"William Sommerwerck" wrote in message
...

But by not switching doors, you are ignoring the new
information that the
prize has to be behind one of the other two doors....

No, it doesn't. That's not correct.

You are sticking with
your original guess that had only a 1/3 chance of being right.
By
switching
doors, you are including the new information that the prize has
to be
behind
one of the other two doors, and your new chance of winning is
50%.

No, it doesn't. Your new chance of winning is 2/3.

***
This is similar to another puzzle. A couple has two children.
What is the probability that the second is a boy? The couple then
volunteers that they are not both girls. Now what is the
probability the second is a boy?

The first case is 1/2. The second case is 2/3.

David