← All parts of this equation

Equation 4 · Part 3 · Evaluating Trajectories, Not Answers

Symbol p

E[cost to first success]=cˉp,\mathbb{E}[\text{cost to first success}] = \frac{\bar{c}}{p},
pp

What this part means

the probability.

Its job in the formula

p occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

Where the article explains it

If a run costs cˉ\bar{c} on average and succeeds with probability p , and the operator simply retries until success, the expected spend to first success is E[cost to first success]=cˉp\mathbb{E}[\text{cost to first success}] = \frac{\bar{c}}{p}.

The passage around this formula

There is also a structural reason cost cannot be separated from reliability. If a run costs cˉ\bar{c} on average and succeeds with probability p , and the operator simply retries until success, the expected spend to first success is E[cost to first success]=cˉp\mathbb{E}[\text{cost to first success}] = \frac{\bar{c}}{p}. 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.

Read this part in the article →

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.

Open the illustrated variables: a letter stands for a value guide →

See this notation across published equations →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.