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General search techniques without common knowledge for imperfect-information games, and application to superhuman Fog of War chess

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
imperfect-informaton gamessubgame solvinggame theory
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 game in which imperfect-information search has been successfully applied.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
If you have any questions, please contact: mingzhang23@m.fudan.edu.cn

Overview

Overall Novelty Assessment

The paper introduces Obscuro, the first superhuman AI for Fog of War chess, advancing depth-limited subgame solving in imperfect-information games. It resides in the 'Depth-Limited and Subgame Solving' leaf, which contains only three papers total, indicating a relatively sparse research direction within the broader taxonomy. This leaf focuses on solving limited game-tree portions without common-knowledge closure, distinguishing it from full-game or equilibrium-based methods. The small sibling count suggests the paper enters a less crowded niche compared to more populated branches like Monte Carlo Tree Search variants or learning-search integration.

The taxonomy reveals neighboring leaves in 'Search Algorithms and Architectures' include 'Online Search and Soundness' (two papers on theoretical guarantees) and 'Monte Carlo Tree Search Variants' (four papers on ISMCTS and determinization). Adjacent branches such as 'Learning-Search Integration' (six papers across three leaves) and 'Game-Theoretic and Opponent Modeling' (three papers) represent alternative paradigms. The paper's avoidance of common-knowledge reasoning and equilibrium computation sets it apart from game-theoretic neighbors, while its explicit search focus differentiates it from learning-heavy unified frameworks like Student of Games.

Among nineteen candidates examined, the KLUSS algorithm contribution shows two refutable candidates out of nine examined, suggesting moderate prior overlap in subgame-solving techniques. The one-sided GT-CFR expansion was not evaluated against any candidates, leaving its novelty uncertain within this limited scope. The Obscuro system contribution examined ten candidates with zero refutations, indicating no direct prior work on superhuman Fog of War chess among the top semantic matches. These statistics reflect a targeted search, not exhaustive coverage, so unexamined literature may contain relevant precedents.

Based on the limited search scope of nineteen top-ranked candidates, the work appears to occupy a sparsely populated research direction with modest algorithmic overlap and no prior superhuman Fog of War chess systems identified. The taxonomy structure confirms that depth-limited solving without common knowledge is less explored than equilibrium-based or learning-integrated approaches. However, the analysis does not cover the full literature landscape, and broader searches or domain-specific venues might reveal additional related efforts.

Taxonomy

Core-task Taxonomy Papers
26
3
Claimed Contributions
19
Contribution Candidate Papers Compared
2
Refutable Paper

Research Landscape Overview

Core task: Imperfect-information game solving through search without common knowledge reasoning. The field of imperfect-information game solving through search has evolved into a rich landscape organized around several complementary directions. At the highest level, the taxonomy distinguishes Search Algorithms and Architectures (which develop core search mechanisms and tree-based methods), Learning-Search Integration (which combines neural networks or reinforcement learning with search), Game-Theoretic and Opponent Modeling (which emphasizes equilibrium computation and adversary reasoning), Cooperative and Multi-Agent Settings (which address team coordination and shared information), Theoretical Foundations and General Frameworks (which provide formal guarantees and abstract models), and Domain Applications and Empirical Studies (which validate techniques in specific games). Within Search Algorithms and Architectures, a particularly active subarea is Depth-Limited and Subgame Solving, where methods like Subgame Solving[1] and Depth-Limited Solving[6] tackle the challenge of reasoning over restricted horizons without recomputing the entire game tree, while works such as Bridge Card Play[3] illustrate early heuristic approaches in card games. A central tension across these branches is the trade-off between computational tractability and solution quality: depth-limited techniques sacrifice global optimality for speed, opponent-modeling approaches like Opponent-Model Search[4] exploit specific adversary assumptions that may not hold in practice, and learning-based methods such as Deep RL Search[5] and Student of Games[7] offer scalability but require extensive training data. Fog of War Chess[0] sits squarely within the Depth-Limited and Subgame Solving cluster, sharing with Subgame Solving[1] and Depth-Limited Solving[6] the goal of efficient local search under partial observability. However, Fog of War Chess[0] distinguishes itself by avoiding common knowledge reasoning entirely, whereas neighboring works often assume some level of mutual belief or equilibrium structure. This design choice positions it as a pragmatic alternative when opponents are unknown or non-equilibrium, complementing the more game-theoretically grounded methods that dominate other branches.

Claimed Contributions

Knowledge-limited unfrozen subgame solving (KLUSS) algorithm

KLUSS is a subgame solving technique for imperfect-information games that avoids reasoning about common knowledge by removing states based on order of knowledge, while unfreezing strategies at distance-1 nodes (unlike KLSS which freezes them). This enables more powerful reasoning about opponent information without enumerating prohibitively large common-knowledge sets.

9 retrieved papers
Can Refute
One-sided GT-CFR tree expansion algorithm

A variant of growing-tree CFR where only one player uses an exploration-exploitation strategy while the other plays their equilibrium strategy directly. This focuses tree expansion on relevant nodes and is formally shown to converge to exact equilibrium given infinite time.

0 retrieved papers
Obscuro: first superhuman AI for Fog of War chess

Obscuro combines the new search techniques (KLUSS and one-sided GT-CFR) to achieve superhuman performance in Fog of War chess, the largest turn-based zero-sum game by imperfect information where superhuman play has been reached and the largest game where imperfect-information search has been successfully applied.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Knowledge-limited unfrozen subgame solving (KLUSS) algorithm

KLUSS is a subgame solving technique for imperfect-information games that avoids reasoning about common knowledge by removing states based on order of knowledge, while unfreezing strategies at distance-1 nodes (unlike KLSS which freezes them). This enables more powerful reasoning about opponent information without enumerating prohibitively large common-knowledge sets.

Contribution

One-sided GT-CFR tree expansion algorithm

A variant of growing-tree CFR where only one player uses an exploration-exploitation strategy while the other plays their equilibrium strategy directly. This focuses tree expansion on relevant nodes and is formally shown to converge to exact equilibrium given infinite time.

Contribution

Obscuro: first superhuman AI for Fog of War chess

Obscuro combines the new search techniques (KLUSS and one-sided GT-CFR) to achieve superhuman performance in Fog of War chess, the largest turn-based zero-sum game by imperfect information where superhuman play has been reached and the largest game where imperfect-information search has been successfully applied.

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