Fair enough! I was using as a heuristic the expected number of compromised guards, which would be 0.02*50 = 1. Moreover, things degrade exponentially over time.

Fair enough! I was using as a heuristic the expected number of compromised guards, which would be 0.02*50 = 1. Moreover, things degrade exponentially over time. If half the guards rotate every month, the chance of choosing a bad guard is after 2 months is >86%, after 4 months is >95%, after 6 months is >98%.