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Equation 9 · Part 1 · A History of How We Learned to Evaluate AI Agents

Symbol k

pass@k  =  Eproblems ⁣[ 1−(n−ck)(nk) ].\text{pass@}k \;=\; \mathbb{E}_{\text{problems}}\!\left[\,1 - \frac{\binom{n-c}{k}}{\binom{n}{k}}\,\right].
kk

What this part means

the especially at small.

Its job in the formula

k is computed from the expected values combined on the right.

Where the article explains it

That last detail forced a genuine statistical problem into agent-adjacent evaluation for the first time: naively estimating the chance that at least one of k sampled attempts succeeds, by drawing exactly k samples and checking, is a high-variance estimator, especially at small k .

The passage around this formula

That last detail forced a genuine statistical problem into agent-adjacent evaluation for the first time: naively estimating the chance that at least one of k sampled attempts succeeds, by drawing exactly k samples and checking, is a high-variance estimator, especially at small k . Chen and colleagues instead drew a larger fixed pool of n samples per problem, counted the number c that passed, and computed an unbiased estimate of the pass rate at budget…

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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 article section

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