What does this equation mean?

averaged over tasks to produce the benchmark’s headline number. The metric is designed to punish an agent whose competence is real but inconsistent across resampled trials — a stochastic policy with true per-trial success probability p has $\text{pass}^k$ $\approx$ $p^k$ , which falls quickly as k grows. But a policy whose output on a given task is deterministic — an empty response, always, regardless of sampling — produces the identical transcript on every trial, so $\text{pass}^k_{\text{deterministic}} = \text{pass}^1 \quad \text{for every } k$. A degenerate exploit is not merely invisible to pass@1; it is more invisible to pas$s^k$, precisely because pas$s^k$ was built to reward consistency, and a fixed, checker-satisfying non-answer is the most consistent thing a policy can produce. The metric engineered to catch the difference between competence and luck cannot, on its own, tell competence apart from a policy that never varies because it never tries.