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Posted on 1/13/15 at 10:50 am to Thib-a-doe Tiger
quote:Yep. Every time you move the door number up, the likelihood gets worse. Now, I want you to think about the fact that you just articulated my point.
By taking it to 1000 doors you change the probability of picking the correct door the first time drastically.
Yes, with 3 doors, the advantage to switching is MUCH smaller than with 10 doors and with 10, the advantage to switching is MUCH smaller than with 100 doors and on and on.
You note though that the ADVANTAGE is SMALLER, not NON existent!!!
Posted on 1/13/15 at 10:53 am to Thib-a-doe Tiger
quote:
By taking it to 1000 doors you change the probability of picking the correct door the first time drastically.
Or even 10 doors
Regardless of how far out you want to extrapolate it (1000 doors, etc.), if you NEVER change your pick, Monte will always eliminate everything EXCEPT 1 car and one goat, leaving you with a 50/50 shot.
Likewise, if you change your pick EVERY time Monte exposes a new goat, he's still going to leave you with a 50/50 shot in the end.
Posted on 1/13/15 at 10:55 am to link
Posted on 1/13/15 at 10:55 am to ShortyRob
I think the best way to run this is to run 2 different tests. One in which you only play all the way through on times when the "host" randomly picks a wrong door and play on from there. Then another test where the "host" knowingly picks a wrong door and you play it out. That would give you a view of how much the host knowing would change your chances
After thinking about it, there is probably a better chance when you change doors, but at 3 doors I don't believe it to be much better than a coin flip.
After thinking about it, there is probably a better chance when you change doors, but at 3 doors I don't believe it to be much better than a coin flip.
This post was edited on 1/13/15 at 10:57 am
Posted on 1/13/15 at 10:58 am to Thib-a-doe Tiger
quote:
After thinking about it, there is probably a better chance when you change doors, but at 3 doors I don't believe it to be much better than a coin flip.
With three doors it's a 66.67% chance when you switch, 33.33% chance when you stay.
With ten doors, 90% chance when you switch, 10% when you stay.
And so on...
Posted on 1/13/15 at 10:58 am to link
quote:
I have to disagree with the "always switch" conclusion. The correct answer about the probability is that it is 50/50.
The problem is not in the math--it is that the setup and explanation of the problem always given is a cheat. The problem is changed in the middle, but the original probabilities are not. That is why it is so counterintuitive.
I agree with you, but my stats teacher in grad school is one of the smartest dudes I know, and he says to switch, so if I were ever in that situation I'd likely switch.
Posted on 1/13/15 at 10:59 am to Thib-a-doe Tiger
quote:
After thinking about it, there is probably a better chance when you change doors, but at 3 doors I don't believe it to be much better than a coin flip.
It isn't MUCH better than a coin flip but it IS better than a coin flip.
The link I gave in page one(I think) actually lays out the test scenario.
Posted on 1/13/15 at 11:00 am to link
quote:
Likewise, if you change your pick EVERY time Monte exposes a new goat, he's still going to leave you with a 50/50 shot in the end.
So, if you played with 1000 doors, 10 times in a row and never switched, you believe you'd win 5 times?
OK.
Posted on 1/13/15 at 11:01 am to link
Mythbusters did this experiment. You won like twice as much if you switched.
Posted on 1/13/15 at 11:04 am to CocomoLSU
quote:
I agree with you, but my stats teacher in grad school is one of the smartest dudes I know, and he says to switch, so if I were ever in that situation I'd likely switch.
same here, FWIW, I used to argue with my Stats professer daily in grad school about this. I always held the belief that the question and the way the game is set up are two different things. Since you know one of the bad doors will be removed, I always believed my odds to be 50/50 to begin with (or to be more clear...33% compared to 33% of the other door.)
Posted on 1/13/15 at 11:06 am to link
quote:What if there were 10 doors.
I always believed my odds to be 50/50 to begin with
Posted on 1/13/15 at 11:07 am to ShortyRob
quote:
I always believed my odds to be 50/50 to begin with
What if there were 10 doors.
And, the question is, "should you switch" and the answer is, yes you goddamned idiot.
I mean, it isn't as if this problem hasn't actually been played out or anything.
Posted on 1/13/15 at 11:10 am to link
quote:
same here, FWIW, I used to argue with my Stats professer daily in grad school about this. I always held the belief that the question and the way the game is set up are two different things. Since you know one of the bad doors will be removed, I always believed my odds to be 50/50 to begin with (or to be more clear...33% compared to 33% of the other door.)
I did the exact same thing. It's the way that it's set up that I had a problem with. I completely understood that the porbabilities of any and all other doors basically shift to the one you didn't choose, but if you know from the start that it will come down to two doors, then the probability was never 1/3, or 1/100, or whatever...it's 1/2.
That being said, I would still most likely switch, especially if it's more than three original doors.
Posted on 1/13/15 at 11:12 am to CocomoLSU
quote:
That being said, I would still most likely switch, especially if it's more than three original doors.
And you'd do this because your probability of winning is GREATER than 50/50!! More doors simply makes it more obvious because the probabilities increase.
If you didn't switch when there were 1000 doors involved, someone should just shoot you.
Posted on 1/13/15 at 11:13 am to CocomoLSU
quote:
but if you know from the start that it will come down to two doors, then the probability was never 1/3, or 1/100, or whatever...it's 1/2.
See, the probability that YOU picked the right one is still 1/3 or 1/10 or 1/however many doors.
So if the host eliminates a door, knowing that it's a wrong one, you're still banking on your 1/3 shot if you stick with your first choice, vs. a 2/3 shot if you switch.
Twice as likely that you win if you switch, because the only way you lose is if you picked it right to begin with... back when the odds were still 1/3.
If you picked one of the two wrong doors (2/3 chance) then he eliminates the other one, and you switch to the right door. So, 2/3 chance that switching gives you a win.
Posted on 1/13/15 at 11:16 am to LSUBoo
It might help if people stopped asking what their odds were of having picked right at the outset and looked at it from the other side of the game.
From Monty's perspective. IE, when you pick, there's a 2/3 chance Monty holds the winner.
Alas, if he didn't open a door and said, "are you sure, or do you want to switch to one of the others?", there would be no sense in doing so.
But, when he does you the favor of eliminating a losing door..............
From Monty's perspective. IE, when you pick, there's a 2/3 chance Monty holds the winner.
Alas, if he didn't open a door and said, "are you sure, or do you want to switch to one of the others?", there would be no sense in doing so.
But, when he does you the favor of eliminating a losing door..............
Posted on 1/13/15 at 11:18 am to CocomoLSU
quote:whoa, really? that makes me feel better.
I did the exact same thing.
Posted on 1/13/15 at 11:19 am to ShortyRob
quote:
It might help if people stopped asking what their odds were of having picked right at the outset and looked at it from the other side of the game.
From Monty's perspective. IE, when you pick, there's a 2/3 chance Monty holds the winner.
Alas, if he didn't open a door and said, "are you sure, or do you want to switch to one of the others?", there would be no sense in doing so.
But, when he does you the favor of eliminating a losing door......
Again, to illustrate the SAME statistical reality but with larger numbers.
If there were 1000 doors, after you picked, the odds would be 99.9% that Monty had the winning door in his possession.
Him choosing to open 998 losing doors does not change that original reality. It merely makes your choice easier.
Posted on 1/13/15 at 11:21 am to The Easter Bunny
quote:Yeah it's really not that hard to verify. probability is pretty easy.
God dammit, dude. Do a fricking experiment at your house with two red cards and a black card and keep track of how many times you win switching vs not.
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