Equation 16 · Part 1 · Measuring AI Agent Reliability: What the Evidence Actually Supports
Symbol k
What this part means
the number of samples.
Its job in the formula
k is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Full expression→Symbol k→Article meaning
Where the article explains it
The obvious approach — generate exactly k samples per problem and check whether any of them pass — has an undesirable property: it is a valid estimate but a high-variance one, since it throws away information every time you happen to generate more or fewer than k samples.
The passage around this formula
The two formulas share the same n , c , and k and the same combinatorial machinery, and that similarity is precisely the point: they are estimating two different probabilities from the same data, one about the best of k attempts and one about the consistency of all k of them. A system can score well on the first and badly on the second, and a report that only states pass@k while an agent is actually being deployed to run the same class of task repeatedly, unsupervised, with no way to pick the lucky run, is answering a question nobody was asking.
Learn the underlying idea
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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Sources cited in the article section
- [2] Evaluating Large Language Models Trained on Code ↗
- [3] tau-bench: A Benchmark for Tool-Agent-User Interaction in Real-World Domains ↗
These citations provide research context; check each source for the exact claim it supports.