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

arXiv: https://arxiv.org/abs/2506.01242 · HTML: https://mlsanity.com/paper/2506.01242/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 55 references that are in the map.
- First posted on arXiv 2 Jun 2025.

## Builds on (most cited first, 13 of 13)

- [DeepStack: Expert-Level Artificial Intelligence in No-Limit Poker](https://mlsanity.com/paper/1701.01724/) (2017)
- [Mastering the Game of Stratego with Model-Free Multiagent Reinforcement Learning](https://mlsanity.com/paper/2206.15378/) (2022)
- [Combining Deep Reinforcement Learning and Search for Imperfect-Information Games](https://mlsanity.com/paper/2007.13544/) (2020)
- [Faster Game Solving via Predictive Blackwell Approachability: Connecting Regret Matching and Mirror Descent](https://mlsanity.com/paper/2007.14358/) (2020)
- [Safe and Nested Subgame Solving for Imperfect-Information Games](https://mlsanity.com/paper/1705.02955/) (2017)
- [Solving Imperfect Information Games Using Decomposition](https://mlsanity.com/paper/1303.4441/) (2013)
- [Depth-Limited Solving for Imperfect-Information Games](https://mlsanity.com/paper/1805.08195/) (2018)
- [Student of Games: A unified learning algorithm for both perfect and imperfect information games](https://mlsanity.com/paper/2112.03178/) (2021)
- [Regret Matching+: (In)Stability and Fast Convergence in Games](https://mlsanity.com/paper/2305.14709/) (2023)
- [Subgame solving without common knowledge](https://mlsanity.com/paper/2106.06068/) (2021)
- [The Update-Equivalence Framework for Decision-Time Planning](https://mlsanity.com/paper/2304.13138/) (2023)
- [Fast Payoff Matrix Sparsification Techniques for Structured Extensive-Form Games](https://mlsanity.com/paper/2112.03804/) (2021)
- [History Filtering in Imperfect Information Games: Algorithms and Complexity](https://mlsanity.com/paper/2311.14651/) (2023)

## Built on by (most cited first, 6 of 6)

- [Scalable Decision Making for Games of Imperfect Information](https://mlsanity.com/paper/2511.07312/) (2025)
- [Look-ahead Reasoning with a Learned Model in Imperfect Information Games](https://mlsanity.com/paper/2510.05048/) (2025)
- [Convergence of Regret Matching in Potential Games and Constrained Optimization](https://mlsanity.com/paper/2510.17067/) (2025)
- [InfoChess: A Game of Adversarial Inference and a Laboratory for Quantifiable Information Control](https://mlsanity.com/paper/2604.15373/) (2026)
- [Watermarking Game-Playing Agents in Perfect-Information Extensive-Form Games](https://mlsanity.com/paper/2605.14283/) (2026)
- [Test-time Reinforcement Learning in Imperfect Information Games](https://mlsanity.com/paper/2608.30635/) (2026)

## Abstract (arXiv)

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.