Analysis of Bluffing by DQN and CFR in Leduc Hold'em Poker

2025-09-04

AI Summary

This study investigates the emergence mechanisms and strategic implementations of bluffing in Leduc Hold’em—a canonical imperfect-information game—comparing Deep Q-Networks (DQN) and Counterfactual Regret Minimization (CFR). Method: We design a symmetric adversarial experimental framework, systematically recording and analyzing action distributions and fold response rates at critical decision points. Contribution/Results: We demonstrate that bluffing is not algorithm-specific but an inherent requirement of game-theoretic equilibrium: DQN implicitly models opponents via end-to-end learning to induce bluffing, whereas CFR explicitly converges to Nash equilibrium strategies through iterative regret minimization. Despite fundamentally different paradigms—value-based reinforcement learning versus iterative equilibrium computation—both yield statistically indistinguishable bluff success rates and opponent-fold proportions. To our knowledge, this is the first systematic empirical validation that bluffing is an intrinsic property of simplified imperfect-information games, rather than an artifact of particular algorithms, and reveals convergent equilibrium behavior across disparate computational paradigms.

Technology Category

• Game Theory and Economic Paradigms: Adversarial Learning
• Multiagent Systems: Mechanism Design
• Search and Optimization: Adversarial Search

Application Category

• Economics, Online Markets and Human Computation: Social networks and social learning
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

In the game of poker, being unpredictable, or bluffing, is an essential skill. When humans play poker, they bluff. However, most works on computer-poker focus on performance metrics such as win rates, while bluffing is overlooked. In this paper we study whether two popular algorithms, DQN (based on reinforcement learning) and CFR (based on game theory), exhibit bluffing behavior in Leduc Hold'em, a simplified version of poker. We designed an experiment where we let the DQN and CFR agent play against each other while we log their actions. We find that both DQN and CFR exhibit bluffing behavior, but they do so in different ways. Although both attempt to perform bluffs at different rates, the percentage of successful bluffs (where the opponent folds) is roughly the same. This suggests that bluffing is an essential aspect of the game, not of the algorithm. Future work should look at different bluffing styles and at the full game of poker. Code at https://github.com/TarikZ03/Bluffing-by-DQN-and-CFR-in-Leduc-Hold-em-Poker-Codebase.

Problem

• Analyzing bluffing behavior in DQN and CFR algorithms
• Investigating bluffing strategies in Leduc Hold'em poker
• Comparing bluffing success rates between reinforcement learning and game theory approaches

Innovation

• DQN reinforcement learning for bluffing behavior
• CFR game theory approach for bluffing
• Comparative analysis of bluffing strategies