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 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?
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Three Curtains
- Thread starter rstrats
- Start date
Kilgore Trout
Misanthropic Humanist
There would be an advantage to changing to curtain 2.
Skwim
Veteran Member
You should switch. But because it's a bit complicated to explain I went to source that does it pretty well.
"Why You Should Always Switch
Think of the probability of you guessing the correct curtain. Let's assume that it is a random guess none of this "I notice that one curtain moved, so I figured there was [nothing] behind it" stuff.
Three curtains, with only one curtain being a winner, means there is a 1 out of 3 chance that you will guess right and win the car. That's about 33 percent. On that first guess, with no additional information, you are likely to be wrong; in fact, you have a 2 out of 3 chance of being wrong. In other words, there is about a 67 percent chance that the car is somewhere behind the two curtains you did not pick.
Once you know that one of those other two curtains does not have the car, that doesn't change the original probability that the car is 67 percent likely to be somewhere behind those two unselected curtains. Remember, [the host] will always have a wrong curtain he can open, no matter which one you choose. The 67 percent chance that the car is behind B or C remains true, even after B is revealed to not be hiding the car. The 67 percent likelihood now transfers to curtain C. That's why you should always switch to the other curtain.
______________________________________________________________________________________________________________________
If you were given the option of swapping your pick of one curtain for both the other two curtains, you'd switch in a second wouldn't you? That's essentially what is offered in the . . . problem.
_____________________________________________________________________________________________________________________
Some figures might be necessary to persuade your inner skeptic. Look at Table 5-1, which shows the probability breakdown for the three options at the start of the game. You have a one-third chance of guessing the winning curtain and a two-thirds chance of picking a nonwinning curtain.
In any situation like this, you should switch. You might be wrong, of course, but you have a better shot of winning that car or whatever other prize you are playing for if you accept any offers to switch. This is always the best strategy, if a few criteria are met:
The host knows what is behind each curtain.
The host reveals one of the unchosen curtains and the prize is not behind it.
Your original choice was random."
source
Think of the probability of you guessing the correct curtain. Let's assume that it is a random guess none of this "I notice that one curtain moved, so I figured there was [nothing] behind it" stuff.
Three curtains, with only one curtain being a winner, means there is a 1 out of 3 chance that you will guess right and win the car. That's about 33 percent. On that first guess, with no additional information, you are likely to be wrong; in fact, you have a 2 out of 3 chance of being wrong. In other words, there is about a 67 percent chance that the car is somewhere behind the two curtains you did not pick.
Once you know that one of those other two curtains does not have the car, that doesn't change the original probability that the car is 67 percent likely to be somewhere behind those two unselected curtains. Remember, [the host] will always have a wrong curtain he can open, no matter which one you choose. The 67 percent chance that the car is behind B or C remains true, even after B is revealed to not be hiding the car. The 67 percent likelihood now transfers to curtain C. That's why you should always switch to the other curtain.
______________________________________________________________________________________________________________________
If you were given the option of swapping your pick of one curtain for both the other two curtains, you'd switch in a second wouldn't you? That's essentially what is offered in the . . . problem.
_____________________________________________________________________________________________________________________
Some figures might be necessary to persuade your inner skeptic. Look at Table 5-1, which shows the probability breakdown for the three options at the start of the game. You have a one-third chance of guessing the winning curtain and a two-thirds chance of picking a nonwinning curtain.
In any situation like this, you should switch. You might be wrong, of course, but you have a better shot of winning that car or whatever other prize you are playing for if you accept any offers to switch. This is always the best strategy, if a few criteria are met:
The host knows what is behind each curtain.
The host reveals one of the unchosen curtains and the prize is not behind it.
Your original choice was random."
source
Fraleyight
Member
I know the thread is old so sorry in advance. I have found the easiest way to explain this is to ask someone to pick three cards out of a deck 2 deuces and 1 ace. Give the three cards to a friend and ask him to memorize the order of the cards then set them face down. You then pick a card and ask him to show you one of the unselected cards. He will always choose to show you a deuce. So by switching you will win every time you start with a deuce because the other deuce will be eliminated. Chances of starting with a deuce are 66 percent therefore you will win 66 percent of the time.