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Pr⁡(all k succeed)=qk\Pr(\text{all }k\text{ succeed})=q^k

Why this formula appears here

This is valuable for search: more attempts increase the chance of finding one acceptable candidate. Production consistency asks a different question. If k required deployments must all succeed, the same independence simplification gives Pr⁡(all k succeed)=qk\Pr(\text{all }k\text{ succeed})=q^k. The first rises with k ; the second falls. τ\tau -bench introduced a repeated-trial metric in this spirit and reported substantial deterioration across repeated tool-agent-user runs in its evaluated setting [ 9 ] . Coding-agent reports should state whether multiple trajectories were sampled and selected, or whether one configured system succeeds repeatedly.

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Pr⁡\Pr

Probability operator

The probability operator gives the chance of the event named inside its brackets or parentheses.

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Published contexts (1)

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Pr⁡(all k succeed)=qk.\Pr(\text{all }k\text{ succeed})=q^k.

Equation 35 · AI Agents & Systems

Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

This is valuable for search: more attempts increase the chance of finding one acceptable candidate. Production consistency asks a different question. If k required deployments must all succeed, the same independence simplification gives Pr⁡(all k succeed)=qk\Pr(\text{all }k\text{ succeed})=q^k. The first rises with k ; the second falls. τ\tau -bench introduced a repeated-trial metric in this spirit and reported substantial deterioration across repeated tool-agent-user runs in its evaluated setting [ 9 ] . Coding-agent reports should state whether multiple trajectories were sampled and selected, or whether one configured system succeeds repeatedly.

Meanings in this article

  • kk: the first rises with.
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