Author: Uri Blass
Date: 14:03:35 09/27/02
Go up one level in this thread
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. 2)p(a1 is the real place of the king) is reduced to 0 if the king is exposed in another square. 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. 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
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