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Equation 19 · Part 1 · Measuring AI Agent Reliability: What the Evidence Actually Supports

Symbol k

k^k
kk

What this part means

k is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

k is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

…APIs, and leave the backend database in a state matching an annotated goal — the authors found that even strong agents succeeded on well under half of tasks at pass@1, and that reliability across repeats fell sharply as k increased: an agent’s pass ^k score in the retail domain dropped below 25% by k=8 , and airline-domain performance, already lower at k=1 , degraded further from there [ 3 ] . Put in words rather than symbols: an agent that a casual observer would call “usually right” on any given try is, on the…

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