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#1
10-23-2007, 12:04 PM
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\"Let\'s make a deal\" problem
This question was posed recently by my statistics instructor. I am curious to see how much a part of conventional wisdom it is.
Lets say you are on the 1970's game show Lets Make a Deal. You reach the segment of the game where you are asked to pick one of three doors. Behind one of the doors is a wonderful prize like a new car. Behind the other two doors are gag prizes such as a can of dog food or a billy goat. After you choose, the host will always open one of the other two doors and reveal a gag prize. He then will give you the option to stick with your original choice or switch to the other unopened door. To give yourself the best chance of winning the grand prize, should you: A) always stick with your first choice. B) always switch to the other door. C) it makes no difference, there is an equal probability that either door is the winner. Please explain why you selected your choice 
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#2
10-23-2007, 12:28 PM
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Re: \"Let\'s make a deal\" problem
[ QUOTE ]
This question was posed recently by my statistics instructor. I am curious to see how much a part of conventional wisdom it is. Lets say you are on the 1970's game show Lets Make a Deal. You reach the segment of the game where you are asked to pick one of three doors. Behind one of the doors is a wonderful prize like a new car. Behind the other two doors are gag prizes such as a can of dog food or a billy goat. After you choose, the host will always open one of the other two doors and reveal a gag prize. He then will give you the option to stick with your original choice or switch to the other unopened door. To give yourself the best chance of winning the grand prize, should you: A) always stick with your first choice. B) always switch to the other door. C) it makes no difference, there is an equal probability that either door is the winner. Please explain why you selected your choice [/ QUOTE ] I google 'Monty Hall problem' and then proceed to offer Monty the prize if he tells how he decides whether to open the other door.... This hits these threads all the time, everyone knows the answer. Hopefully someone will lock this thread soon, and put it out of its misery.
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#3
10-24-2007, 12:32 AM
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Re: \"Let\'s make a deal\" problem
Sorry, buddy. I searched all the forums and saw no previous posts about this topic. So you are saying that everyone with a basic knowledge of probability knows the solution immediately and their eyes roll back into their heads when they hear it mentioned because it is so basic. That is really why I wanted to post, to get a feel for how well known the paradox is.
It seems as though one could design a money making scheme around this principle, but it would be fruitless if everyone knows the solution.
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#4
10-24-2007, 01:54 AM
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Re: \"Let\'s make a deal\" problem
It's not your fault. There's no way you could have known to search for Monty Hall. But there have been many threads on the subject in this forum. There probably should be a sticky.
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#5
10-24-2007, 09:22 AM
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Re: \"Let\'s make a deal\" problem
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#7
11-04-2007, 12:10 PM
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Re: \"Let\'s make a deal\" problem
[ QUOTE ]
It seems as though one could design a money making scheme around this principle, but it would be fruitless if everyone knows the solution. [/ QUOTE ] Daniel Negreanu posted a video recommending just that last year when he found out about this trick. He played it with an ace, king, and queen with the goal being to find the ace. Find someone who isn't good with math, show them the game, then take the remaining card for yourself. If you win they pay you $10, if they win then you pay $15. They will see a 50/50 game, and results that heavily favor them, so they should be all for playing it... even though the odds are really in your favor. I don't think this would actually work too well though. The game is complicated enough to not be understood right away, and it's also complicated enough for them to suspect a trick. And it definitely won't take long for them to notice that you're winning twice as often as they are.
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#8
11-04-2007, 12:15 PM
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Re: \"Let\'s make a deal\" problem
BTW I was reading another forum that discussed this recently. It didn't take long for everyone to agree that switching is obviously the best choice.
But then someone brought up the show Deal Or No Deal, and sooooooooo many people couldn't understand the odds on that game, the discussion lasted forever. It was impossible to get some people to understand that there's a difference between a game that is purely random, and a game that is manipulated by someone with knowledge of where the prizes are.
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