" 

 ::::::: Ordinary people won't be perplexed. They know by symmetry that switching is OK but a waste of time (if you don't open your envelope). They don't really understand probability calculations anyway, so they know there is something wrong with the argument, but don't care what.Regarding Smullyan's version, they also know the answer (it doesn't matter whether you switch or not) so they know which argument of Smullyan's is correct. As writer after writer has stated, the problem of both original TEP and of TEP without probability is using the same symbol (original) or the same words (Smullyan) to denote two different things. It's a stupid problem and has a simple resolution.  Well, and if we are allowed to look in our envelope, then everything is different. But no longer very interesting for laypersons. It turns out to be a fact of life that there are ""theoretical"" situations (but I can simulate them on a computer for you, they are not that theoretical!) where according to conditional expectation value you should switch, whatever. OK, and this is just a fact about a random variable with infinite expectation value: if I give you X you'll always be disappointed compared to its expectation. But to get its expectation I would have to give you the average of millions and millions of copies of X. Eventually the average will be so large that you'll prefer the swap whatever the value of the X I gave you first. Then there are all kinds of nice calculations about whether or not you should switch given a prior distribution of X and there are cute things about what to do if you don't want to trust a prior ... then you should randomize. It's all rather technical, isn't it. Only interesting for specialists. By the way this is *not* theoretical since I can approximate a distribution with infinite expectation with one with very very very large finite expectation. I can create approximately the same paradox without actually using infinite values. Syverson does that. It's very technical and hardly interesting for ordinary folk.   "