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Equation 33 · Part 1 · Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex

Symbol q

Pr⁡(at least one success)=1−(1−q)k.\Pr(\text{at least one success})=1-(1-q)^k.
qq

What this part means

the probability.

Its job in the formula

q is one of the signed contributions combined to compute the quantity on the left.

Where the article explains it

If independent attempts each succeed with probability q , then Pr⁡(at least one success)=1−(1−q)k\Pr(\text{at least one success})=1-(1-q)^k.

The passage around this formula

Code-generation research often reports pass@\mathrm{pass@}k : the probability that at least one of k sampled solutions passes. If independent attempts each succeed with probability q , then Pr⁡(at least one success)=1−(1−q)k\Pr(\text{at least one success})=1-(1-q)^k. 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

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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

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