I finally got it! It's because whether the host has opened a door or not doesn't matter. You know from the start that one out of three doors has a car behind

I finally got it! It's because whether the host has opened a door or not doesn't matter. You know from the start that one out of three doors has a car behind it, and his opening one of the remaining doors doesn't change it. He just shows you what you already know. When you select your door, you know there is a 1/3 chance that your door has a car behind it, and a 2/3 chance that it doesn't. The host opens another door, and there is still a 2/3 chance your door has no car. It has only been proven that the door the host opened has no car behind it. EDIT: To clarify, I'll rephrase. When you select your door, you know it has a 1 in 3 chance of hiding the car, and importantly, you know that there is a 2 in 3 chance that the car is not behind your door. When the host opens his door, you still know there is a 2 in 3 chance that your door doesn't have a car behind it, but are now guaranteed that, if you chose the wrong door in the first place, you will now choose the right door. It's not that the host's door is eliminated from the possibilities, it's that you can either open your door or effectively open all the rest of the doors to find the car. Which would you choose?