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At p = 0.05 , a safeguard that looks 95% reliable per attempt, twenty tries already succeed with probability 1-(0.95)^{20} 0.64 , and by sixty tries cumulative success exceeds 0.95 — a per-attempt figure that reads as strong evidence of robustness collapses once retrying is free, which is precisely the black-box search loop several of the documented attacks above run automatically. This is not a result reported by any single cited study; it is the elementary shape of what those studies demonstrate empirically, and it is the reason a reported single-attempt block rate, on its own, answers a narrower question than it is usually taken to answer.
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Equation 5 · AI Safety
Ten Failure Modes That Define Deployed AI Safety Systems
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.
At p = 0.05 , a safeguard that looks 95% reliable per attempt, twenty tries already succeed with probability 1-(0.95)^{20} 0.64 , and by sixty tries cumulative success exceeds 0.95 — a per-attempt figure that reads as strong evidence of robustness collapses once retrying is free, which is precisely the black-box search loop several of the documented attacks above run automatically. This is not a result reported by any single cited study; it is the elementary shape of what those studies demonstrate empirically, and it is the reason a reported single-attempt block rate, on its own, answers a narrower question than it is usually taken to answer.