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Equation 10 · Part 4 · Comparing the Main Approaches to Claude Code and Agentic Development Tools

superscript

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

What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

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 exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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