Im not sure what you mean by "expected number." Do you mean if you try to guess how many inmates the warden has managed to guarantee will fail? Per the article,

Im not sure what you mean by "expected number." Do you mean if you try to guess how many inmates the warden has managed to guarantee will fail? Per the article, the warden can guarantee that an "arbitrarily large finite number of them" will fail. But it's still always finite despite being unbounded. If you want to predict a lower bound on the number of failures the warden has guaranteed, you just have to guess a larger natural number than the warden. :)