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Post by Supertramp78 on Jun 18, 2009 10:25:10 GMT -5
If you REALLY want to wrap your brain around something let's DO increase the number of doors to 100. Now you have a 99% chance of NOT getting a car. You pick a door and the game show host opens 98 doors that DON'T have a car. Now there are two doors. The you picked originally that had a 99% chance of being a car and the other door that still has that original 1% chance of being a car. If you keep what you have, your chances of winning is 1%, equal to your original chances of winning. If you switch, your chances of winning now go up to 99%, equal to your chances of not picking the car on your first pick.
Math is fun.
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Post by knobtwister on Jun 18, 2009 10:26:41 GMT -5
10 pages and still no reference to Hitler. ;D
Although Bill did bring up 'Number Nazis'.
Don
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Post by Supertramp78 on Jun 18, 2009 10:43:31 GMT -5
The odds in the original three door problem are never 50/50 by the way. The odds are based at the time you make a pick and the number of options you had when you made that pick.
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Post by millring on Jun 18, 2009 10:55:11 GMT -5
Here's what the game actually is:
There is the 'tramp team.
There is the Omaha team.
The 'tramp team gets to pick a door. Any door. Doesn't matter which door. Anyone could pick it for them and walk away.
The Omaha team always gets the other two doors.
Then you are asked which team you want to be on.
The reveal is misdirection in the long game.
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Post by Supertramp78 on Jun 18, 2009 11:00:06 GMT -5
Exactly. the Omaha team has a 66% chance of winning while my sorry team only has 33%. Switching in the original game allows you to bail on my team and go to his.
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Deleted
Deleted Member
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Post by Deleted on Jun 18, 2009 11:08:42 GMT -5
Here's what the game actually is: There is the 'tramp team. There is the Omaha team. The 'tramp team gets to pick a door. Any door. Doesn't matter which door. Anyone could pick it for them and walk away. The Omaha team always gets the other two doors. Then you are asked which team you want to be on. The reveal is misdirection in the long game. EXACTLY. Revealing the goat-door does absolutely NOTHING, except create the illusion that your odds are now "even" between the two unopened doors.. But, they are not even SINCE Monte knew it was a goat-door. In effect. Monte is offering you a chance to switch, and pick BOTH of the doors you didn't originally choose. This trade is disguised by the fact that Monte revealed the goat door, and took it out of play, thus creating the illusion that the switch is even-up for one door. |
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Post by Supertramp78 on Jun 18, 2009 11:14:17 GMT -5
Which is why it is never a 50/50 choice. It does make it really confusing to a lot of smart people though. But as someone else said, gamblers understand it instantly. Probability wonks call it the 'variable change' theory. I don't know if that is a real theory, but it doesn't change the fact that the odds of winning increase to 66% if you switch.
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Post by Supertramp78 on Jun 18, 2009 11:33:48 GMT -5
"I think Tramp's big chart a couple pages ago pegs the error. It essentially cherry picks 3 of the 9 independent possible outcomes of the game (3 doors means 3 possible contestant picks times 3 possible pize locations = 9 independent outcomes). If the chart were expanded to include the other 6 outcomes, it would be easy to cross out the six that are eliminated with the contestant's first pick and then the seventh that is eliminated with the openning of the door."
You think? Let's do it.
Scenario 1 = car,goat,goat
Scenario 2 = goat,car,goat
Scenario 3 = goat,goat,car
Nine contestants, one for each door in each scenario. One pass they all keep their original door, the next pass they all switch.
Scenario 1 = car behind door 1:
contestant 1 picks door 1 (car)
contestant 2 picks door 2 (goat)
contestant 3 picks door 3 (goat)
Scenario 2 = car behind door 2:
contestant 4 picks door 1 (goat)
contestant 5 picks door 2,(car)
contestant 6 picks door 3,(goat)
Scenario 3 = car behind door 3:
contestant 7 picks door 1,(goat)
contestant 8 picks door 2,(goat)
contestant 9 picks door 3,(car)
If in the above situation, NOBODY switches, then contestants 1,5 and 9 win. That's three contestants out of 9 or 1/3.
Now let's let them switch.
