# Solving Large Imperfect Information Games Using CFR+

arXiv: https://arxiv.org/abs/1407.5042 · HTML: https://mlsanity.com/paper/1407.5042/

## Key facts

- Cited by 78 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jul 2014.

## Built on by (most cited first, 30 of 78)

- [Language Agents with Reinforcement Learning for Strategic Play in the Werewolf Game](https://mlsanity.com/paper/2310.18940/) (2023)
- [Suspicion-Agent: Playing Imperfect Information Games with Theory of Mind Aware GPT-4](https://mlsanity.com/paper/2309.17277/) (2023)
- [A Unified Approach to Reinforcement Learning, Quantal Response Equilibria, and Two-Player Zero-Sum Games](https://mlsanity.com/paper/2206.05825/) (2022)
- [XDO: A Double Oracle Algorithm for Extensive-Form Games](https://mlsanity.com/paper/2103.06426/) (2021)
- [Multi-agent Reinforcement Learning: A Comprehensive Survey](https://mlsanity.com/paper/2312.10256/) (2023)
- [Last-iterate Convergence in Extensive-Form Games](https://mlsanity.com/paper/2106.14326/) (2021)
- [Near-Optimal Learning of Extensive-Form Games with Imperfect Information](https://mlsanity.com/paper/2202.01752/) (2022)
- [A Survey on Self-play Methods in Reinforcement Learning](https://mlsanity.com/paper/2408.01072/) (2024)
- [Simple Uncoupled No-Regret Learning Dynamics for Extensive-Form Correlated Equilibrium](https://mlsanity.com/paper/2104.01520/) (2021)
- [Model-Free Learning for Two-Player Zero-Sum Partially Observable Markov Games with Perfect Recall](https://mlsanity.com/paper/2106.06279/) (2021)
- [Efficient Deviation Types and Learning for Hindsight Rationality in Extensive-Form Games](https://mlsanity.com/paper/2102.06973/) (2021)
- [Learning Strategic Language Agents in the Werewolf Game with Iterative Latent Space Policy Optimization](https://mlsanity.com/paper/2502.04686/) (2025)
- [Regret Matching+: (In)Stability and Fast Convergence in Games](https://mlsanity.com/paper/2305.14709/) (2023)
- [Reevaluating Policy Gradient Methods for Imperfect-Information Games](https://mlsanity.com/paper/2502.08938/) (2025)
- [Model-Free Online Learning in Unknown Sequential Decision Making Problems and Games](https://mlsanity.com/paper/2103.04539/) (2021)
- [Adapting to game trees in zero-sum imperfect information games](https://mlsanity.com/paper/2212.12567/) (2022)
- [RL-CFR: Improving Action Abstraction for Imperfect Information Extensive-Form Games with Reinforcement Learning](https://mlsanity.com/paper/2403.04344/) (2024)
- [Adaptively Perturbed Mirror Descent for Learning in Games](https://mlsanity.com/paper/2305.16610/) (2023)
- [Search in Imperfect Information Games](https://mlsanity.com/paper/2111.05884/) (2021)
- [Mutation-Driven Follow the Regularized Leader for Last-Iterate Convergence in Zero-Sum Games](https://mlsanity.com/paper/2206.09254/) (2022)
- [HSVI can solve zero-sum Partially Observable Stochastic Games](https://mlsanity.com/paper/2210.14640/) (2022)
- [From Average-Iterate to Last-Iterate Convergence in Games: A Reduction and Its Applications](https://mlsanity.com/paper/2506.03464/) (2025)
- [A Marriage between Adversarial Team Games and 2-player Games: Enabling Abstractions, No-regret Learning, and Subgame Solving](https://mlsanity.com/paper/2206.09161/) (2022)
- [Minimizing Weighted Counterfactual Regret with Optimistic Online Mirror Descent](https://mlsanity.com/paper/2404.13891/) (2024)
- [How Far Are LLMs from Professional Poker Players? Revisiting Game-Theoretic Reasoning with Agentic Tool Use](https://mlsanity.com/paper/2602.00528/) (2026)
- [Learning Correlated Equilibria in Mean-Field Games](https://mlsanity.com/paper/2208.10138/) (2022)
- [Last-Iterate Convergence Properties of Regret-Matching Algorithms in Games](https://mlsanity.com/paper/2311.00676/) (2023)
- [Real-Time Parallel Counterfactual Regret Minimization](https://mlsanity.com/paper/2605.19928/) (2026)
- [Public Information Representation for Adversarial Team Games](https://mlsanity.com/paper/2201.10377/) (2022)
- [Discovering Multiagent Learning Algorithms with Large Language Models](https://mlsanity.com/paper/2602.16928/) (2026)

## Abstract (arXiv)

Counterfactual Regret Minimization and variants (e.g. Public Chance Sampling CFR and Pure CFR) have been known as the best approaches for creating approximate Nash equilibrium solutions for imperfect information games such as poker. This paper introduces CFR^+, a new algorithm that typically outperforms the previously known algorithms by an order of magnitude or more in terms of computation time while also potentially requiring less memory.