On Wednesday, 8 October 2014 at 07:00:38 UTC, Dominikus Dittes
Scherkl wrote:
On Wednesday, 8 October 2014 at 01:22:49 UTC, Timon Gehr wrote:
If he would ever open the right door, you would just take it
too.
Almost. If he opens the winning door, he gives you another very
important information: the correctness of your first choice. If
you already know if your first choice is correct or wrong, then
having the host opening a door (does not matter which of the
remaining two, in this case) solves the problem without ambiguity.
But, when you make your second choice, you still not know if your
first choice was correct or not. The only thing that you know is
that the chance that your first choice was correct is two times
less than the chance it was wrong.
So you bet that your first choice was wrong, and you move on to
the next problem, which, assuming this bet, now becomes a
non-ambiguous problem.
The key is this: "how would a third person bet on my first
choice?" Reasonably, he would bet that the choice is wrong. So
why wouldn't I do the same?