Scenario 1 = car behind door 1:
contestant 1 picks door 1 (car), Door 2 or 3 is revealed and he switches and gets a goat
contestant 2 picks door 2 (goat), Door 3 is opened, switches to 1 and gets a car
contestant 3 picks door 3 (goat), Door 2 is opened, switches to 1 and gets a car
Scenario 2 = car behind door 2:
contestant 4 picks door 1 (goat) Door 3 is opened, switches to 2 and gets a car
contestant 5 picks door 2,(car) Door 1 or 3 is revealed and he switches and gets a goat
contestant 6 picks door 3,(goat) Door 1 is opened, switches to 2 and gets a car
Scenario 3 = car behind door 3:
contestant 7 picks door 1,(goat) Door 2 is opened, switches to 3 and gets a car
contestant 8 picks door 2,(goat) Door 1 is opened, switches to 3 and gets a car
contestant 9 picks door 3,(car) Door 1 or 2 is revealed and he switches and gets a goat
If they switch then contestants 2,3,4,6,7 and 8 win cars. That's six contestants out of 9 or 2/3.
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Post by omaha on Jun 18, 2009 12:52:40 GMT -5
The point of Tramp's post (if I may be so bold as to say so) is that this is not like chess or some other game where there are literally trillions of possible outcomes.
The entire solution space to this game is contained in Tramp's post. 100% of it.
The burden, then, on someone who disagrees with the "1/3 if you hold, 2/3 if you switch" position is to find a scenario that (a) supports your view and (b) is NOT found in Tramp's post.
And what you are going to run up against is "b" : There are no possible scenarios other than those Tramp has listed.
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Post by Supertramp78 on Jun 18, 2009 13:01:12 GMT -5
'The folks who have the right answer (switching is better) can't frame the other side of the debate."
Yeah. I don't understand the incorrect argument at all.
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Post by paulschlimm on Jun 18, 2009 13:06:01 GMT -5
You could be on my team. I'd detain Tramp and Omaha, and have them waterboarded. I'd use breaching charges to blow open all three doors at the same time. My team would form into three four-man stacks, toss in flash bangs, and clear the rooms behind the doors.
If we killed anyone accidentally, we'd put purple dye on their index fingers, spread some "I HEART Ahmedinejad" literature around the bodies, and send pictures to Fox News.
Game over. I win.
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Post by aquaduct on Jun 18, 2009 13:09:11 GMT -5
OK. Now that makes sense.
Now I've got to go back and rediscover the meaning of "independent" and "mutually exclusive" so I can make the math work without pictures.
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Post by Supertramp78 on Jun 18, 2009 13:09:29 GMT -5
Why do you hate America?
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Post by omaha on Jun 18, 2009 13:11:40 GMT -5
You could be on my team. I'd detain Tramp and Omaha, and have them waterboarded. The little-known secret about waterboarding is that those with advanced math skills are immune to it's torments. I understand that Shiek Kaleed Muhammed can't add two plus two, which explains why he sang like a canary after just a few drops. |
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Post by millring on Jun 18, 2009 13:15:02 GMT -5
You could be on my team. I'd detain Tramp and Omaha, and have them waterboarded. I'd use breaching charges to blow open all three doors at the same time. My team would form into three four-man stacks, toss in flash bangs, and clear the rooms behind the doors. If we killed anyone accidentally, we'd put purple dye on their index fingers, spread some "I HEART Ahmedinejad" literature around the bodies, and send pictures to Fox News. Game over. I win. Besides the simple elegance of this solution, the beauty of it lies in the fact that you get to have the car AND the goats. |
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Post by Supertramp78 on Jun 18, 2009 13:15:47 GMT -5
but the goats are dead and the car is on fire.
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Post by millring on Jun 18, 2009 13:17:32 GMT -5
but the goats are dead and the car is on fire. Exactly why everyone wants to be on Jeff "my glass is half full" Omaha's team. |
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Post by Supertramp78 on Jun 18, 2009 13:19:18 GMT -5
his glass is 66% full if he switches
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Post by millring on Jun 18, 2009 13:20:17 GMT -5
100% full if he recruits Schlimm.
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Post by Supertramp78 on Jun 18, 2009 13:20:58 GMT -5
but probably broken
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