The Monty Hall Problem - Would you switch to Door #2?

Umm, the correct answer is to switch doors. It has been discussed ad naseum as you mention. The simplest way to see that the switch doors gives you a 2/3's chance of winning is as follows.

Without loss of generality, assume that you always pick door 1.

If the car is placed randomly, you have a 1/3 chance of getting the car. To see this, note that when not switching, you only win if your initial guess has the car behind it, which happens 1/3 times.

When you switch doors you only win if not switching loses. Since not switching wins 1/3 times, switching wins 2/3 times.

You can write a simple program to simulate the game and see that switching wins 2/3 times.

Wait so he's arguing that switching wont make a difference?

The host is guaranteed to open up one door that is a goat. So, instead of thinking at the beginning that you have 1/3 chance of picking the car, instead think that you have 2/3 chance of picking a goat. If you pick a goat and you switch, then you win because the host HAS to show you the other goat. So think about it that way: try to pick a goat and not the car at the beginning. That is the simplest way I can explain why your chance of winning is 66% if you switch when asked as opposed to staying with your original choice.