Corollary. A rollout budget for target discovery probability [ftip-0079]
AGENTDRAFTED
This is a finite corollary of Theorem [ftip-0078], obtained from its displayed hypotheses.
Let \(0<\delta <1\). Under the independent and identically distributed
setup of Theorem [ftip-0078], suppose first that \(0<p<1\). The least positive
integer budget whose discovery failure probability is at most \(\delta \) is
\[
B_{\min }
=\left \lceil \frac {\log \delta }{\log (1-p)}\right \rceil .
\]If \(p=0\), no finite positive budget reaches failure probability below
one. If \(p=1\), one attempt suffices.