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Subject: Re: New and final solution of the Monty Hall Dilemma

Author: Gerrit Reubold

Date: 14:16:33 09/27/02

Go up one level in this thread


On September 27, 2002 at 17:03:35, Uri Blass wrote:

>On September 27, 2002 at 16:25:54, Gerrit Reubold wrote:
>
>>On September 27, 2002 at 16:14:08, Uri Blass wrote:
>>
>>>On September 27, 2002 at 15:47:15, Peter Berger wrote:
>>>
>>>>On September 27, 2002 at 15:27:35, Uri Blass wrote:
>>>>
>>>>>On September 27, 2002 at 15:18:52, Peter Berger wrote:
>>>>>
>>>>>>On September 27, 2002 at 15:11:12, Uri Blass wrote:
>>>>>>
>>>>>>>On September 27, 2002 at 14:58:25, Peter Berger wrote:
>>>>>>>
>>>>>>>>On September 27, 2002 at 14:33:22, Uri Blass wrote:
>>>>>>>>
>>>>>>>>>Correction:
>>>>>>>>>I meant one and only one of us is right if incredible luck happened.
>>>>>>>>>of course in most cases we will discover that both of us wrong.
>>>>>>>>>
>>>>>>>>>Uri
>>>>>>>>
>>>>>>>>Read http://www.talkchess.com/forums/1/message.html?254769 . I am your friend on
>>>>>>>>g5 :).
>>>>>>>>
>>>>>>>>Peter
>>>>>>>
>>>>>>>I read it and replied it without the friend.
>>>>>>>simulation prove that out of 64000 games
>>>>>>>only 2000 are practically played and
>>>>>>>I win 1000 out of 2000 by not switching.
>>>>>>>
>>>>>>>With the friend I get the same and I see no reason to prefer a1 and not g5 if I
>>>>>>>know that the host does not choose g5.
>>>>>>>
>>>>>>>If the host choose random squares the game is
>>>>>>>practically the same because all the squares are the same
>>>>>>>from the host point of view when he knows nothing about them.
>>>>>>>
>>>>>>>Uri
>>>>>>
>>>>>>The right assumption IMHO is not that the friend sits on g5 but that the friend
>>>>>>always sits on the other field left the host didn't expose.
>>>>>>
>>>>>>Peter
>>>>>
>>>>>We assume that the host does not know the right square.
>>>>>
>>>>>suppose that the host strategy is not to expose a random square.
>>>>>
>>>>>62/64 of the games are canceled because the host exposed
>>>>>the king
>>>>>
>>>>>Let look only in 64000 game that the host did not expose g5
>>>>>
>>>>>62000 of them are canceled
>>>>>I win 1000 of them and the friend win 1000 of them.
>>>>>
>>>>>The same is for 64000 games when the host did not expose g4.
>>>>>
>>>>>For every square that the host does not expose I have the same number
>>>>>of wins and losses.
>>>>>
>>>>>Uri
>>>>
>>>>One last trial - to keep the analogy with the original Monty problem and the
>>>>adding of additional doors.
>>>>
>>>>I think it is just like this:
>>>>
>>>>1.) You have the first choice -> you take a1
>>>>2.) The host starts opening doors, he opens 62 of them and none has the king (he
>>>>is just lucky or he knows, doesn't matter).
>>>
>>>It is important.
>>>
>>>>3.) Then he adresses me : Which of the 64 fields that don't have Uri on them do
>>>>you want to choose -> I choose the one not exposed yet
>>>>4.) Then he adresses you: do you want to keep with your square or change to
>>>>Peter's?
>>>>
>>>>There are only two interesting squares left - one of them has the king. But I
>>>>think you will agree that yours sucks compaired to mine.
>>>>
>>>>Peter
>>>
>>>If the king was not exposed by luck then I do not agree.
>>>
>>>Last try to explain:
>>>Let suppose he does not know where is the king.
>>>
>>>Let suppose that I am not allowed to change my choice and I win only if I chose
>>>the king.
>>>My chances are 1/64 to be right.
>>
>>Agreed.
>>
>>>
>>>1)Do you agree that if he expose the king when he expose 62 squares then it is
>>>bad luck for me and I lost the game?
>>
>>No. The game is canceled in this case. We assume the king is not exposed.
>
>I was talking about a new game and not about the old game.
>
>The rules in the new game game is that I win if the king is in a1 and I lose if
>the king is in another square.
>
>I will try to explain more clearly(I will not talk about winning the game but
>about your probability to be right in guessing)
>
>1)P(a1 is the real place of the king)=1/64 in the beginning of the game.

Agreed.

>
>2)p(a1 is the real place of the king) is reduced to 0 if the king is exposed in
>another square.

Agreed, but that doesn't matter, because in the game which I discuss the king is
_not_ exposed.

>
>3)p(a1 is the real place of the king) is increased if the king is not exposed
>because it is not logical to assume that exposing squares can reduce the
>probability of the king to be in a1 and cannot increase the probability of the
>king to be in a1.

No, looking at squares do not change the probability of the king being in a1,
neither increase nor decrease.


>
>It means that the probability that you are right to assume that the king is not
>in a1 is more than 1/64 if you know that the king is not exposed.
>
>Uri

Greetings,
Gerrit



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