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The Monty Hall Paradox Investigated By Mythbusters

Hits: 17965 | Rating: (3.2) | Category: Science | Added by: kitteh9lives
Page: 1 2 Next >   Jump to: Bottom    Last Post
Zagger
Male, 30-39, Europe
 108 Posts
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.

davymid
Male, 30-39, Europe
 12130 Posts
Monday, November 28, 2011 9:34:13 PM
Psycholady did a better job than I did of explaining it. You should be a teacher!

Psycholady33
Female, 18-29, Western US
 61 Posts
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.

patchgrabber
Male, 30-39, Canada
 5745 Posts
Monday, November 28, 2011 7:05:08 AM
I think it's called the Monty Hall PROBLEM, not paradox, and it's simple probability.

davymid
Male, 30-39, Europe
 12130 Posts
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?

SarahofBorg
Female, 18-29, Eastern US
 3573 Posts
Sunday, November 27, 2011 7:35:07 PM
I'll never understand why this is true. It makes no damn sense.

uatme
Male, 18-29, Canada
 1027 Posts
Sunday, November 27, 2011 6:34:49 PM
Where is the paradox?

thelonious
Male, 40-49, Southern US
 3246 Posts
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?

thelonious
Male, 40-49, Southern US
 3246 Posts
Sunday, November 27, 2011 1:03:07 PM
JoeYC - LOL

thelonious
Male, 40-49, Southern US
 3246 Posts
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.

Link_Hiei
Male, 18-29, Eastern US
 5190 Posts
Sunday, November 27, 2011 12:01:36 PM
Mythbusters are awesome.

randomxnp
Male, 30-39, Europe
 1271 Posts
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.

MrPeabody
Male, 30-39, Eastern US
 1795 Posts
Sunday, November 27, 2011 10:35:42 AM
A pair of Docks


BlankTom
Male, 30-39, Eastern US
 6560 Posts
Sunday, November 27, 2011 8:39:20 AM
even better...


A Pair of Docs

BlankTom
Male, 30-39, Eastern US
 6560 Posts
Sunday, November 27, 2011 8:37:20 AM


A Pair of Ducks

SmagBoy1
Male, 40-49, Southern US
 4243 Posts
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.

JoeYC
Male, 18-29, Europe
 725 Posts
Sunday, November 27, 2011 7:16:29 AM
thelonious - owned by a teenager! lol!


marcus2
Male, 13-17, Europe
 678 Posts
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.

john_dies
Male, 18-29, Western US
 60 Posts
Sunday, November 27, 2011 2:31:21 AM
I love it when the Mythbusters dabble in phenomenology.

thelonious
Male, 40-49, Southern US
 3246 Posts
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.

mervviscious
Male, 40-49, Midwest US
 1807 Posts
Saturday, November 26, 2011 10:22:44 PM
they couldn't bust a myth because they suck...

thelonious
Male, 40-49, Southern US
 3246 Posts
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.

PacoP42
Male, 13-17, Western US
 1081 Posts
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.

spultra13
Male, 18-29, Eastern US
 175 Posts
Saturday, November 26, 2011 9:13:26 PM
Twice the misuse the word "paradox". It's really just a tricky question.

thelonious
Male, 40-49, Southern US
 3246 Posts
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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