So why go to all the bother of presenting this problem? My intention was to get people to look their own thinking. IMO HOW we come to know/believe things is quite important. We all need to make decisions, but IMO we also need to be flexible enough to change our views of things when new information (as well as information in novel forms) becomes available.
For me, the Monte Hall problem really drove this home.
Incidentally I also believe that (to a much larger extent than is known) we are biologically hard wired to think in certain ways. Occasionally (albeit rarely) this interferes with our interpreting reality correctly. It's my hunch that this is a big part of our problem in understanding quantum mechanics. My thoughts went in much the same direction as those that freshstart expressed in this regard.
None of the verbal explanations that I have read anywhere (in this thread or online) have convinced me that either choice to switch or stay is preferable. I had to do my own decision tree and compare the results in order to be convinced. It was as simple as counting the wins and losses.
For me a problem still remains in how to succinctly and verbally express the mechanism by which the increased probability of a positive outcome is conveyed to only one of the remaining choices. This defies me. Can anyone do this?
So to sum up I'll just repeat the wisdom of a bumper sticker I spotted a few years ago. It said "Don't believe everything you think". I've taken that to heart.
I'm glad so many of you had fun with the thread.