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Equation 4 · Part 1 · Evaluating Trajectories, Not Answers

Symbol E

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

What this part means

The expected value operator: the probability-weighted average of the quantity inside its brackets.

Its job in the formula

E is part of the quantity the equation computes from the expression on the right.

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.

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Learn the underlying idea

Probability assigns a number from 0 to 1 to an event under a stated model. Zero means impossible within that model; one means certain.

Open the illustrated probability: a quantified chance 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.