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Equation 2 · Part 1 · The Hardest Unsolved Problems in AI Agent Evaluation and Reliability

Symbol k

pass@k=1−(1−p)k,passk=pk,\text{pass@}k = 1-(1-p)^k, \qquad \text{pass}^k = p^k,
kk

What this part means

k is part of the quantity the equation computes from the expression on the right.

Its job in the formula

k is part of the quantity the equation computes from the expression on the right.

The passage around this formula

…trials rather than single runs. τ-bench formalizes the distinction with two related quantities. If a single attempt succeeds with probability p , and attempts are treated as independent, pass@k=1−(1−p)k,passk=pk\text{pass@}k = 1-(1-p)^k, \qquad \text{pass}^k = p^k. where pass@ k is the probability that at least one of k attempts succeeds, and pass ^k is the probability that all k succeed [ 3 ] . The two statistics move in opposite directions as k grows: pass@ k climbs toward certainty, which is the right question when a system can retry until something works or a human…

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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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