Interesting. My first 'intuition' was that, since there's 2 doors remaining, they each have a 50% chance of having the car behind them, so it doesn't matter which one I pick. But then I started thinking, if we make it into a rule that the 'talk show host' changes the door randomly after your first choice, then this might influence the chances somehow, though I could not specify how by just superficially thinking about it without math.