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 Zagger
Male, 30-39, Europe
 108 Posts
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Tuesday, November 29, 2011 8:40:31 AM
I think the easiest way to understand it is like this:
First you take the game host out of the equation. Then you imaging you have 10 doors.
You then have the choice of opening 1 door or 9 doors.
Set up like this it's quite obvious that you have the best chances of winning if you open 9 doors instead of 1.
The thing that confuses people, I think, is that it's someone else opening the doors for you. |
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 davymid
Male, 30-39, Europe
11674 Posts
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Monday, November 28, 2011 9:34:13 PM
Psycholady did a better job than I did of explaining it. You should be a teacher! |
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 Psycholady33
Female, 18-29, Western US
60 Posts
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Monday, November 28, 2011 9:22:39 AM
Here's another way to think of it:
Let's name the possible outcomes "Win", "Fail 1" and "Fail 2"
If you had chosen door with "Fail 1", Host will open "Fail 2" door. You switch and you get "Win".
If you had chosen door with "Fail 2", Host will open "Fail 1" door. You switch and you get "Win".
If you had chosen door with "Win", Host will open "Fail 1" or "Fail 2" door. You switch and you get another "Fail".
You win 2 out of 3 times if you switch.
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 patchgrabber
Male, 30-39, Canada
5252 Posts
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Monday, November 28, 2011 7:05:08 AM
I think it's called the Monty Hall PROBLEM, not paradox, and it's simple probability. |
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davymid
Male, 30-39, Europe
11674 Posts
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Sunday, November 27, 2011 8:29:18 PM
Sarah, think of it this way, it might help. As Dixxy alluded to earlier, say there are 1000 doors. The chances of you picking one at random as being the right door are tiny (0.1%), so let's assume you pick the wrong door.
Monty then has 999 doors left to open for you, and he has to open doors that do not contain the prize. So he opens the 998 wrong doors for you, leaving the one that contains the prize, and your door. The fact that he opened those other doors doesn't change the fact that you had a 0.1% chance of picking the right door in the beginning - the conditions haven't changed.
So, if there are 1000 doors, sticking will win you the prize 0.1% of the time, while switching will win you the prize 99.9% of the time.
Boiling it down to 3 doors is the simplest form of the puzzle where it still works, but the odds are 33% vs 67% rather than 0.1% vs 99.9%. Either way, you should always switch.
Clear as mud? |
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 SarahofBorg
Female, 18-29, Eastern US
3526 Posts
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Sunday, November 27, 2011 7:35:07 PM
I'll never understand why this is true. It makes no damn sense. |
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 uatme
Male, 18-29, Canada
790 Posts
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Sunday, November 27, 2011 6:34:49 PM
Where is the paradox? |
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 thelonious
Male, 40-49, Southern US
3200 Posts
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Sunday, November 27, 2011 1:20:05 PM
SmagBoy1
To me, it SEEMS like if you are a switcher, meaning you will switch doors, you want your first pick to be an empty door. That will guarantee you a win. You have 2/3 chance of picking an empty door on your first pick. Therefore, a better chance than picking a prize the first time.
So where's the paradox? |
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thelonious
Male, 40-49, Southern US
3200 Posts
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Sunday, November 27, 2011 1:03:07 PM
JoeYC - LOL |
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thelonious
Male, 40-49, Southern US
3200 Posts
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Sunday, November 27, 2011 1:02:17 PM
@marcus2
No, the beach ball explodes from the pressure releasing all the air. Do you really believe what you wrote?
I was pointing out that both the beach ball and this Monty issue are easily explained phenomenon and not paradoxes. So, thanks for playing. |
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 Link_Hiei
Male, 18-29, Eastern US
5157 Posts
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Sunday, November 27, 2011 12:01:36 PM
Mythbusters are awesome. |
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randomxnp
Male, 30-39, Europe
769 Posts
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Sunday, November 27, 2011 10:41:31 AM
It's not a myth. it's an easily proved mathematical fact.
If it is pointed out that to win by switching you have to pick incorrectly initially, whereas to win by sticking you have to pick correctly initially it becomes obvious that the switcher will win 2/3 but the sticker will only win 1/3. |
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 MrPeabody
Male, 30-39, Eastern US
1435 Posts
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Sunday, November 27, 2011 10:35:42 AM
A pair of Docks
 |
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 BlankTom
Male, 30-39, Eastern US
6532 Posts
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Sunday, November 27, 2011 8:39:20 AM
even better...
A Pair of Docs |
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BlankTom
Male, 30-39, Eastern US
6532 Posts
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Sunday, November 27, 2011 8:37:20 AM
A Pair of Ducks |
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 SmagBoy1
Male, 40-49, Southern US
2734 Posts
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Sunday, November 27, 2011 8:19:56 AM
To those of you saying this isn't a paradox, why are you saying that? A paradox is defined as, "A seemingly contradictory statement that may nonetheless be true (e.g. The paradox that standing is more tiring than walking)."
So, the paradox here, quite obviously (and even stated no less than three times in the video), is that even though it *seems* like sticking with your original choice is no more or less mathematically/statistically beneficial, in fact, switching gives you a 33% increased chance of being correct. That, right there, is a paradox.
So, even though looking at two unopened doors *seems* like a 50/50 proposition, it is, given the set-up, actually a 33.33/66.66 proposition, in favor of switching. It's *seemingly* contradictory to think that switching helps you, but, in fact, it's true that switching helps. Paradox. |
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 JoeYC
Male, 18-29, Europe
725 Posts
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Sunday, November 27, 2011 7:16:29 AM
thelonious - owned by a teenager! lol!
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marcus2
Male, 13-17, Europe
678 Posts
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Sunday, November 27, 2011 5:38:46 AM
@thelonious
I don't think you know what a paradox is. The beach ball loses bouyancy because of the pressure/weight of the water pushing down on it. |
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 john_dies
Male, 18-29, Western US
59 Posts
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Sunday, November 27, 2011 2:31:21 AM
I love it when the Mythbusters dabble in phenomenology. |
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thelonious
Male, 40-49, Southern US
3200 Posts
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Saturday, November 26, 2011 11:11:19 PM
No. They suck BECAUSE they could not bust a myth. Like Zeus. Please try to keep up. |
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 mervviscious
Male, 40-49, Midwest US
1777 Posts
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Saturday, November 26, 2011 10:22:44 PM
they couldn't bust a myth because they suck... |
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thelonious
Male, 40-49, Southern US
3200 Posts
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Saturday, November 26, 2011 10:22:27 PM
Like the "beach ball paradox". If you take an inflated beach ball deep enough into the ocean, it suddenly becomes non-buoyant. It's a flucking paradox. |
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 PacoP42
Male, 13-17, Western US
1081 Posts
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Saturday, November 26, 2011 10:16:37 PM
guys, they are using the word paradox as in the fact that "switching gives you better odds" seems absurd but is true. |
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spultra13
Male, 18-29, Eastern US
175 Posts
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Saturday, November 26, 2011 9:13:26 PM
Twice the misuse the word "paradox". It's really just a tricky question. |
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thelonious
Male, 40-49, Southern US
3200 Posts
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Saturday, November 26, 2011 9:12:02 PM
Look at it this way, Monty is helping you to eliminate wrong doors. It is not even close to a paradox. If you are a programmer just think through how you could simulate this. Once you've got the code in your head or otherwise, it becomes clear. Paradox? WTF |
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