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Equation 3 · Part 1 · How AI Security Defenses Actually Work

Symbol P_hit

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

What this part means

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

Its job in the formula

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

The passage around this formula

The shared structural fact underneath both techniques, and the reason they are described here as one machine rather than two, is what a search process buys once it is automated rather than performed by hand. A single human red-teamer trying prompt variations by hand might realistically test dozens of candidates against a target in a working day. An automated pipeline built on either GCG- or PAIR-style search can attempt thousands of candidates 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…

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A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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