Unexpected Hanging Paradox One problem with this is that "surprise" seems to be used in two rather incompatible ways. One is the sense of an emotional reaction that someone has based on not expecting something. That doesn't necessarily have anything at all to do with logic. An individual can expect (and so not be surprised) or not expect (and so be surprised) any arbitrary thing, for any reason imaginable, or even for no reason--it can just be purely intuitive. Of course, in this sense of surprise, we can't predict, with any certainty, whether anyone will be surprised by anything or not.
"Surprise" also seems to be used here in the sense of whether a better-than-chance prediction is possible using some logical metric.
The problem with the supposed conundrum on this end is that the ONLY situation where we could make a better-than-chance prediction is once noon has passed on Thursday.
For example, say that whether the prisoner is going to be hanged on any given day (M-Th at least, since otherwise Friday is set) is determined by an "ideal coin," so that the flips are really random. Well, on every day, Monday through Thursday, there's no way to predict, better than chance, whether the prisoner will be hanged, because on every one of those days, the answer is literally determined by chance. The only way we can make a prediction better than chance at some point in that process is once noon has passed on Thursday.