Quote:
I know the correct answer. What I want is a simple explanation to non-believers


I went through this myself a few weeks ago... trying to understand why switching makes a difference, and it took me a bit of thinking to come up with a layman's explanation.

Here is my layman's explanation.

1. Because you chose first, and...
2. Because Monty always knows which door has the car, and...
3. Because Monty always has to show you a goat...

Then your choice limits his choice. His choice is non-random most of the time. In fact...

If you chose a goat to begin with, then he has no choice at all. He's got to show you the other goat.

And since your chance of choosing a goat to begin with was 2 out of 3, then 2 out of 3 times, Monty is showing you the other goat.

So 2 out of 3 times, if you switch, you win.

Yes, it's totally counterintuitive, but it works only because of the three conditions above. If you didn't choose first or if Monty didn't know where the car was, then it would be random.

Here is another explanation with a roulette-wheel metaphor showing why Monty's knowledge changes the outcome.

Here are two simulators which can act as proofs:
http://www.grand-illusions.com/simulator/montysim.htm
http://math.ucsd.edu/~crypto/Monty/monty.html

Enjoy!