Equation 6 · Evaluating Trajectories, Not Answers

What does this equation mean?

1 - (1-p)^k \qquad \text{against} \qquad p^k .

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This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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p

Symbol p

the per-attempt success probability.

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k

Symbol k

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

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p^k

Symbol p^k

$p^k$ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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subtraction

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

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superscript

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.

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How to interpret it

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What the article says around this equation

The two quantities point in opposite directions as sampling increases. With per-attempt success probability p and independent attempts, compare $1 - (1-p)^k \qquad \text{against} \qquad p^k$ . The first rises toward one; the second falls toward zero. They are computed from the same runs and answer entirely different questions, and reporting the first while the deployment depends on the second is the most common quiet misrepresentation in agent evaluation.

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