Equation 10 · The Hardest Unsolved Problems in AI Agent Evaluation and Reliability
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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 best of several drafts, while pass ^k falls toward zero, which is the right question for an agent deployed without a human standing by to catch the failures. Yao and colleagues report that state-of-the-art function-calling agents solved under half of τ-bench’s tasks on a single attempt, and that their pass ^k scores fell substantially with repeated trials of the same task under…
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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 best of several drafts, while pass ^k falls toward zero, which is the right question for an agent deployed without a human standing by to catch the failures. Yao and colleagues report that state-of-the-art function-calling agents solved under half of τ-bench’s tasks on a single attempt, and that their pass ^k scores fell substantially with repeated trials of the same task under identical starting conditions, exposing an inconsistency that a single pass rate could not reveal on its own [ 3 ] .
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