Emergent World Beliefs: Exploring Transformers in Stochastic Games

TL;DR

This paper investigates how transformer-based large language models can develop internal representations of stochastic environments, like poker, capturing both deterministic and probabilistic aspects without explicit training for these features.

Contribution

The study extends understanding of emergent world models in LLMs to incomplete information domains, demonstrating their ability to learn and represent stochastic environment features.

Findings

Models learn hand ranks and equity without explicit instruction

Internal representations correlate with theoretical belief states

Probes show representations are decodeable and meaningful

Abstract

Transformer-based large language models (LLMs) have demonstrated strong reasoning abilities across diverse fields, from solving programming challenges to competing in strategy-intensive games such as chess. Prior work has shown that LLMs can develop emergent world models in games of perfect information, where internal representations correspond to latent states of the environment. In this paper, we extend this line of investigation to domains of incomplete information, focusing on poker as a canonical partially observable Markov decision process (POMDP). We pretrain a GPT-style model on Poker Hand History (PHH) data and probe its internal activations. Our results demonstrate that the model learns both deterministic structure, such as hand ranks, and stochastic features, such as equity, without explicit instruction. Furthermore, by using primarily nonlinear probes, we demonstrated that these representations are decodeable and correlate with theoretical belief states, suggesting that LLMs are learning their own representation of the stochastic environment of Texas Hold'em Poker.