Equation 25 · Part 1 · OpenAI Model Systems from First Principles: Weights, Post-Training, and Inference Compute
Symbol p
What this part means
the probability.
Its job in the formula
p is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Full expression→Symbol p→Article meaning
Where the article explains it
If a single attempt succeeds with probability p and attempts were independent, the probability that at least one of k succeeds is
The passage around this formula
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
Learn the underlying idea
A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.
Open the illustrated variables: a letter stands for a value guide →
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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 ↗
These citations provide research context; check each source for the exact claim it supports.