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The Monty Hall Paradox Investigated By Mythbusters

Would you `stick` or `switch`?

submitted by: kitteh9lives
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The Monty Hall Paradox Investigated By Mythbusters. Would you `stick` or `switch`?
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Hits: 17919 | Favorites: 7 | Emailed: 2 | Rating: 3.2 | Category: Science | Date: 11/26/2011
 
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Zagger
Male, 30-39, Europe
 108 Posts
Tuesday, November 29, 2011 8:40:30 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
 12009 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 9:22:38 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
 5683 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
 12009 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?

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