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Subject: Re: Monty Hall: The Proof only for trials > n=3

Author: Sune Fischer

Date: 05:41:51 09/28/02

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On September 28, 2002 at 07:49:50, Rolf Tueschen wrote:

>On September 28, 2002 at 05:53:07, Omid David wrote:
>
>>We have to understand what the "switch" operation does here: If our first choice
>>was correct, it will turn it into false; and if our first choice was false, it
>>will turn into correct. So in order to eventually succeed, we have to initially
>>choose the correct door in "stay" method, and the *wrong* door in "switch"
>>method.
>>
>>Thus, the operation "switch" merely "negates" the probability, i.e. if the
>>initial probability was x%, it will now become (100-x)%.
>>
>>For n doors, the success probability of "stay" will be (100/n)%, and the success
>>probability of "switch" will be (100 - 100/n)%.
>>
>>Examples:
>>
>>In the case of 3 doors, the initial probability was 33% (x=33), so after the
>>"switch" operation, it will become 67% (100-33=67).
>
>This is mathematical nonsense. No definition here. See my answer to Bruce in
>CTF.
>
>Rolf Tueschen

I think it is time to give in, actually it isn't very complicated at all:

Assume the hosts always opens to a goat (by luck or not):

You first pick a car (1/3), you switch and pick a car (0%)
You first pick a goat (2/3), you switch and pick a car (100%)

So by always switching you get 66.66% chance of a win.
With N>3 the odds gets even better.

How the host is supposed to "always" pick a goat by shear luck
is a different question, in fact it seems contradictory to
you assumption about luck, but if you only run 1 experiment you
don't have worry about those questions.

-S.

>
>>
>>For 10,000 doors, the success probability of "switch" will be 99.99%, while
>>"stay" will only have a 0.01% probability of success.
>>
>>In Marilyn vos Savant's example with 777,777 doors, the probability of success
>>with "switch" will be 99.99987%.
>>
>>Omid.



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