On Sat, 28 Oct 2006 06:35:31 GMT, "Bob Weinberger"
wrote:


"Wolfgang" wrote in message
oups.com...
Actually, I believe your exactly right about the 2/3.

Um.....well, it's been a couple hours since I last looked at the
solution, so I could be wrong.

The key is that the removal process is not random.

Yep.

Wolfgang

Yes, the key from a pure mathematical probability standpoint is that the
removal process is not random.

Not as I see. As I see it, those supporting 50-50 odds aren't looking
at the situation properly. I vaguely remembered the puzzle with Marilyn
vos Savant, and of the explanations I saw, none really phrased the
explanation both simply _and_ accurately (not that they aren't out
there, I just didn't see them). Here's my explanation:

Look at in reverse. Given the way Wolfgang phrased it, by switching,
you essentially get to pick two boards. Let's change the phrasing such
that if once you had picked board #1, he had given you the choice of
sticking to that choice (1 chance in 3) or switching to pick _both_ of
the two remaining boards (2 chances in 3), most people can easily see
the odds advantage of switching and as such, would switch to picking two
boards. You know one of the two will not and cannot have a five under
it.

At that point, Wolfgang turns one board of your two over and it's the
one that isn't the five. He now offers you the choice of switching back
to board #1. If you switch, you have traded your two-board pick back to
Wolfgang for your original one board (1 chance in 3) pick. The fact that
one board of your two-board (2 chances in 3) pick is now revealed is not
material to the odds. You knew and expected that one of the two boards
of your two-board choice couldn't and wouldn't have the five under it,
so why would the fact that things are as you expected and as they have
to be influence your new choice?

This explanation is for the puzzle as Wolfgang explained, not all
possible variants. For example, if a third person walks up at the point
after the first board is turned over and is offered a chance to get in
on things by picking one of the two remaining boards, their odds are
50-50, but they had different "rules" (this "each "hand's" _rules_ are
different" is why blackjack ain't a heads-up game). And secondly, if
you continue to play and Wolfgang is free to "change the rules" in every
"game," the proper choice could change depending on what he does or
doesn't do.

TC,
R