View Poll Results: Should the contestant stick with his door, or switch?
Stick with his original door, but it's close
0
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Voters: 51. You may not vote on this poll
Interesting logic problem
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Originally Posted by ninethreeeleven,Oct 18 2005, 08:34 AM
I figured that Monte knew that you chose right and then chose to open "one of the other doors to reveal a goat"
So when I said I wanted to switch I meant switch from 50/50 to the first choice.
It should be 50/50 in my opinion, but the text in the first post says "one of the other doors to reveal a goat" Its my assumption that Monte picked one of the other doors at random, not caring which one because he knew that the person chose right.
He is the one now picking at random, because as long as he doesn't show the person thier door, he knows the other 2 doors have goats behind them, because Monte knows that the person picked the correct door.
Maybe I read into it too much, but I feel that you should always go with your instincts.
So when I said I wanted to switch I meant switch from 50/50 to the first choice.
It should be 50/50 in my opinion, but the text in the first post says "one of the other doors to reveal a goat" Its my assumption that Monte picked one of the other doors at random, not caring which one because he knew that the person chose right.
He is the one now picking at random, because as long as he doesn't show the person thier door, he knows the other 2 doors have goats behind them, because Monte knows that the person picked the correct door.
Maybe I read into it too much, but I feel that you should always go with your instincts.
If you (initially) choose a door with a goat Monty knows that you've chosen a goat and which of the remaining doors hides the car; he will always show you the other door with the goat. In this case, Monty doesn't have a choice; there's only one door he can open.
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From: Nowhere
Door 1 = Car
Door 2 = Goat
Door 3 = Goat
If you pick #1, Monte picks either 2 or 3 and your choice is right - don't switch.
If you pick #2, Monte picks 3 and your choice is wrong - switch.
If you pick #3, Monte picks 2 and your choice is wrong - switch.
In 2/3 of the cases you should be switching versus 1/3 of the cases in which you shouldn't. So even though picking from 2 is 50/50, you should switch.
The exception to this would be if you were an avid fan and had a statistical database indicating higher than nominal probabilities of the car being behind a given door or higher than nominal probabilities of Monte showing 2 vs 3. Of course that's another thread.
Door 2 = Goat
Door 3 = Goat
If you pick #1, Monte picks either 2 or 3 and your choice is right - don't switch.
If you pick #2, Monte picks 3 and your choice is wrong - switch.
If you pick #3, Monte picks 2 and your choice is wrong - switch.
In 2/3 of the cases you should be switching versus 1/3 of the cases in which you shouldn't. So even though picking from 2 is 50/50, you should switch.
The exception to this would be if you were an avid fan and had a statistical database indicating higher than nominal probabilities of the car being behind a given door or higher than nominal probabilities of Monte showing 2 vs 3. Of course that's another thread.
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Originally Posted by WestSideBilly,Oct 18 2005, 08:54 AM
The exception to this would be if you were an avid fan and had a statistical database indicating higher than nominal probabilities of the car being behind a given door or higher than nominal probabilities of Monte showing 2 vs 3.
[QUOTE=magician,Oct 18 2005, 08:52 AM]Assume that his choice is unbiased; i.e., he will choose each door 50% of the time.
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[QUOTE=WestSideBilly,Oct 18 2005, 08:54 AM] Door 1 = Car
Door 2 = Goat
Door 3 = Goat
If you pick #1, Monte picks either 2 or 3 and your choice is right - don't switch.
If you pick #2, Monte picks 3 and your choice is wrong - switch.
If you pick #3, Monte picks 2 and your choice is wrong - switch.
Door 2 = Goat
Door 3 = Goat
If you pick #1, Monte picks either 2 or 3 and your choice is right - don't switch.
If you pick #2, Monte picks 3 and your choice is wrong - switch.
If you pick #3, Monte picks 2 and your choice is wrong - switch.
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From: Yorba Linda, CA
What's interesting - to me, at least - is that the voting is very nearly symmetric: roughly 1/2 say it doesn't matter, and roughly 1/4 each say definitely stick or definitely switch.
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Originally Posted by SIIK2NR,Oct 18 2005, 09:04 AM
To Monte the answer is obvious but to the contestent they still have no advantage.
It's luck... bottom line.
It's luck... bottom line.
What if there were five doors?
Ten?
One hundred?
One million?
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No matter what door the car is behind.....you will always be shown a goat behind another door...
Because you get to pick FIRST....you have a statistical chance of 1:3 of getting it right... If you want to stick with those odds....then you don't switch your choice.
After the other door is opened you are offered to switch, which in essence gives you no longer a 1:3 but a 50/50 chance. It's 50/50 of either you getting it right or that you picked the wrong one.
The only way to do it would be in your mind...BEFORE you pick 1 of 3 doors, is to pick 2 doors in your head of which side the car is in your opinion. Pick one of the two doors in your mind and tell Monte. After he opens the second door and it's the other door in your mind....then stay with your original pick because you already ruled out that the other other door was not what you would have picked anyway. So why switch now?
If Monte picks the door that you did not pick in your mind as one of the original 2 then you are left with the 2 doors you had in your mind in the first place.... and it's a true 50/50.
Because you get to pick FIRST....you have a statistical chance of 1:3 of getting it right... If you want to stick with those odds....then you don't switch your choice.
After the other door is opened you are offered to switch, which in essence gives you no longer a 1:3 but a 50/50 chance. It's 50/50 of either you getting it right or that you picked the wrong one.
The only way to do it would be in your mind...BEFORE you pick 1 of 3 doors, is to pick 2 doors in your head of which side the car is in your opinion. Pick one of the two doors in your mind and tell Monte. After he opens the second door and it's the other door in your mind....then stay with your original pick because you already ruled out that the other other door was not what you would have picked anyway. So why switch now?
If Monte picks the door that you did not pick in your mind as one of the original 2 then you are left with the 2 doors you had in your mind in the first place.... and it's a true 50/50.
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From: San Diego, Wess-Side!!
Originally Posted by magician,Oct 18 2005, 09:09 AM
Suppose that, instead of three doors, there were four (one car and three goats), and that after you choose Monte shows you two doors with goats, leaving your door and one other. Is it still an even bet?
What if there were five doors?
Ten?
One hundred?
One million?
What if there were five doors?
Ten?
One hundred?
One million?
If your given options till only 2 doors remain...then the odds are always 50/50. Probability no longer plays into effect because Monte is also making choices during this process and he cannot emliminate or choose the door with the car in it.
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From: San Diego, Wess-Side!!
Did you read my post on the flaw behind your theory?
it's 50/50. Monte always makes the 2nd choice so probability is ruled out. He systematically rules out one of the 3 doors. Guaranteeing you a 50/50 shot.
If you had to pick 2 doors to eliminate and then were offered to change your mind after he showed you that one of the choices you made was wrong...then your have probability and statistical changes.
But you don't pick 2.....you only pick 1 and the other is a guaranteed pick to your advantage.
it's 50/50. Monte always makes the 2nd choice so probability is ruled out. He systematically rules out one of the 3 doors. Guaranteeing you a 50/50 shot.
If you had to pick 2 doors to eliminate and then were offered to change your mind after he showed you that one of the choices you made was wrong...then your have probability and statistical changes.
But you don't pick 2.....you only pick 1 and the other is a guaranteed pick to your advantage.