[Bill Graham]

William Sommerwerck wrote:
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.

No. You now know that the prize is not behind door $3, so your chance of
winning in the, "second game" is 50-50. But you had to buy yourself this
chance at the second game. You did this by switching doors.