How reliable are LLMs when it comes to playing dice?

• URL: http://arxiv.org/abs/2606.07515v2
• Date: Thu, 11 Jun 2026 16:52:41 GMT
• Title: How reliable are LLMs when it comes to playing dice?
• Abstract summary: We investigate the reasoning capabilities of large language models through a controlled benchmarking study on discrete probability problems.<n>Models achieve an average accuracy of 0.96 on standard problems but only 0.59 on counterintuitive ones.<n> Embedding misleading suggestions in the prompt reduces performance by up to 34%, with no model proving immune.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We investigate the probabilistic reasoning capabilities of large language models through a controlled benchmarking study on discrete probability problems. We constructed two datasets, respectively a set of standard exercises and a set of counterintuitive exercises, designed to trigger heuristic reasoning, and evaluated 8 state-of-the-art models, each tested with and without Chain-of-Thought prompting. Models achieve an average accuracy of 0.96 on standard problems but only 0.59 on counterintuitive ones. We further provide empirical evidence of token bias: performance drops by over 20% when canonical formulations are replaced by disguised variants. Embedding misleading suggestions in the prompt reduces performance by up to 34%, with no model proving immune. Taken together, the reported findings suggest that current LLMs are not yet genuine probabilistic reasoners, despite their success in advanced mathematical problems.

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