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Equation 10 · Part 3 · Comparing the Main Approaches to Claude Code and Agentic Development Tools

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

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

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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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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