Item — HN Reader

That's a great question! I think the person who can articulate that intuitively should win the car!

My stab at it: If he doesn't know, then he's essentially another contestant, and his odds are the same 1 in 3 as yours. You've made selections one after the other, but since your selection has yet to be revealed as either right or wrong, you are essentially just picking different options from the same scenario. There are exactly equal chances that you won the car, he flubs and reveals the car, or he reveals a goat.

1 comments

I like frankc's intuitive explanation of the original game given in another comment:

The way I explain is to expand it but also change the frame of reference to so its clear that the host is an adversary. Imagine we play a game called "who has the Ace of Diamonds"? I deal you one card face down and I deal me 51 cards. I look at my cards and then choose 50 of them to show you, none of which are the Ace of Diamonds. Do you want to keep your card or take the one I have not turned over?

Now imagine the same set up, but instead, after dealing the cards, I don't look at them. I then proceed to turn 50 of mine over one after the other and, though unlikely, I happen to not reveal the Ace of Diamonds. Now, is it any more likely the last card I haven't turned over yet is the card, than it is that you have it?

The game is no different in this case to one person lining up all 52 cards and turning them over one by one along the line. If you get to 50 cards and you still haven't found it, that obviously doesn't mean it's more likely to be the end card than the penultimate one.