Large Language Models Are Bad Dice Players: LLMs Struggle to Generate Random Numbers from Statistical Distributions

TL;DR

This study reveals that large language models struggle to accurately sample from probability distributions, especially in independent requests, impacting their reliability in stochastic applications.

Contribution

It provides the first large-scale, statistically rigorous evaluation of LLMs' native probabilistic sampling capabilities, highlighting significant limitations.

Findings

Batch sampling achieves 7% median validity

Independent requests pass nearly none of the distributions

Sampling fidelity worsens with distribution complexity and sample size

Abstract

As large language models (LLMs) transition from chat interfaces to integral components of stochastic pipelines and systems approaching general intelligence, the ability to faithfully sample from specified probability distributions has become a functional requirement rather than a theoretical curiosity. We present the first large-scale, statistically powered audit of native probabilistic sampling in frontier LLMs, benchmarking 11 models across 15 distributions. To disentangle failure modes, we employ a dual-protocol design: Batch Generation, where a model produces $N{=}1000$ samples within one response, and Independent Requests, comprising $N{=}1000$ stateless calls. We observe a sharp protocol asymmetry: batch generation achieves only modest statistical validity, with a 7% median pass rate, while independent requests collapse almost entirely, with 10 of 11 models passing none of the distributions. Beyond this asymmetry, we reveal that sampling fidelity degrades monotonically with distributional complexity and aggravates as the sampling horizon $N$ increases. Finally, we demonstrate how the propagation of these failures into downstream real-world application tasks introduces systematic biases: models fail to enforce uniform answer-position constraints in Multiple Choice Question generation and systematically violate demographic targets in attribute-constrained text-to-image prompt synthesis. These findings indicate that current LLMs lack a functional internal sampler, necessitating external tools for applications requiring statistical guarantees.