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Outbidding and Outbluffing Elite Humans: Mastering Liar’s Poker via Self-Play and Reinforcement Learning

NeurIPS 2026 · Multi-agent systems and games › Games and equilibria · approach: Cooperation and social dilemmas · 0 citations (OpenAlex)

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Trains Solly, a small MLP agent via self-play with multi-player R-NaD (actor-critic regularized Nash dynamics), that beats elite humans and LLMs (GPT-4.1, o3) at reduced-format 3x3 and 5x5 Liar's Poker.

Problem

Multi-player imperfect-information games like Liar's Poker, where all players stay engaged across bidding rounds, lack AI agents that reach elite human play; Nash equilibrium guarantees do not extend cleanly beyond two players.

Approach

Extends two-player R-NaD (used in DeepNash) to n-player self-play with a small MLP, evaluated primarily against elite human players and LLMs rather than by equilibrium computation, using best-response DQN exploiters to estimate exploitability.

Key results

• Solly won 60% of 1,000 heads-up 3x3 hands against GPT-4.1 and 55% against o3 with equity of $19 and $9 per 100 hands.
• Against elite humans, Solly won 48% of 100 heads-up 3x3 hands (-$4 equity) and 55% of 100 heads-up 5x5 hands (+$10 equity).
• In 3x3 3-player games vs two elite humans, Solly won 54% of 100 hands with $17 equity, a difference not statistically significant (mean 0.17, SE 0.15).

Surprising findings

• Solly rebid in roughly 33% of 3-player hands versus about 8% for humans, a bluffing pattern atypical of human strategy.
• Against elite humans heads-up 3x3, Solly's win rate was 48%, with negative equity, so it did not clearly beat humans in that setting.

Limitations

• Human sample small (100 hands per configuration, five to seven players), so statistical significance was not reached.
• Only reduced-format games (3x3, 5x5) were tested; full 8x10 game not solved.
• LLM evaluation used limited prompting and few preliminary multi-player tests with no TTC for Solly.

Experimental setup

Benchmarks: 3x3 2-player Liar's Poker 3x3 3-player Liar's Poker 5x5 2-player Liar's Poker

Metrics: win rate equity (money won per 100 hands) best response score standard error

Baselines: GPT-4.1 OpenAI o3 Deterministic binomial baseline model DQN best response Elite human players

Builds on: R-NaD DeepNash OpenSpiel DQN

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