---
title: "Large Language Models Are Bad Dice Players: LLMs Struggle to"
description: "LLMs are increasingly used inside pipelines that need genuinely random output, such as synthetic data, simulations and test… 48 references."
authors: ["Minda Zhao", "Yilun Du", "Mengyu Wang"]
year: 2026
venue: "Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)"
source: "https://aclanthology.org/2026.acl-long.1051/"
doi: "10.18653/v1/2026.acl-long.1051"
licence: "CC BY 4.0 (ACL Anthology)"
licence_url: "https://creativecommons.org/licenses/by/4.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/zhao-2026-large-language-models-are-bad/"
---
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# Large Language Models Are Bad Dice Players: LLMs Struggle to Generate Random Numbers from Statistical Distributions

**Authors:** Minda Zhao, [Yilun Du](https://md.research.elamur.ai/free/en/authors/yilun-du/) and [Mengyu Wang](https://md.research.elamur.ai/free/en/authors/mengyu-wang/) · **Year:** 2026 · **Venue:** [Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)](https://md.research.elamur.ai/free/en/venues/acl/) ([ACL 2026](https://md.research.elamur.ai/free/en/venues/acl/2026/)) · **Publisher:** [Association for Computational Linguistics](https://md.research.elamur.ai/free/en/publishers/association-for-computational-linguistics/) · **Licence:** [CC BY 4.0 (ACL Anthology)](https://creativecommons.org/licenses/by/4.0/)

**Links:** [Publisher's page](https://aclanthology.org/2026.acl-long.1051/) · [PDF](https://aclanthology.org/2026.acl-long.1051.pdf) · [DOI 10.18653/v1/2026.acl-long.1051](https://doi.org/10.18653/v1/2026.acl-long.1051) · [OpenAlex](https://openalex.org/W7166808055)

**Citations:** 0 citations (OpenAlex, 2026-10-14)

## Summary
LLMs are increasingly used inside pipelines that need genuinely random output, such as synthetic data, simulations and test construction. This paper asks whether they can draw samples from a requested probability distribution without calling external code. The authors audit 11 frontier models on 15 distributions, grouped into three complexity tiers, at temperature 1.0. Each setting uses N=1000 samples under two protocols. In batch generation, a single response contains all samples. In independent requests, each of 1000 stateless calls returns one sample. Outputs are compared with NumPy/SciPy reference samples using KS and chi-square goodness-of-fit tests (α=0.01) and the Wasserstein-1 distance. Results are poor overall, and independent sampling fails almost completely. Fidelity drops as distributions get more complex and, unexpectedly, as N grows. The failures also carry over to practical tasks: answer positions in generated MCQs and demographic attributes in text-to-image prompts both stray from their targets. The authors conclude that LLMs have no working internal sampler, so tasks that need statistical guarantees should rely on external tools.

## Key points
- Batch generation reaches a median pass rate of only 7%. Under independent requests, 10 of the 11 models pass no distribution at all.
- Pass rates decline from Tier I (Uniform, Gaussian, Bernoulli) to Tier III (e.g., Cauchy, Student's t, Gamma, Weibull). No model passes on Cauchy or Chi-Square.
- A sample-size sweep (N from 50 to 2000) on Gaussian and Bernoulli with DeepSeek-V3.2 and Kimi-K2 shows inverse scaling: W1 rises with larger N in both protocols.
- In prompt synthesis with U.S. Census targets, every deviation is significant (p\<0.001). One model, for example, produced 97.2% female prompts when the target was roughly 50/50.
- Code and data are available on GitHub at Mininda/LLM_Bad_Dice_Player.

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

## Institutions

- [Harvard University](https://md.research.elamur.ai/free/en/universities/harvard-university/) — University, Cambridge, United States · 126 works · 45,130 citations

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## Cite

Cite as: Minda Zhao, Yilun Du and Mengyu Wang. 2026. Large Language Models Are Bad Dice Players: LLMs Struggle to Generate Random Numbers from Statistical Distributions. Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers).

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@inproceedings{zhao2026large,
  title = {{Large Language Models Are Bad Dice Players: LLMs Struggle to Generate Random Numbers from Statistical Distributions}},
  author = {Minda Zhao, Yilun Du and Mengyu Wang},
  booktitle = {Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)},
  year = {2026},
  doi = {10.18653/v1/2026.acl-long.1051},
  url = {https://doi.org/10.18653/v1/2026.acl-long.1051}
}
```

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*Updated 2 November 2026*