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Equation 2 · Part 5 · The Hardest Unsolved Problems in AI Agent Evaluation and Reliability

superscript

pass@k=1−(1−p)k,passk=pk,\text{pass@}k = 1-(1-p)^k, \qquad \text{pass}^k = p^k,
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What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

The passage around this formula

Large language model agents are not deterministic in practice, even holding the prompt and the environment fixed, and this is why the tool-use literature evaluates repeated 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 picks the…

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Learn the underlying idea

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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Sources cited in the surrounding passage

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