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Exposure per gap=1−(1−p)g\text{Exposure per gap} = 1-(1-p)^g

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Now suppose each individual tool call has some small, independent probability p of being consequential and wrong in a way a reviewer would have caught. The probability that at least one such call executes, unreviewed, inside a single gap of g calls is Exposure per gap=1−(1−p)g\text{Exposure per gap} = 1-(1-p)^g. This is the same “at least one” shape that shows up whenever independent trials are combined, applied here to the opposite question from the one it usually answers: not how many attempts are needed before one succeeds, but how many unwatched actions occur before one goes wrong. For small g , exposure grows almost linearly — each additional ungated action adds roughly p more exposure — so coarsening from asking every time to…

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Exposure per gap=1−(1−p)g.\text{Exposure per gap} = 1-(1-p)^g.

Equation 10 · AI Agents & Systems

Comparing the Main Approaches to Claude Code and Agentic Development Tools

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

Now suppose each individual tool call has some small, independent probability p of being consequential and wrong in a way a reviewer would have caught. The probability that at least one such call executes, unreviewed, inside a single gap of g calls is Exposure per gap=1−(1−p)g\text{Exposure per gap} = 1-(1-p)^g. This is the same “at least one” shape that shows up whenever independent trials are combined, applied here to the opposite question from the one it usually answers: not how many attempts are needed before one succeeds, but how many unwatched actions occur before one goes wrong. For small g , exposure grows almost linearly — each additional ungated action adds roughly p more exposure — so coarsening from asking every time to…

Meanings in this article

  • pp: the independent probability.
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