# Single Deep Counterfactual Regret Minimization

arXiv: https://arxiv.org/abs/1901.07621 · HTML: https://mlsanity.com/paper/1901.07621/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jan 2019.

## Built on by (most cited first, 20 of 20)

- [XDO: A Double Oracle Algorithm for Extensive-Form Games](https://mlsanity.com/paper/2103.06426/) (2021)
- [A Survey on Self-play Methods in Reinforcement Learning](https://mlsanity.com/paper/2408.01072/) (2024)
- [ESCHER: Eschewing Importance Sampling in Games by Computing a History Value Function to Estimate Regret](https://mlsanity.com/paper/2206.04122/) (2022)
- [The Power of Regularization in Solving Extensive-Form Games](https://mlsanity.com/paper/2206.09495/) (2022)
- [Search in Imperfect Information Games](https://mlsanity.com/paper/2111.05884/) (2021)
- [How Far Are LLMs from Professional Poker Players? Revisiting Game-Theoretic Reasoning with Agentic Tool Use](https://mlsanity.com/paper/2602.00528/) (2026)
- [DanZero+: Dominating the GuanDan Game through Reinforcement Learning](https://mlsanity.com/paper/2312.02561/) (2023)
- [DanZero: Mastering GuanDan Game with Reinforcement Learning](https://mlsanity.com/paper/2210.17087/) (2022)
- [A Policy-Gradient Approach to Solving Imperfect-Information Games with Best-Iterate Convergence](https://mlsanity.com/paper/2408.00751/) (2024)
- [CFR-MIX: Solving Imperfect Information Extensive-Form Games with Combinatorial Action Space](https://mlsanity.com/paper/2105.08440/) (2021)
- [Hierarchical Deep Counterfactual Regret Minimization](https://mlsanity.com/paper/2305.17327/) (2023)
- [A Survey of Decision Making in Adversarial Games](https://mlsanity.com/paper/2207.07971/) (2022)
- [Supervised and Reinforcement Learning from Observations in Reconnaissance Blind Chess](https://mlsanity.com/paper/2208.02029/) (2022)
- [Multi-agent Reinforcement Learning in OpenSpiel: A Reproduction Report](https://mlsanity.com/paper/2103.00187/) (2021)
- [Offline Equilibrium Finding](https://mlsanity.com/paper/2207.05285/) (2022)
- [D2CFR: Minimize Counterfactual Regret with Deep Dueling Neural Network](https://mlsanity.com/paper/2105.12328/) (2021)
- [L2E: Learning to Exploit Your Opponent](https://mlsanity.com/paper/2102.09381/) (2021)
- [Game-Theoretic Robust Reinforcement Learning Handles Temporally-Coupled Perturbations](https://mlsanity.com/paper/2307.12062/) (2023)
- [Local Updates, Global Learning (LUGL): Playing Games with non-incremental Learners](https://mlsanity.com/paper/2609.03660/) (2026)
- [GPU-CFR: 80x Faster Counterfactual Regret Minimization by Compiling the Game to Static Dataflow and CUDA Graph Replay](https://mlsanity.com/paper/2609.11923/) (2026)

## Abstract (arXiv)

Counterfactual Regret Minimization (CFR) is the most successful algorithm for finding approximate Nash equilibria in imperfect information games. However, CFR's reliance on full game-tree traversals limits its scalability. For this reason, the game's state- and action-space is often abstracted (i.e. simplified) for CFR, and the resulting strategy is then translated back to the full game, which requires extensive expert-knowledge and often converges to highly exploitable policies. A recently proposed method, Deep CFR, applies deep learning directly to CFR, allowing the agent to intrinsically abstract and generalize over the state-space from samples, without requiring expert knowledge. In this paper, we introduce Single Deep CFR (SD-CFR), a simplified variant of Deep CFR that has a lower overall approximation error by avoiding the training of an average strategy network. We show that SD-CFR is more attractive from a theoretical perspective and empirically outperforms Deep CFR with respect to exploitability and one-on-one play in poker.