View Poll Results: Should the contestant stick with his door, or switch?
Stick with his original door, but it's close
0
0%
Voters: 51. You may not vote on this poll
Interesting logic problem
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From: Columbus
Go play this applet and let us know the results.
http://www.stat.sc.edu/%7Ewest/javah...MakeaDeal.html
I played 50 times. Look at the odds.
Switched choices 25 times - 18 winners
Didn't switch 25 times - 8 winners
http://www.stat.sc.edu/%7Ewest/javah...MakeaDeal.html
I played 50 times. Look at the odds.
Switched choices 25 times - 18 winners
Didn't switch 25 times - 8 winners
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Joined: Jul 2004
Posts: 8,796
Likes: 2
From: San Diego, Wess-Side!!
Originally Posted by WestSideBilly,Oct 18 2005, 10:00 AM
But he doesn't pick first. Monte's choice depends on yours.
Back to the REAL show... Yes, Monte's choice is dependant on the contestant, but the CONTESTANT does not know if Monte is forced or randomizing his decision. That is why the contestant can pick any door they want FIRST. It doesn't matter because the end result to the CONSTESTANT is 50/50. AND is the same as if Monte DID infact choose first....he STILL cannot choose the one with the car.
Monte's decision is NOT based on the contestants decision.....that is why he can pick FIRST or SECOND.....DOESN'T MATTER.
Monte's decision is based on which door the car is behind. Because there are 3 doors to start....the end result again is 50/50.
Thread Starter
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From: Yorba Linda, CA
Originally Posted by SIIK2NR,Oct 18 2005, 09:48 AM
Once you stopped using the fair six sided dice to choose for Monte....it's no longer relevant...
When Monty has a choice, it's decided randomly and fairly (using the die).
When Monty doesn't have a choice, he shows the only door he can.
[QUOTE=SIIK2NR,Oct 18 2005, 09:48 AM]Monte picks the door he HAS TO.... but to the contestant it is just like Monte rolled the dice to pick it.
Joined: May 2001
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From: Nowhere
Originally Posted by Ubetit,Oct 18 2005, 01:02 PM
Go play this applet and let us know the results.
http://www.stat.sc.edu/%7Ewest/javah...MakeaDeal.html
I played 50 times. Look at the odds.
Switched choices 25 times - 18 winners
Didn't switch 25 times - 8 winners
http://www.stat.sc.edu/%7Ewest/javah...MakeaDeal.html
I played 50 times. Look at the odds.
Switched choices 25 times - 18 winners
Didn't switch 25 times - 8 winners
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Posts: 4,938
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From: limerick
Originally Posted by SIIK2NR,Oct 18 2005, 01:04 PM
At first glance this systems seems to work but it is not without flaws.
To Monte the answer is obvious but to the contestent they still have no advantage.
If you pick #2 and it is a goat..... you don't know that yet.
Monte has the option of #1 or #3 and he will pick #3. Although Monte has no choice but to pick #3.....you don't know that. You are still led to believe that he could have picked either #1 or #3.
So in essence you are in the same situation as if you had picked #1 in the first place. You would think you were right and wouldn't change your mind and in fact would have picked a goat.
They system is to the Game show advantage.
The odds after drawing out 1 of 3 balls is not 33% after drawing one of the balls out. The odds of "probability" will be slightly in your favor but the true odds would be 50/50.
It's luck... bottom line.
To Monte the answer is obvious but to the contestent they still have no advantage.
If you pick #2 and it is a goat..... you don't know that yet.
Monte has the option of #1 or #3 and he will pick #3. Although Monte has no choice but to pick #3.....you don't know that. You are still led to believe that he could have picked either #1 or #3.
So in essence you are in the same situation as if you had picked #1 in the first place. You would think you were right and wouldn't change your mind and in fact would have picked a goat.
They system is to the Game show advantage.
The odds after drawing out 1 of 3 balls is not 33% after drawing one of the balls out. The odds of "probability" will be slightly in your favor but the true odds would be 50/50.
It's luck... bottom line.
http://en.wikipedia.org/wiki/Monty_Hall_problem
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From: Nowhere
Originally Posted by SIIK2NR,Oct 18 2005, 01:07 PM
That was in reference to CHANGE THE SHOW....
Back to the REAL show... Yes, Monte's choice is dependant on the contestant, but the CONTESTANT does not know if Monte is forced or randomizing his decision. That is why the contestant can pick any door they want FIRST. It doesn't matter because the end result to the CONSTESTANT is 50/50. AND is the same as if Monte DID infact choose first....he STILL cannot choose the one with the car.
Monte's decision is NOT based on the contestants decision.....that is why he can pick FIRST or SECOND.....DOESN'T MATTER.
Monte's decision is based on which door the car is behind. Because there are 3 doors to start....the end result again is 50/50.
Back to the REAL show... Yes, Monte's choice is dependant on the contestant, but the CONTESTANT does not know if Monte is forced or randomizing his decision. That is why the contestant can pick any door they want FIRST. It doesn't matter because the end result to the CONSTESTANT is 50/50. AND is the same as if Monte DID infact choose first....he STILL cannot choose the one with the car.
Monte's decision is NOT based on the contestants decision.....that is why he can pick FIRST or SECOND.....DOESN'T MATTER.
Monte's decision is based on which door the car is behind. Because there are 3 doors to start....the end result again is 50/50.
In the 3 door game (or any amount of doors greater than 2, where all but 2 are opened to reveal goats after the contestent chooses), Monte does not have a choice - the door he opens is dictated by the contentesten's choice. You're right, the contestant doesn't know if Monte randomized or was forced, but statistically the contestant is twice as likely to win by switching. A sample of 1 would appear to be 50/50 (he either won or lost), but the greater the sample size, the clearer it becomes that switchers are more likely to win.
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From: San Diego, Wess-Side!!
Originally Posted by Ubetit,Oct 18 2005, 10:02 AM
Go play this applet and let us know the results.
http://www.stat.sc.edu/%7Ewest/javah...MakeaDeal.html
I played 50 times. Look at the odds.
Switched choices 25 times - 18 winners
Didn't switch 25 times - 8 winners
http://www.stat.sc.edu/%7Ewest/javah...MakeaDeal.html
I played 50 times. Look at the odds.
Switched choices 25 times - 18 winners
Didn't switch 25 times - 8 winners
I totally agree with the probability at the very begining being 2/3 of getting it wrong.....therefore changing your decision at the end would statistically show the advantage.
This goes back to my original statement of 1:3 odds of picking the right one and sticking with it.
Also covered when I gave the example of picking a GOAT instead of a car and then switching at the end.
Bottom line....
I was wrong...
Although the final decision is 50/50.....the laws of probability favor switching due to the initial 2/3 advantage during the first pick.
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Posts: 8,796
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From: San Diego, Wess-Side!!
"MY" mistake is when I gave the example of trying to pick a goat instead of a car with the first 3 doors that the solution always ended up to switch at the final decision and I didn't catch that... therefore missing the advantage.
I was set up!!! 
I was set up!!!
Thread Starter
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From: Yorba Linda, CA
Originally Posted by SIIK2NR,Oct 18 2005, 10:18 AM
Although the final decision is 50/50.....the laws of probability favor switching due to the initial 2/3 advantage during the first pick.
If you simply mean that there are two choices - one correct, one incorrect - then you are right.
If you mean that one choice is correct 50% of the time and the other is correct 50% of the time - what, I suspect, most people mean when they say "50/50" - then you're wrong.
The final decision is not 50/50; it's 33.333/66.667 (stay/switch).