Let's consider three Monty Hall strategies---never switch doors, flip a coin to switch doors, and always switch doors.
We all agree that on our initial choice, we win 33% of the time. If you never switch doors, and choose to ignore the extra info, your odds stay at 33%.
But now you know one door has a goat. If you take this as information only about the goat door you see, you might as well flip a coin between the two remaining doors ("Heads I switch, tails I stand pat.") Now your odds of winning are 50%.
But if you realize that Monty gave you information not just about the door he showed, but also about the door he didn't show, then you switch every time and your odds go up to 67% of winning.
Does that help?I will never call anyone who makes an honest effort to understand something new a dunce. I am a mathematician, and I have taught in a number of areas---including math and firearms training; I consider the ability to find the right way to explain something to somebody, especially somebody with a different background on a subject, to be one of the top goals of an instructor.I know I'm over my head when I play with mathematicians and statisticians, but I'm not finding the plain English explanations convincing---though if you guys are in fact real world working statisticians I will have no choice but to bow to your professional
opinion. I guess you have no obligation to convince a "dunce."