Dear Gnu -- try to free up your understanding as Howard Jones did:
I couldn't understand this to begin with. Light dawned when I stopped thinking about chances of winning and thought about your chances of losing. which I suggested upthread:
...consider that switching turns a correct initial guess into a loss but turns an incorrect initial guess into a win. Since the initial guess is twice as likely to be incorrect as correct, switching is twice as likely to win the prize.Poor chap, you'll likely be embarassed when light finally dawns, but not so much as Paul Erdős and quite a few other distinguished mathematicians who stumbled over this problem. What fun!