I'll toss in another nudge to intuition. You select one of the hundred doors. Then Monty takes the other 99 and opens door after door, displaying goats, but whe

I'll toss in another nudge to intuition. You select one of the hundred doors. Then Monty takes the other 99 and opens door after door, displaying goats, but when he reaches one of them, he carefully skips over it, then continues to the last door showing goat after goat. Then he says, "Okay, the car is either behind the door you selected or the one I selected by skipping over it. There's only one car, so if you picked the right one, then I had to pick a random goat door to skip, but if the door you picked was the wrong one, the door I skipped was the one with the car. And, unlike you, I know which door has the car. Would you like to keep the door that you originally picked or switch to the one that I just picked?" You don't know where the car is; he does. Do you want your pick or his?