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Equation 31 · Part 1 · The Economics and Physical Limits of Running AI Agents at Scale

Symbol q

q1−q∑ici\frac{q}{1-q}\sum_i c_i
qq

What this part means

q is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

q is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

Holding qiq_i = q constant across the trajectory — a simplification, since real failure rates are neither constant nor independent — the expected extra cost from retries is q1−q\frac{q}{1-q}∑i\sum_i cic_i , and because cic_i increases with i , that extra cost is weighted toward the trajectory’s most expensive, latest steps rather than distributed evenly across it. A one-percent per-step retry rate is a rounding error at step five. Applied at step two hundred of an uncached or lightly cached loop, it is a rounding error on a much larger number.

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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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