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Equation 3 · Part 2 · How AI Security Defenses Actually Work

Symbol k

Phit(k)=1−(1−p)k.P_{\mathrm{hit}}(k) = 1 - (1-p)^{k}.
kk

What this part means

pushed into the thousands, which a machine can do overnight and a human red-team cannot do at all.

Its job in the formula

k is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Where the article explains it

Even a strategy with a very low per-attempt success rate becomes a near-certain eventual hit once k is pushed into the thousands, which a machine can do overnight and a human red-team cannot do at all.

The passage around this formula

…against a running target in the same interval, entirely unattended. If a given search strategy succeeds against a defended target with independent per-attempt probability p , the probability that at least one of k automated attempts succeeds is Phit(k)=1−(1−p)kP_{\mathrm{hit}}(k) = 1 - (1-p)^{k}. Even a strategy with a very low per-attempt success rate becomes a near-certain eventual hit once k is pushed into the thousands, which a machine can do overnight and a human red-team cannot do at all. This is precisely why Anthropic’s…

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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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