You are a contestant on a game show. There are three curtains. Behind one of the curtains is a new car. You are asked to choose one of the curtains. Lets say that you choose curtain #1. The host of the show - who knows where the car is so as not to end the game prematurely - opens curtain #3 and there is no car behind it. The host now gives you a choice. You can stay with curtain #1 or you can change your choice to curtain #2. The question now is: would it be to your advantage to stay with curtain #1, or would it be to your advantage to change to curtain #2 or would there be no advantage either way?

lol I see that. I just dont see the point. Assuming the two curtains are exactly the same, there would be no advantages or disadvantage to choosing either curtain-other then the obvious, one of them has a car behind it, but no way to know that, until after you choose. Number 3 is out of the question, leaving only 2 left-be 50% chance either way you go. Maybe the host took out number 3 as a hint that you have the wrong one-or maybe he just wants you to think that. So I kinda dont see the point lol but for sake of argument lets stay with number 1 and see where it takes me

The only person with 'advantage' is the person who knows what's behind each curtain-The game show host. The player simply has to 'play' the odds. "Stay with curtain #1!"

Seem to be lots of ways of looking at this one. 2/3 of the time you will pick an empty curtain. On these occasions, host has to open the other empty curtain....

There was a study done about the "Monte Hall effect" where most contestants would switch. Turns out the original selection was correct more often.

HisManySongs, re: "There was a study done about the 'Monte Hall effect' where most contestants would switch. Turns out the original selection was correct more often." Actually, the study would have shown just the opposite. You improve your chances from 1/3 to 2/3 by switching.

No you wouldnt belief, not unless you knew that the first choice was wrong. If you choose it, but switch before learning, your chances is still 1/3, regardless of how many times you switch. The only way to increase it, is if it had say a lifeline like from who wants to be a millionaire, and the host showed you one of the empty ones and let you choose from the two remaining.

Look at it this way: What if after your initial pick of curtain #1, I told you that you could stay with #1 or switch to BOTH #2 and #3? My guess is that you would switch so that you could look behind both curtains in spite of the fact that you KNOW that at least one of the curtains does not have a car behind it. Lets say that the first curtain that you open is #3 and you find that there is no car behind it. You now get to open curtain # 2, giving you 2 chances. What is the difference if you open curtain #3 or the host opens curtain #3 for you? Either way, you get to look behind curtain # 2. You can also think of it as two areas. Area "A" contains curtain #1 and area "B"contains curtains #2 and #3. There is a 1/3rd chance that the car is in area "A" and a 2/3rds chance that it is in area 'B". Before opening any curtains, you KNOW that at least one of the curtains in area "B" doesn't have the car behind it. So by opening a curtain in area "B"that doesn't have a car behind it doesn't change the 2/3rds odds that area "B" still has a car in it.

but thats changing the paremeters of the scenario. If you can choose 2, regardless of whether it was the host removing one your you being able to choose both 2 and 3, then yes, it goes to 2/3 chance. If the scenario was changed to allow me to choose both 2 and 3 if I changed it, then yes I would change because it would increase to 2/3rds a chance. But with the original scenario, I would stick with my original choice-after all, it would be 1/3 a choice either way.

The scenario hasn't changed. Yet another way of looking at it is that the odds have not changed. Your pick stays at 1/3 so what ever is remaining must carry the 2/3 odds for the sum to add up. I'm pretty sure the switch is right as a probability problem but HisManySongs raises an interesting point that in a study most people switched and most people lost. Supposing we have a mean host who knows where the car is and is quite clever at steering a person to a particular choice. If he believes a person would switch, he might attempt to guide them to the car in the first place...

allowing someone to pick 2 curtains, does change the odds from 1/3 to 2/3. If all he does is say you can change choice, without revealing the first curtain, but you can still only choose one curtain-the odds are still 1/3 because that first curtain might still be the car. Like you said, the host could be intentionally trying to missteer-in fact, seeing how much cars are, I would assume he is, and not trust a thing he has to say. If you can only choose ONE curtain to open, no matter which one you actually choose-its 1/3.

It would be to your advantage to stay with # 1. Since the host knows where the car is and is part of the game show...he cannot be trusted...if he knew you selected the wrong curtain he would not have opened curtain # 3.

KingJ, re: "...if he knew you selected the wrong curtain he would not have opened curtain # 3." Huh? You're going to have to explain that one.

jonbanjo, re: "... HisManySongs raises an interesting point that in a study most people switched and most people lost. As I said in post #11, the study would have shown just the opposite. You improve your chances from 1/3 to 2/3 by switching.

the_patriot13, re: "If all he does is say you can change choice, without revealing the first curtain, but you can still only choose one curtain-the odds are still 1/3 because that first curtain might still be the car." Do you agree or disagree that there is a 2/3 chance that the car is behind one of the 2 curtains you didn't pick, even though you KNOW that it is not behind at least one of them?