` ::::Glkanter, you forgot to point out that Morgan do not just say that the player should swap but say that the odds of winning if she does so are exactly 2/3.  In their words, ``...had we adopted conditions implicit in the problem, the answer is 2/3, period``.    :, what you are suggesting completely misses the point of this article in my opinion.  The only reason that the MHP is notable and that we have this article at all is that most people think the answer (probability of winning by switching) is 1/2 when it is actually 2/3.  This is one of the most tenacious and unintuitive simple mathematical problems known.  Most people get the answer wrong and strongly resist any reasoning the gives them the correct answer.  The first duty of this article, therefore, is to tackle the simple mathematical puzzle and convince readers of the correct answer.   :It is possible, with some contrivance, to turn the MHP into an undergraduate level conditional probability problem, a valuable and instructive problem, but no more notable than most of the other problems that might be found in a probability text book.  Our arguments here about the conditional nature of the problem are of no interest whatever to almost everyone, and building the article around a so called neutral position helps no one.  The subject should be presented to the reader in the same way as most other technical subjects, a complete simple treatment first followed by a more detailed treatment for those interested.  :So let me make my position absolutely clear. The conditional treatment of the MHP (as typified by the paper by Morgan et al) does nothing but obfuscate a simple and highly unintuitive simple mathematical puzzle. For those that have not read it my complete criticism of Morgan's paper can be hound here . It is, of course, an interesting problem for those studying conditional probability but it is of no interest to anybody else and thus should only form a minor part of this article.  My suggestions have been aimed at reaching a compromise so that we can end this argument. I would really like to see the 'conditional' section greatly reduced   `