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Published equation contexts

1−(1−p)kagainstpk1 - (1-p)^k \qquad \text{against} \qquad p^k

Why this formula appears here

The two quantities point in opposite directions as sampling increases. With per-attempt success probability p and independent attempts, compare 1−(1−p)kagainstpk1 - (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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kk

Symbol k

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pkp^k

Symbol p^k

pkp^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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Published contexts (1)

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

Equation 6 · Agent Evaluation

Evaluating Trajectories, Not Answers

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

The two quantities point in opposite directions as sampling increases. With per-attempt success probability p and independent attempts, compare 1−(1−p)kagainstpk1 - (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.

Meanings in this article

  • pp: the per-attempt success probability.
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