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Equation 18 · Part 4 · What Alignment Actually Costs

Symbol p

E[Cfind]=cp.\mathbb{E}[C_{\mathrm{find}}] = \frac{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

Put in economic terms, if a single red-team attempt costs c and succeeds with probability p , the expected cost of finding one more genuine failure is E[Cfind]=cp\mathbb{E}[C_{\mathrm{find}}] = \frac{c}{p}.

The passage around this formula

…grew larger, while plain language models, prompted models, and rejection-sampling models showed a flat trend with scale [ 5 ] . Put in economic terms, if a single red-team attempt costs c and succeeds with probability p , the expected cost of finding one more genuine failure is E[Cfind]=cp\mathbb{E}[C_{\mathrm{find}}] = \frac{c}{p}. Holding c roughly fixed at crowdworker wage rates, a falling p as RLHF hardens a model means the expected cost per discovered failure rises mechanically with every round of safety training — the same defensive work…

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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.

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Sources cited in the surrounding passage

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