Equation 25 · OpenAI Model Systems from First Principles: Weights, Post-Training, and Inference Compute
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the probability. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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The parallel-sampling case makes the shape of the returns explicit. If a single attempt succeeds with probability p and attempts were independent, the probability that at least one of k succeeds is
Sources cited in the article section
- [9] Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters ↗
- [1] GPT-5 System Card ↗
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