Measure whether an agent can repeat a successful result—not just produce one. pass^k estimates the chance that every one of k repeated attempts at the same task succeeds. It answers a consistency question, not whether an agent is safe to leave unattended overnight.
What pass^k measures
For a given task, pass^k is the probability that all k trials succeed. The τ-bench paper defines the trials as independent and identically distributed (i.i.d.) and averages the task-level measure across tasks. In practical terms, it asks: if the agent repeats this task k times under comparable conditions, how often should every attempt work?
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That differs from pass@k, which asks whether at least one of k attempts succeeds. Anthropic explains the distinction with a hypothetical per-trial success rate of 75% over three trials: the probability that all three succeed is approximately 42%. This is an illustration, not a measured result for a real agent. Anthropic’s agent-evaluation explanation discusses both measures.
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Estimate pass^k from repeated trials
For one task, run the agent n times using a fixed task definition and success rubric. If c of those n runs succeed, the τ-bench paper gives this unbiased estimator for pass^k:
Estimated pass^k = C(c, k) / C(n, k)
Here, C(a, b) is the number of ways to choose b items from a. The estimate is the fraction of all possible groups of k observed runs in which every run succeeded. It is defined when n is at least k; if fewer than k runs were observed, there are not enough trials to form such a group.
For example, if 8 of 10 observed runs succeed and k is 3, the estimate is C(8, 3) / C(10, 3), or 56/120—about 46.7%. This describes the task-level estimate from those observations; it is not a guarantee about future runs.
For a task suite, calculate the task-level estimate and average it across tasks, as specified by τ-bench. Do not take an aggregate single-run success rate for a varied task suite and simply raise it to the kth power: that shortcut treats the suite as if it were one homogeneous task and can misrepresent its repeated-run consistency. The τ-bench paper at PMLR defines the metric and estimator. (Use the paper’s exact URL: https://proceedings.mlr.press/v267/asai25a.html.)
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Design an evaluation that answers the deployment question
Fix the task and success condition
Keep the task definition and rubric unchanged across repeated runs. Specify what counts as completion, what errors make a run fail, and how borderline outcomes are scored. Otherwise, a change in the measurement may reflect a changed definition rather than a change in agent reliability.
Match the work the agent will actually do
Build the evaluation set around the tasks the unattended agent is expected to perform. A task-level repeated-run metric is only useful for the intended decision if its tasks resemble that work. The cited metric definition does not provide a universal recipe for representativeness, so describe how the suite relates to the planned workload rather than implying that a benchmark automatically represents production.
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Keep comparisons like for like
When comparing agents or configurations, use the same task definitions, success rubric, k, and comparable run conditions. State what counts as an independent run; repeated executions that share state or conditions may not answer the same question as independent trials.
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- The task suite and task-level outcomes
- The chosen k and the number n of observed trials per task
- The success criteria and treatment of borderline results
- What counted as an independent run and the conditions held constant
These details let a reader understand what the reported number does and does not represent. A single score without them can hide variation among tasks or leave the meaning of a “trial” unclear.
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What the number cannot certify
pass^k measures repeated task success under the evaluation’s conditions. It does not, by itself, establish security, resilience to tool failures, or long-horizon operational safety. The cited work defines the statistic but does not set a universal pass^k threshold, confidence level, sample size, or operational safeguards that certify an agent for overnight use. The broader subject of agent reliability is also treated as an active research area in a 2026 proceedings paper: arXiv:2602.02475.
Do not treat a benchmark’s trial count as a deployment rule. τ-bench reports using more than 40 GPT-4-turbo trials per τ-retail task during benchmark construction for tasks with zero or low success rates. That is a description of how that benchmark was constructed, not a general minimum for measuring an agent before unattended operation.
Use pass^k as evidence about consistency on a defined set of tasks, then make the overnight decision using the broader requirements of the application. The metric can inform that decision; the sources defining it do not make it a complete operational safety case.
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