General search techniques without common knowledge for imperfect-information games, and application to superhuman Fog of War chess
Brian Zhang, Tuomas Sandholm
Abstract
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 calculation needed in regular chess, they require reasoning about information gathering, the opponent's knowledge, signaling, etc. The most popular variant, Fog of War (FoW) chess (a.k.a. dark chess), has been a major challenge problem in imperfect-information game solving since superhuman performance was reached in no-limit Texas hold'em poker. We present Obscuro, the first superhuman AI for FoW chess. It introduces advances to search in imperfect-information games, enabling strong, scalable reasoning. Experiments against the prior state-of-the-art AI and human players -- including the world's best -- show that Obscuro is significantly stronger. FoW chess is the largest (by amount of imperfect information) turn-based zero-sum game in which superhuman performance has been achieved and the largest zero-sum game in which imperfect-information search has been successfully applied.
Ask about this paper
Your agent reads all of it.
Lune indexed this paper to the last equation, along with the top-tier papers that cite it. Ask a question and the answer quotes them.
Your agent calls
Luneget_paper_fulltext
Free to start. No credit card required.
Terminal
Install the CLIlune papers fulltext 932f75df-7738-42af-8bbf-62dfd69281cfCited by top-tier papers2
- Convergence of Regret Matching in Potential Games and Constrained OptimizationIoannis Anagnostides, Emanuel Tewolde, Brian Hu Zhang, Ioannis Panageas et al.ICLR 2026 · 6 citations
- Look-ahead Reasoning with a Learned Model in Imperfect Information GamesOndrej Kubícek, Viliam LisýICLR 2026 · 3 citations
Builds on8
- Combining Deep Reinforcement Learning and Search for Imperfect-Information GamesNoam Brown, Anton Bakhtin, Adam Lerer, Qucheng GongNeurIPS 2020 · 205 citations
- Faster Game Solving via Predictive Blackwell Approachability: Connecting Regret Matching and Mirror DescentGabriele Farina, Christian Kroer, Tuomas SandholmAAAI 2021 · 91 citations
- Regret Matching+: (In)Stability and Fast Convergence in GamesGabriele Farina, Julien Grand-Clément, Christian Kroer, Chung-Wei Lee et al.NeurIPS 2023 · 22 citations
- Subgame solving without common knowledgeBrian Hu Zhang, Tuomas SandholmNeurIPS 2021 · 21 citations
- Opponent-Limited Online Search for Imperfect Information GamesWeiming Liu, Haobo Fu, Qiang Fu, Wei YangICML 2023 · 7 citations
Related papers
- Deep Synoptic Monte-Carlo Planning in Reconnaissance Blind ChessGregory ClarkNeurIPS 2021 · 10 citations
- No-Regret Strategy Solving in Imperfect-Information Games via Pre-Trained EmbeddingYanchang Fu, Shengda Liu, Pei Xu, Kaiqi HuangAAAI 2026
- The Update-Equivalence Framework for Decision-Time PlanningSamuel Sokota, Gabriele Farina, David J. Wu, Hengyuan Hu et al.ICLR 2024 · 5 citations
- Opponent-Model Search in Games with Incomplete InformationJunkang Li, Bruno Zanuttini, Véronique VentosAAAI 2024 · 1 citation
- Pipeline PSRO: A Scalable Approach for Finding Approximate Nash Equilibria in Large GamesStephen McAleer, John B. Lanier, Roy Fox, Pierre BaldiNeurIPS 2020 · 98 citations
