Lemieux66
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May 10th, 2014 at 1:45:04 PM permalink
I posted a thread about this about a month ago and people explained it to me. So now I understand you should always switch. However, how about this scenario. You don't know if the number is computer generated or selected by a human.

You have 90 million numbers to choose from. You pick 7. You find out it's either 7 or 76,432,529. Would you switch?

Pardon me if this is an odd question. I have time to kill lol.
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EdCollins
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May 10th, 2014 at 2:14:38 PM permalink
Recall that always switching is based upon the host (Monty) knowing in advance which door contains the prize, and that after you make a selection, he always reveals a door that doesn't contain the prize.

So as long as he knows where the prize is, and always reveals a door that doesn't have the prize, it doesn't make any difference if that door with the prize was randomly selected or selected by a human. (Say, one of his staff members backstage.)

And yes, assume there are 90 million numbers to chose from. I chose Lucky #7. If Monty knows what the winning number is, and eliminates every single number except #7 and #76,432,529, I would switch so fast your head would spin. In fact, I'd already be counting my prize winnings.
dwheatley
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May 10th, 2014 at 2:21:27 PM permalink
Yes... your question is used to make people see why switching makes sense in the 3 door problem.
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Lemieux66
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May 10th, 2014 at 2:24:10 PM permalink
Quote: dwheatley

Yes... your question is used to make people see why switching makes sense in the 3 door problem.



Oh I know it makes sense in a 3 door problem. I was just pondering if psychology of which numbers can be picked can play a role. I also made it 90 million because if a human picked it chances are he will pick a "normal" number rather than some gigantic random number.
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MangoJ
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May 10th, 2014 at 3:02:27 PM permalink
Quote: Lemieux66

Oh I know it makes sense in a 3 door problem. I was just pondering if psychology of which numbers can be picked can play a role. I also made it 90 million because if a human picked it chances are he will pick a "normal" number rather than some gigantic random number.



The example with the large number of doors is used for education. Any non-retarded player facing 90 million minus 2 doors should immediately recognize that door #76,432,529 must contain the prize, because it is highly unlikely that #7 was the right door chosen at the beginning.
GWAE
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May 10th, 2014 at 5:13:15 PM permalink
Quote: MangoJ

The example with the large number of doors is used for education. Any non-retarded player facing 90 million minus 2 doors should immediately recognize that door #76,432,529 must contain the prize, because it is highly unlikely that #7 was the right door chosen at the beginning.



why is it unlikely. Wouldn't it have the same odds of being chosen at the beginning?
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onenickelmiracle
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May 10th, 2014 at 5:36:58 PM permalink
Quote: GWAE

why is it unlikely. Wouldn't it have the same odds of being chosen at the beginning?

The way I always understood was You're trading a 1/3 chance for a 1/2 chance and although you don't know you're trading away luck, you do know the second choice switching has better probabilities.
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michael99000
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May 10th, 2014 at 5:43:11 PM permalink
Quote: GWAE

why is it unlikely. Wouldn't it have the same odds of being chosen at the beginning?



Wouldn't the right door being #7 mean that given a 1 in 90 million chance of guessing right, you guessed right? That seems unlikely.

So the two choices here are

A) you took a guess that had a 1 in 90 million chance of being correct and you were correct ( the right door is #7)

Or

B) you guessed wrong, and the right door is the other one , #76,432,259
Lemieux66
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May 10th, 2014 at 5:45:49 PM permalink
Quote: michael99000

Wouldn't the right door being #7 mean that given a 1 in 90 million chance of guessing right, you guessed right? That seems unlikely.

So the two choices here are

A) you took a guess that had a 1 in 90 million chance of being correct and was correct ( the right door is 7)

Or

B) you guessed wrong, and the right door is the other one , 76,432,259



While this is true, would you feel that if a person picked the number it's more likely to be 7 than 76,432,259? Would that alter your opinion?
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MangoJ
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May 10th, 2014 at 7:11:44 PM permalink
Quote: Lemieux66

While this is true, would you feel that if a person picked the number it's more likely to be 7 than 76,432,259? Would that alter your opinion?



What person picked what number ? person=player or person=host ? number=7 or number=76,432,259 ?

You do realize that the player picking 7 or any other number (say, 12,345,678) is irrelevant here. All it counts is that the player sees *his* previously chosen door and a totally different door unopened - while he knows for certain that his chosen door cannot be opened by the host beforehand, and he knows that one of those two remaining doors must contain the price.

You don't need to do any math here, just try to imagine what the host would need to do if you picked the correct door beforehand, and what the host would need to do if you didn't picked the correct door. Or, if you like - what the host would need to do if the price was in door #1, if the price was in door #2, ...

I guess you could play that game with a 4 year old on 100 doors, and they would get it right pretty fast....

Is your point that "7" seems like a human-selected number and "76,432,259" seems like a computer-random number ? Then you completely miss the essence.
DJTeddyBear
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May 11th, 2014 at 1:03:18 AM permalink
There are several threads on this, but this one includes a link to a NY Times interview with Monty where Monty explains why you might want to ignore the math. In short, Monty can be a dick.

https://wizardofvegas.com/forum/off-topic/general/4396-the-monty-hall-paradox-interview-with-monty-hall/
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AxiomOfChoice
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May 11th, 2014 at 11:02:19 AM permalink
Quote: DJTeddyBear

There are several threads on this, but this one includes a link to a NY Times interview with Monty where Monty explains why you might want to ignore the math. In short, Monty can be a dick.

https://wizardofvegas.com/forum/off-topic/general/4396-the-monty-hall-paradox-interview-with-monty-hall/



That article is talking about a different problem, where the host has the option of opening a door and offering a switch, or not, and possibly offering you cash to switch or not switch. This problem is a game theoretic one that is, IMO, more interesting.

In the problem which is generally referred to as "The Monte Hall problem", the host always opens a losing door and always offers you a switch. This is a simple probability problem with an obvious answer.

The article also claims that in the show, he usually did not always offer the switch. I'm not sure if that's correct; that's not how I remember the show, but it was a long time ago and I was young when I watched it.
JoePloppy
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May 11th, 2014 at 11:16:21 AM permalink
Quote: Lemieux66

While this is true, would you feel that if a person picked the number it's more likely to be 7 than 76,432,259? Would that alter your opinion?



If it was a person from the audience that picked the number, I might stick with lucky 7.
If the host or someone involved with the show, I would switch faster than a hooker with a broke john.
If we assume the host has done this before, unlikely 7 would be chosen. Maybe on the 1st show.
Unless it was someone from the audience you have to go with 50% over 0.00000111111%
I'd have to take a good looong stare at the guy/girl in the audience who picked the number.
Maybe announce to him/her "if I win I'll give you 100,000". See if I can get a read. If I didn't see anything, switch.
2/3
Lemieux66
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May 11th, 2014 at 11:25:08 AM permalink
Quote: JoePloppy

If it was a person from the audience that picked the number, I might stick with lucky 7.
If the host or someone involved with the show, I would switch faster than a hooker with a broke john.
If we assume the host has done this before, unlikely 7 would be chosen. Maybe on the 1st show.
Unless it was someone from the audience you have to go with 50% over 0.00000111111%
I'd have to take a good looong stare at the guy/girl in the audience who picked the number.
Maybe announce to him/her "if I win I'll give you 100,000". See if I can get a read. If I didn't see anything, switch.



You're the man.
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