Google DeepMind study finds LLMs can’t reliably roll their own dice

Ask a large language model to pick a random number, and it will happily oblige. According to new research from Google DeepMind, it just won’t be very random about it. A paper titled “The Illusion of Stochasticity in LLMs” argues that reliable random sampling is a basic requirement for AI agents. It also argues that today’s models don’t meet it. What the researchers found The study was produced by Google DeepMind in collaboration with the National University of Singapore. Its listed authors include Xiangming Gu, Soham De, Michalis K. Titsias, Larisa Markeeva, Petar Veličković, and Razvan Pascanu. The paper carries the arXiv ID 2604.06543. It was submitted on April 8, 2026, revised on August 2, 2026, and presented at the COLM 2026 conference. The core problem is a disconnect between knowing and doing. LLMs can estimate probabilities well and handle the underlying math. Yet when asked to actually produce outputs that follow a given distribution, they fall short. The researchers tested models on sampling from standard distributions, including uniform and Gaussian ones. They ran the results through Chi-Square and Kolmogorov-Smirnov tests, two common statistical checks for whether a set ...