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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

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…

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

In imperfect-information games, the optimal strategy in a subgame may depend on the strategy in other, unreached subgames. Thus a subgame cannot be solved in isolation and must instead consider the strategy for the entire game as a whole,…

Artificial Intelligence · Computer Science 2017-11-20 Noam Brown , Tuomas Sandholm

In imperfect-information games, subgame solving is significantly more challenging than in perfect-information games, but in the last few years, such techniques have been developed. They were the key ingredient to the milestone of superhuman…

Computer Science and Game Theory · Computer Science 2021-12-06 Brian Hu Zhang , Tuomas Sandholm

Poker, also known as Texas Hold'em, has always been a typical research target within imperfect information games (IIGs). IIGs have long served as a measure of artificial intelligence (AI) development. Representative prior works, such as…

Artificial Intelligence · Computer Science 2024-01-17 Chenghao Huang , Yanbo Cao , Yinlong Wen , Tao Zhou , Yanru Zhang

Since the advent of AI, games have served as progress benchmarks. Meanwhile, imperfect-information variants of chess have existed for over a century, present extreme challenges, and have been the focus of decades of AI research. Beyond…

Computer Science and Game Theory · Computer Science 2026-03-03 Brian Hu Zhang , Tuomas Sandholm

Games have a long history as benchmarks for progress in artificial intelligence. Approaches using search and learning produced strong performance across many perfect information games, and approaches using game-theoretic reasoning and…

Poker is an imperfect information game that has served as a long-standing benchmark for decision-making under uncertainty. To maximize utility beyond the Nash equilibrium, an agent can deviate from Nash-equilibrium policies to exploit…

Machine Learning · Computer Science 2026-05-12 Vlad Murgoci , Matthijs Spaan , Yaniv Oren

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

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

Dominance is a fundamental concept in game theory. In normal-form games dominated strategies can be identified in polynomial time. As a consequence, iterative removal of dominated strategies can be performed efficiently as a preprocessing…

Computer Science and Game Theory · Computer Science 2026-03-26 Sam Ganzfried

We study the problem of adapting to a known sub-rational opponent during online play while remaining robust to rational opponents. We focus on large imperfect-information (zero-sum) games, which makes it impossible to inspect the whole game…

Computer Science and Game Theory · Computer Science 2025-02-11 David Milec , Vojtěch Kovařík , Viliam Lisý

Artificial Intelligence (AI) has achieved great success in many domains, and game AI is widely regarded as its beachhead since the dawn of AI. In recent years, studies on game AI have gradually evolved from relatively simple environments…

Artificial Intelligence · Computer Science 2020-04-02 Junjie Li , Sotetsu Koyamada , Qiwei Ye , Guoqing Liu , Chao Wang , Ruihan Yang , Li Zhao , Tao Qin , Tie-Yan Liu , Hsiao-Wuen Hon

Limited lookahead has been studied for decades in perfect-information games. We initiate a new direction via two simultaneous deviation points: generalization to imperfect-information games and a game-theoretic approach. We study how one…

Computer Science and Game Theory · Computer Science 2020-03-20 Christian Kroer , Tuomas Sandholm

Unlike perfect information games, where all elements are known to every player, imperfect information games emulate the real-world complexities of decision-making under uncertain or incomplete information. GPT-4, the recent breakthrough in…

Artificial Intelligence · Computer Science 2024-09-04 Jiaxian Guo , Bo Yang , Paul Yoo , Bill Yuchen Lin , Yusuke Iwasawa , Yutaka Matsuo

AI researchers have long focused on poker-like games as a testbed for environments characterized by multi-player dynamics, imperfect information, and reasoning under uncertainty. While recent breakthroughs have matched elite human play at…

Artificial Intelligence · Computer Science 2026-05-04 Richard Dewey , Janos Botyanszki , Ciamac C. Moallemi , Andrew T. Zheng

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

Poker is in the family of imperfect information games unlike other games such as chess, connect four, etc which are perfect information game instead. While many perfect information games have been solved, no non-trivial imperfect…

Computer Science and Game Theory · Computer Science 2024-01-15 Prathamesh Sonawane , Arav Chheda

Many real-world applications can be described as large-scale games of imperfect information. To deal with these challenging domains, prior work has focused on computing Nash equilibria in a handcrafted abstraction of the domain. In this…

Machine Learning · Computer Science 2016-06-29 Johannes Heinrich , David Silver
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