Three Curtains

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rstrats

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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?
 
Really depends on the knowledge and goal of the host. If he knows where the car is and is puropsefully leading you astray or if he is trying to help you, the odds (in terms of his knowledge) one way or the other may change. But regardless your knowledge does not (assuming you do not know if he intends to help or not).

In the beginning the odds are 1 out of 3. After your choice the odds (objectively) change to 50%. But you do not know the odds of him being for or against you. So his selection of curtain #2 remains 50/50. If there are no penalties (that is curtain #2 does not sentence you to a fine or forfiture) the odds of what you know (50/50 instead of 1 out of 3) should lead you to take the curtain (all other factors being equal).
 
radarmark,

re: "If he [the host] knows where the car is..."

He does



re: "...and is puropsefully leading you astray..."

He isn't.


re: ".... or if he is trying to help you..."

He isn't.
　


re: "In the beginning the odds are 1 out of 3. After your choice the odds (objectively) change to 50%."

At no time do any of the curtains have a 50% chance.
 
If there is a car, and if the only choices left are curtains 2 or 3... the car must be between one of the two. I can do division. Please explain your answer, rstrats.
 
radarmark,

re: "If there is a car, and if the only choices left are curtains 2 or 3..."

After the host opens curtain #3, the only choices left are curtains #1 and #2. Curtain #3 is out of the picture. There is a 1/3rd chance that it is curtain #1 and a 2/3rds chance that is curtain #2.
 
Oh, so what is behind curtain #1 (your choice) is never revealed. I did not see that in the original statement. Voila! You are totally correct.

Maybe I need to get my glasses checked!
 
Jayhawker Soule,

re: "Switch...if only to pi$$ off Monte Hall."


But wouldn't it also improve your odds of getting the car?
 
With curtain #3 revealed the changes of picking the correct car is 50%, no matter which of the other two curtains you pick.

Aloha.. Allen
 
AllenPapapetrou,

What would you do if after your initial pick of curtain #1, and before any curtain was opened, the host told you that you could stay with #1 or switch to BOTH #2 and #3?
 
rstrats said:
AllenPapapetrou,

What would you do if after your initial pick of curtain #1, and before any curtain was opened, the host told you that you could stay with #1 or switch to BOTH #2 and #3?
Click to expand...

Hi rstrats,

Mathematically, the odds are still 1 in 3 regardless of what the host says.

Assuming my initial pick came from my gut, I'd stick with it.
Aloha.. Allen:cool:
 
rstrats said:
Why would you want to stick with only one door when you could switch to two doors?
Click to expand...

Like I'm stickling to my prior response, I'm sticking to my first, gut, feeling without any additional relevant info.

Relevant Info, such as:
One curtain was picked at random to be empty
Of the remaining two curtains the next empty curtain was picked:
a. By drawing a random number between 1 and 100 for each of the other curtains.
b. If the number for the left hand curtain was higher than the number for the other curtain and the number for the other curtain was over 70 then the left hand curtain remains empty.

Now what are the odds for curtain I first picked.

The odds are the same because what I suggested as relevant information is Not actually relevant. Thus, I stay with my first pick.

Aloha.. Allen

 
AllenPapapetrou,

I still don't see why you think that being given the chance to look behind 2 curtains isn't better than having only 1 curtain to look behind.
 
rstrats said:
AllenPapapetrou,

I still don't see why you think that being given the chance to look behind 2 curtains isn't better than having only 1 curtain to look behind.
Click to expand...

What! I never meant to imply that.

With 3 curtains the odds are 1 out of three.
With 2 curtains the odds are 1 out of two.

Thus, the odds on my gut feeling have just improved.

Aloha.. Allen:cool:

 
Don't do it Allen,

your curtain only has a crumby Kia Rio behind it! Take the other one. That's where the patio set and BBQ grill are! :D
 
You're right, NJ!

I don't need another car. I'll go with my gut feeling for the lanai accoutrements.

Aloha.. Allen:cool:
 
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