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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 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?
 
One of the issues is that people make a deal about whether or not the game show host knows which door the prize is behind in which case they say it makes no difference if you switch doors, but I don't think that it's an issue. In the scenario given he opens the door with no prize so I don't understand why it matters whether he happened to pick the door with no prize by accident or whether or chose it deliberately. Surely the dynamics logic remains the same and it's worth your while changing to increase your odds.
 
This gets even worse when one of 100 curtains is chosen and 98 are revealed without he prize. When it comes down to the original curtain that you picked versus the other one, you actually have a 99% chance of being right if you pick the curtain that you stayed with and a 1% of being right if you chose the curtain that is left.
 
ryan said:
This gets even worse when one of 100 curtains is chosen and 98 are revealed without he prize. When it comes down to the original curtain that you picked versus the other one, you actually have a 99% chance of being right if you pick the curtain that you stayed with and a 1% of being right if you chose the curtain that is left.
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Now that's an interesting way of thinking about it and makes me rethink what I said above.

If the game show host didn't know where the prize was and opened 98/99 other doors and by pure blind luck didn't come across the prize, then the odds of that are 1/100, the same as if you picked the prize yourself by chance. Of course, 98/100 times this won't happen and one of the opened 98 doors will contain the prize, but we aren't dealing with the situation as we're specifically thinking about a situation where 98 doors are opened and no prize is revealed by pure chance therefore there's now a 50/50 chance of it being behind either door and you can't improve your odds by changing your choice.

If on the other hand, the game show host DID know where the prize was, then the odds of you having picked the prize up front are still 1/100 but 99/100 that the remaining door contains the prize and you should definitely change your first choice.

So am I now right in reconsidering my position that it is indeed important to factor into the puzzle whether or not the game show host knows where the prize is?

I hate this discussion precisely because I'm so easily swayed one way then another by what appears to be impeccable logic either way.
 
Oops, I was wrong. The curtain that you didn't choose is the one with a 99% chance of having the prize.

It doesn't matter if the game show host knows where the prize is as long as the curtain picked by the host is not the prize.

I have the same problem as you. 50/50 makes sense, but 1/100 makes sense too because you started off with a 1/100 chance of being right.

Don't feel bad; read this,

"Many readers of vos Savant's column refused to believe switching is beneficial despite her explanation. After the problem appeared in Parade, approximately 10,000 readers, including nearly 1,000 with PhDs, wrote to the magazine, most of them claiming vos Savant was wrong (Tierney 1991). Even when given explanations, simulations, and formal mathematical proofs, many people still do not accept that switching is the best strategy (vos Savant 1991a). Paul Erdős, one of the most prolific mathematicians in history, remained unconvinced until he was shown a computer simulation confirming the predicted result (Vazsonyi 1999)."

from http://en.wikipedia.org/wiki/Monty_Hall_problem .
 
Archimedes said:
One of the issues is that people make a deal about whether or not the game show host knows which door the prize is behind in which case they say it makes no difference if you switch doors, but I don't think that it's an issue. In the scenario given he opens the door with no prize so I don't understand why it matters whether he happened to pick the door with no prize by accident or whether or chose it deliberately. Surely the dynamics logic remains the same and it's worth your while changing to increase your odds.
Click to expand...
But the game show host HAS to know where the prize is.
the whole point of revealing what's behind one curtain, to give you the second choice.
For the show, this adds the drama of you sweating bullets and glancing at the studio audience shouting 'switch!' and 'stay pat!'

For the puzzle, it's forcing you to understand the dynamics of the second choice.

In either case, if he randomly chooses the prize, there's no more choosing to do. You lost, there's no way to choose the prize, now, the second probability problem is a big dumb goose egg and the studio audience all shouts "I KNEW IT!" Or 'fuck Obama,' depending on the network....

So anyway, the revealed curtain HAS to be a non-prize. They cannot risk it being the prize.
 
Keith&Co.

re: "But the game show host HAS to know where the prize is."

Yes, that is what is stated in the OP.
 
Keith&Co. said:
But the game show host HAS to know where the prize is.
the whole point of revealing what's behind one curtain, to give you the second choice.
For the show, this adds the drama of you sweating bullets and glancing at the studio audience shouting 'switch!' and 'stay pat!'
Click to expand...
Nope, there's nothing in the given scenario that indicates that the gameshow host reveals a particular door because he knows it doesn't contain a prize. It's entirely consistent with the scenario given that a particular door without a prize was revealed because he was drunk and accidentally picked a particular door .

We are merely given a scenario where the gameshow host picked a door that happened to reveal a non-prize. Whether that's because he knew where the prize was or because

For the puzzle, it's forcing you to understand the dynamics of the second choice.

In either case, if he randomly chooses the prize, there's no more choosing to do. You lost, there's no way to choose the prize, now, the second probability problem is a big dumb goose egg and the studio audience all shouts "I KNEW IT!" Or 'fuck Obama,' depending on the network....

So anyway, the revealed curtain HAS to be a non-prize. They cannot risk it being the prize.
Click to expand...
Who cannot reveal was as a non-prize? The non-existent people who are hosting the non-existent competition? Bollocks. We are only dealing with the question and situation dealt to us in the OP. Everything else is irrelevant and superfluous.
 
Monty Haul. Long since solved, you switch. Monte Carlo it if you don't believe that.
 
My bad, it does indeed state that the game show host knows where the prize is. Previous versions I've read didn't specify it.
 
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