Topic: The Monty Hall Problem

[BlackLight]

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1 [but the door is not opened], and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

[Solipsist]

Yes, as the other door has twice better odds.

[FreebirdSTF]

I need to dig up the Snopes thread about this for those who want to see a lengthy discussion of it all.

[BobbyR]

IIRC Gerry wrote a long disertation on it on one of the old boards

[FreebirdSTF]

Isn't one of the issues that people always point to the fact that the host knows what is behind the doors and that changes the odds?
 
Maybe, influences the odds or influences the decision is a better way of putting it.

[Chus-Kay]

Yes, as the other door has twice better odds.

this is the right answer.

[BlackLight]

Isn't one of the issues that people always point to the fact that the host knows what is behind the doors and that changes the odds?
 
Maybe, influences the odds or influences the decision is a better way of putting it.

If the host didn't know where the car was, he might reveal the car when he opened the first door. I think the host could potentially swing the outcome a certain way if he wanted to. But I don't think just knowing where the car is would do that on its own.

If the host didn't know which door had the car:

You pick a door. Your odds of winning are 1/3. The host opens a separate door. If he reveals the car, you lose. If he reveals the goat, the game continues, and the odds lay out the same as they would if the host did know where the car was - your odds of winning are 1/3 if you stay on the first choice, and 2/3 if you switch.

[BigDaddy]

Yep, the only way you win by staying is if you picked the right door in the first place, with odds 1/3.  So, switching pays.