Equation 3 · Part 1 · OpenAI and Claude on Formal Reasoning: What the Benchmarks Show, and Where They Mislead
Symbol p_k
What this part means
the probability that at least one succeeds.
Its job in the formula
is part of the quantity the equation computes from the expression on the right.
Full expression→Symbol p_k→Article meaning
Where the article explains it
If a single attempt at a problem succeeds with probability p , and k attempts were independent, the probability that at least one succeeds is
The passage around this formula
Consider what the o1 numbers alone expose about how these gains are produced. If a single attempt at a problem succeeds with probability p , and k attempts were independent, the probability that at least one succeeds is . a curve that climbs fast and then saturates. It is tempting to read o1’s jump from 74% (one sample) to 83% (64-sample consensus) to 93% (1,000-sample rerank) as roughly this shape. It is not, for two reasons that matter for how the number should be read. First, repeated attempts by one model on one problem are correlated — the same misconception that causes one failure tends to recur — so the realised gain from added samples falls well below what…
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A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.
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Sources cited in the surrounding passage
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