I just meant that the argument Smullyan presents does not involve probabilities, random variables, distributions, expected values, etc. (This can be verifie

I just meant that the argument Smullyan presents does not involve probabilities, random variables, distributions, expected values, etc. (This can be verified by reading it again and checking those concepts do not appear. ;)). The fact that he doesn't uses those words does not mean he doesn't use those concepts. The Smullyan version is simply less precisely stated and anyone solving it would first have to go through the trouble to convert the phrasing to incorporate the usual, well defined mathematical words. Solving it any other way is just handwaving.