If you take any finite subset of N prisoners, it's easy to see that they won't do better than chance, so the expectation is for N/2 of them to guess wrongly. S

If you take any finite subset of N prisoners, it's easy to see that they won't do better than chance, so the expectation is for N/2 of them to guess wrongly. Since N can be arbitrarily large, your intuition is correct.