Equation 27 · Part 2 · 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 part of the quantity the equation computes from the expression on the right.
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 . which is concave in k and saturates quickly. Two caveats destroy any naive extrapolation from it. Attempts from one model on one prompt are strongly correlated, so realised gains fall well below…
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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.
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Sources cited in the surrounding passage
These citations provide research context; check each source for the exact claim it supports.