelligence and machine learning (Samuel, 1959; Tesauro, 1995; Campbell et al., 2002; Gelly et al., 2012; Bowling et al., 2015). A game is a domain of conﬂict or cooperation between several entities (Myerso”
A Unified Game-Theoretic Approach to Multiagent Reinforcement Learning (2017, background): “We now show results for a Leduc poker where strong benchmark algorithms exist, such as counter-factual regret (CFR) minimization [108, 11].”
Poker-CNN: A Pattern Learning Strategy for Making Draws and Bets in Poker Games Using Convolutional Networks (2015, background): “They have achieved competitive performance against the worlds best heads-up No Limit Texas Hold’em players (Rutkin 2015), and found an effective equilibrium solution for heads-up Limit Texas Hold’em (Bowling et al. 2015).”
Q-Learning: Theory and Applications (2020, background): “successes of reinforcement learning in complex games like chess, go, and poker (Bowling et al. 2015, Mnih et al. 2015, Silver et al. 2017).”
Exploring Large Language Models for Communication Games: An Empirical Study on Werewolf (2023, background): “And superhuman performance has been achieved in some incomplete information games, such as heads-up poker (Bowling et al., 2015; Brown and Sandholm, 2018).”
Fictitious Self-Play in Extensive-Form Games (2015, background): “Counterfactual regret minimization (CFR) is the first approach which essentially solved an imperfect-information game of real-world scale (Bowling et al., 2015).”
Libratus: The Superhuman AI for No-Limit Poker (2017, background): “2Heads-up limit Texas Hold’em, a significantly smaller game with 1013 decision points, was essentially solved in 2015 [Bowling et al., 2015; Tammelin et al., 2015].”
Time and Space: Why Imperfect Information Games are Hard (2018, methodology): “, I introduced the notion of essentially solved [9] to answer the question of when an approximation is good enough.”
Multi-Agent Reinforcement Learning: A Selective Overview of Theories and Algorithms (2019, background): “9 × 1014 information sets in total (Bowling et al., 2015), where a player is required to take an action at each information set.”
Actor-Critic Policy Optimization in Partially Observable Multiagent Environments (2018, methodology): “Near-optimal solutions for heads-up limit Texas Hold’em were found with tabular methods using state aggregation, powered by policy iteration algorithms based on regret minimization [101, 86, 12].”
Dynamic Thresholding and Pruning for Regret Minimization (2017, methodology): “CFR+, a variant of CFR with RM, was recently used to essentially solve Limit Texas Hold’em, the largest imperfectinformation game ever to be essentially solved and the first that is played competitively by humans (Bowling et al. 2015; Tammelin et al. 2015).”
Online Monte Carlo Counterfactual Regret Minimization for Search in Imperfect Information Games (2015, methodology): “This oﬄine approach has been remarkably successful in Computer Poker [2, 12, 32, 31, 21].”
Computing Approximate Equilibria in Sequential Adversarial Games by Exploitability Descent (2019, methodology): “Based on CFR, recent techniques have solved heads-up limit Texas Hold’em [ Bowling et al. , 2015 ] and beat human professionals in no-limit Texas Hold’em [ Morav ˇ c ´ ık et al. , 2017; Brown and Sandholm, 2017 ] .”
Algorithms for computing strategies in two-player simultaneous move games (2016, unknown): “CFR has gained much attention due to its success in computing Poker AI strategies, and recently an application of CFR has solved Heads Up Limit Texas Hold’em Poker [29].”
Deep Counterfactual Regret Minimization (2018, methodology): “Forms of tabular CFR have been used in all recent milestones in the benchmark domain of poker (Bowling et al., 2015; Moravčı́k et al., 2017; Brown & Sandholm, 2017) and have been used in all competitive agents in the Annual Computer Poker Competition going back at least six years.”