Well, since the host knows what door is the winning one, he will always be taking away one of the losing possibilities when he opens a door after your choice.

Initial choice - 33% chance of winning, 66% chance of being wrong

Once he removes one losing door, you still have a 66% chance of being wrong, since you selected a door when there were 3 choices. Now that he has removed one DEFINITE wrong choice, it should be obvious that the other door has a much better chance of being the correct one, but not by 50/50 odds, but by 66/33 odds, since you have only a 33% chance of having selected the right one initially.

Sorry, it's 6:30AM, that may have made no sense at all. I love stuff like this though!

 

Based on that theory if two people were to secretly select say doors #1 and #2 respectively, then the prob of each person's alternative being the winner after door #3 was eliminated would both be 66% which is impossible.

If you have three balls in a bag. One red, one yellow and one blue. Your first selection yields a red ball. What's the prob that your second selection is blue?

IMO this analogy is identical in that the circumstances have been altered once one of the alternatives has been removed. Why should we descriminate against the original selection and not recalculate the prob of the existing situation? The original prob of the three alternatives is 33% so why shouldn't the alternate door in the second selection process be a 33% too?

 

After the 3rd door is removed, your odds improve to 50%.

 

Always switch.

 

I've used this on my friends and even after the explanation they don't believe me.

 

Absolutely right.

You've missed two subtle points. First, the selection isn't secret; Monte knows which door you select before he reveals a goat behind one of the other doors. Second, if two people select doors #1 and #2 respectively, and door #1 has a goat and door #2 has a goat, Monte isn't going to show the car behind door #3. So . . . now what?

 

Now we switch chanels to The Price is Right.

 

Chicken!

 

Crap you need to switch.

 

I figured that Monte knew that you chose right and then chose to open "one of the other doors to reveal a goat"
So when I said I wanted to switch I meant switch from 50/50 to the first choice.

It should be 50/50 in my opinion, but the text in the first post says "one of the other doors to reveal a goat" Its my assumption that Monte picked one of the other doors at random, not caring which one because he knew that the person chose right.
He is the one now picking at random, because as long as he doesn't show the person thier door, he knows the other 2 doors have goats behind them, because Monte knows that the person picked the correct door.
Maybe I read into it too much, but I feel that you should always go with your instincts.