Think of it this way. In the original problem, there was a 1/3 chance of your original choice being the car, and a 2/3 chance of the other two. The host knowing

Think of it this way. In the original problem, there was a 1/3 chance of your original choice being the car, and a 2/3 chance of the other two. The host knowing which door to open gives you information without changing the odds, so there's still a 2/3 chance you picked wrong. When the host does not know which door to pick, there's a 1/3 chance that you picked right, a 1/3 chance that the host opens the door with the car, and a 1/3 chance that you should switch. The host opening the door with the car ends that branch, so you're left with 2/3 of the original probability, and your odds for either branch remaining are 50:50.