After my last post, I started thinking about other ways to extend the Monty Hall problem to more doors. If you want to take your intuition in a very different direction, try this: there’s a car behind one of 100 doors. You, the player, get to pick 98 doors. Then Monty opens one of the two remaining doors, showing you the car isn’t there. He asks you if you want to stand pat or trade one of the doors you originally picked for the remaining unopened door.
The same general logic still applies. Your original win probability is 98/100. If you switch, you lose only if the car was behind the door you gave up (probability 1/100), so your win probability after switching is 99/100. Now I don’t know about you, but in this version, I find it really hard to make my brain grasp intuitively that there’s anything to be gained by switching. Which might be a little more evidence for a psychological basis for loss aversion, or the endowment effect, or whatever you want to call that phenomenon whereby people are reluctant to give up, or risk, what they already have. Or maybe it shows our inability (or unwillingness) to distinguish between numbers once they get really big.