Three Curtains

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 of course 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?

Easy, change your choice.
it seems crazy but there is a statistical advantage.

Anyone disagree with Hobbes Choice?

I can't quite remember where I read it, and obviously do not yet emotionally understand it, but apparently this is a mathematical trick: your odds actually DO increase if you switch curtains to #2, but most people stick to their original choice for psychological reasons.

Let me try to figure it out.

Your odds are 1/3 (33%) when you first make a choice. However, after the 3rd curtain is revealed, there is now a 50/50 chance, and hence, if you were to make a decision at that point, your odds would be 50%.

So somehow, even though you could have originally picked the middle one first and then switched to the first one for the 50% chance, somehow, picking curtain #2 gives you a 50% chance of winning while staying with curtain one only gives you a 33% chance.

Sreru,

re: "Your odds are 1/3 (33%) when you first make a choice. However, after the 3rd curtain is revealed, there is now a 50/50 chance..."


Actually, that is incorrect. 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 the host knowingly 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.

Ah yes, that is much better.

So yeah, if you look at it as if A is one possibility and B is another, from the start, and the question was "would you rather open A or open both in B" you would obviously choose B - so this way you are choosing B retroactively.

Thanks for the riddle!

Sreru,

So you're changing your post #4 comment from "... after the 3rd curtain is revealed, there is now a 50/50 chance..." to "...after the 3rd curtain is revealed, there is a 2/3rds chance of getting the car by switching"?

Yes, I suppose so!