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Equation 10 · Part 2 · How Benchmark Contamination Actually Works in Agentic Evaluation

Symbol p^k

passk≈pk\text{pass}^k \approx p^k
pkp^k

What this part means

pkp^k is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

pkp^k is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

averaged over tasks to produce the benchmark’s headline number. The metric is designed to punish an agent whose competence is real but inconsistent across resampled trials — a stochastic policy with true per-trial success probability p has passk\text{pass}^k ≈\approx pkp^k , which falls quickly as k grows. But a policy whose output on a given task is deterministic — an empty response, always, regardless of sampling — produces the identical transcript on every trial, so

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An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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