Grokking Agentic Design Patterns
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Probabilistic Defenses: What the Model Gives You and What You Add

Suppose that a detector catches 99 percent of injection attempts, and that an attacker can try as many variations as they like. Each attempt succeeds with a chance of 0.01, so the chance that at least one succeeds grows with each try.

AttemptsChance that all are caughtChance that at least one succeeds
10.991 percent
100.904About 10 percent
1000.366About 63 percent
5000.007About 99 percent

The figures assume independent attempts, which favors the defender, because a real attacker learns from each failure

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