::I am sure that you have both heard the statement that every statistic is the answer to a question, the problem is, which question?  Once you have a clearly-defined, well-posed question the answer is much easier.  Whitaker's question is not such a question.   
 ::: And 80% of statistics are just made up. Seriously, you hit the nail on the head, Martin. And MHP is *both* a popular brain-teaser *and* a popular vehicle for teaching conditional probability in the probability class,  *and* a splendid vehicle for teaching game theory, too. It challenges our conceptions of probability and it challenges the "experts" in communicating with ordinary folk. And that's why it is so fascinating.