3 ms·
> The expected value of Nb would still be 50 if all the prisoners checked the same subset of boxes, but the chance of the prisoners surviving would clearly be 0
by peeters 8y ago
> The expected value of Nb would still be 50 if all the prisoners checked the same subset of boxes, but the chance of the prisoners surviving would clearly be 0.
Yes I should have expanded. The probability of escape is
∏ (i = 1..N) Ni / N
So if some Ni is 0, the whole thing is 0. My point was that if you're choosing randomly, then as N goes to infinity, "Ni / N" already converges to 0.5 . So your strategy is ensuring optimality, but you'd get there if you took it to the limit anyway.
As a quick test I did 1000 trials. The minimum overlap in those 1000 trials was 26. 95% of the time it was above 35. For N = 1000, 95% of the time it was above 440.