# Do LLMs Play Dice? Exploring Probability Distribution Sampling in Large Language Models for Behavioral Simulation

arXiv: https://arxiv.org/abs/2404.09043 · HTML: https://mlsanity.com/paper/2404.09043/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 46 references that are in the map.
- First posted on arXiv 13 Apr 2024.

## Builds on (most cited first, 19 of 19)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [GLM: General Language Model Pretraining with Autoregressive Blank Infilling](https://mlsanity.com/paper/2103.10360/) (2021)
- [Galactica: A Large Language Model for Science](https://mlsanity.com/paper/2211.09085/) (2022)
- [Using Large Language Models to Simulate Multiple Humans and Replicate Human Subject Studies](https://mlsanity.com/paper/2208.10264/) (2022)
- [S3: Social-network Simulation System with Large Language Model-Empowered Agents](https://mlsanity.com/paper/2307.14984/) (2023)
- [Pre-Trained Language Models for Interactive Decision-Making](https://mlsanity.com/paper/2202.01771/) (2022)
- [Do LLM Agents Exhibit Social Behavior?](https://mlsanity.com/paper/2312.15198/) (2023)
- [AI-Augmented Surveys: Leveraging Large Language Models and Surveys for Opinion Prediction](https://mlsanity.com/paper/2305.09620/) (2023)
- [Exploring Human-Like Translation Strategy with Large Language Models](https://mlsanity.com/paper/2305.04118/) (2023)
- [Are you in a Masquerade? Exploring the Behavior and Impact of Large Language Model Driven Social Bots in Online Social Networks](https://mlsanity.com/paper/2307.10337/) (2023)
- [Think Before You Speak: Cultivating Communication Skills of Large Language Models via Inner Monologue](https://mlsanity.com/paper/2311.07445/) (2023)
- [Knowledge Boundary and Persona Dynamic Shape A Better Social Media Agent](https://mlsanity.com/paper/2403.19275/) (2024)

## Built on by (most cited first, 14 of 14)

- [Enough Coin Flips Can Make LLMs Act Bayesian](https://mlsanity.com/paper/2503.04722/) (2025)
- [Fourier Head: Helping Large Language Models Learn Complex Probability Distributions](https://mlsanity.com/paper/2410.22269/) (2024)
- [The Illusion of Stochasticity in LLMs](https://mlsanity.com/paper/2604.06543/) (2026)
- [Reasoning Under Uncertainty: Exploring Probabilistic Reasoning Capabilities of LLMs](https://mlsanity.com/paper/2509.10739/) (2025)
- [Playing games with Large language models: Randomness and strategy](https://mlsanity.com/paper/2503.02582/) (2025)
- [Flipping Against All Odds: Reducing LLM Coin Flip Bias via Verbalized Rejection Sampling](https://mlsanity.com/paper/2506.09998/) (2025)
- [Large Language Models Are Bad Dice Players: LLMs Struggle to Generate Random Numbers from Statistical Distributions](https://mlsanity.com/paper/2601.05414/) (2026)
- [Codifying Character Logic in Role-Playing](https://mlsanity.com/paper/2505.07705/) (2025)
- [Frontier Models Can Take Actions at Low Probabilities](https://mlsanity.com/paper/2603.02202/) (2026)
- [Scaling Law in LLM Simulated Personality: More Detailed and Realistic Persona Profile Is All You Need](https://mlsanity.com/paper/2510.11734/) (2025)
- [D-Models and E-Models: Diversity-Stability Trade-offs in the Sampling Behavior of Large Language Models](https://mlsanity.com/paper/2601.17865/) (2026)
- [DynamicPO: Dynamic Preference Optimization for Recommendation](https://mlsanity.com/paper/2605.00327/) (2026)
- [Can LLMs Take Retrieved Information with a Grain of Salt?](https://mlsanity.com/paper/2605.06919/) (2026)
- [AI Literacy: An Exercise in Power-Knowledge](https://mlsanity.com/paper/2607.27547/) (2026)

## Abstract (arXiv)

With the rapid advancement of large language models (LLMs) for handling complex language tasks, an increasing number of studies are employing LLMs as agents to emulate the sequential decision-making processes of humans often represented as Markov decision-making processes (MDPs). The actions in MDPs adhere to specific probability distributions and require iterative sampling. This arouses curiosity regarding the capacity of LLM agents to comprehend probability distributions, thereby guiding the agent's behavioral decision-making through probabilistic sampling and generating behavioral sequences. To answer the above question, we divide the problem into two main aspects: sequence simulation with known probability distribution and sequence simulation with unknown probability distribution. Our analysis indicates that LLM agents can understand probabilities, but they struggle with probability sampling. Their ability to perform probabilistic sampling can be improved to some extent by integrating coding tools, but this level of sampling precision still makes it difficult to simulate human behavior as agents.