Why Temperature 0 Isn't Deterministic

In September 2025, Horace He and colleagues at Thinking Machines Lab ran a simple experiment. They sent the prompt "Tell me about Richard Feynman" to Qwen3-235B 1,000 times at temperature 0 and asked for 1,000 tokens each time. Temperature 0 means the model always picks its most probable token, so you would expect 1,000 identical answers. They got 80 unique completions. What caught my eye is where the answers split. All 1,000 completions were identical for the first 102 tokens. At token 103, 992 of them continued with "Queens, New York" and 8 with "New York City." Eight runs in a thousand flipped at a single token, after 102 tokens where none did. Their post explains why outputs differ at all. This article asks a different question: how often should a token flip, and why does that risk arrive in sudden spikes? I'll derive a one-line formula, check it with a simulation, and test it on a real model. Everything runs on a laptop,…