Equation 4 · Evaluating Trajectories, Not Answers
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
Read it piece by piece
Symbol E
The expected value operator: the probability-weighted average of the quantity inside its brackets.
Symbol barc
barc occurs above the fraction bar. The numerator is divided by the entire denominator below it.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →How to interpret it
With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
There is also a structural reason cost cannot be separated from reliability. If a run costs on average and succeeds with probability p , and the operator simply retries until success, the expected spend to first success is . which means a cheap unreliable agent and an expensive reliable one can occupy the same operating point. Reporting either number alone conceals which one you have bought. The honest artefact is a curve — quality against spend, produced by sweeping the effort level and the retry policy — rather than a point, and the honest comparison places two systems at matched spend and asks which reaches further.
Sources cited in the article section
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