[Ed Dantes]

Here's an old braintwister...

Suppose you're on 'Let's Make a Deal'. You have the option of choosing one of three doors, one of which contains a new car, and the other two contain junk prizes (like a donkey).

You choose your door. The host knows which door the prize is behind, but, he wants to make a deal... So he opens one of the two doors you didn't choose, and the one he knows does NOT contain the prize.

So now there are two doors. One contains the car, one does a donkey.

He offers you the chance to switch the door you chose. Do you take him up on the offer, or does it matter?

[Fumblerooskies]

You switch the door you chose.

Not sure the math behind it...but I saw a similar question in the Movie "21".

[mrmacphisto]

Obviously switch it. Monty opens all three doors in the scenario : the two I didn't choose and the one he knows doesn't contain the prize. As mentioned, two contain junk and one contains the new car. Since the third door (not one of the two I didn't choose and thus, by process of elimination, the one I did choose) is one he knows doesn't contain the prize, this means the prize is behind one of the doors I didn't choose. So, switch.

Unless this is all just a trick question you've devised to make a fool out of me.

[LUconn]

I saw the movie and I still disagree with the answer. At the point where he opens one of the doors, the only thing you truly know for sure is that it is NOT behind the door he's opened. It's essentially a new game at that point and you can choose either door again. I understand that when there's 3 doors there's a 66.6% chance it's behind one of the doors you didn't pick but like I said, at that point in the game after he's opened one, it's 50/50.

[Ed Dantes]

I didn't see the movie, in fact, I had no idea the question was asked in the movie... I just saw a clip of some guy on Deal or No Deal blow $1,000,000 messing up this problem. I asked my wife this question and she missed it, too (saying, 'you always go with your first instinct).

(Note to self: Do not let her represent the family on a game show).

Here's a way to understand it. Suppose instead of three doors, there are 1,000,000. You pick your door. 999,998 other doors are eliminated, so there's only two doors remaining -- the one they didn't eliminate, and the one you picked.

You're offered to switch. You still have a one-out-of-a-million chance of getting it right*. On the other hand, there is a 999,999 / 1,000,000 chance that the other one contains the prize. Therefore, it is always in your best interest to switch.

*So you're telling me there's a chance... Yes!

[Hold My Own]

you ever play that game back in the day "Mind Trap" It's a bunch of mind teasers that are a lot of fun to try and figure out

[mrmacphisto]

The way your riddle was worded, Ed, it's clear that the door chosen by the contestant is not the one containing the car.