Author: Rolf Tueschen
Date: 13:48:25 09/27/02
Go up one level in this thread
On September 27, 2002 at 16:09:31, Peter Berger wrote: >On September 27, 2002 at 16:02:33, Rolf Tueschen 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). >>>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 >> >> >>Let's see, the problem is identic with the Monty Hall case. We have two fields >>still closed, right? Then we had a 50% chance to open the King either on a1 ot >>the other field. Period. >> >>Rolf Tueschen > >Thanks for answering and your honesty. > >Do you agree to a match under these exact conditions where you get 10 € every >time you win and I get 5 € every time I win when you have to be the guy who >makes the first choice? > >(pete, looking forward to a little extra income :) ) No, I must confess something. In the speed here I made a mistake. What you did on the chessboard or others , also Marilyn, with their million doors or cups, the whole thing is asymmetric - as Uri made clear. But I come back to the original question of three doors only. Then I choose 1 door. From the others the host can always take one with a goat, very simple. And then for the condition of only one single trial, it makes no practical difference. While in the case of 1 million where I must make my choice this becomes different. Also with your 64 squares already. Since I am always trying to figure out what I would do as the candidate I was a bit dreaming too much. Also I think now that Marilyn made a really fine example. But we are still not through the case with the only three doors. Here I still see that my door has the same probability or chance than the other door. But the number three is magic because the host is only allowed to take away one. For only one event or trial it's then 50:50. From the eyes of the candidate. From four doors (or squares in your game) on upwards I would then also say that switching is better. Let me make clear that I would switch in 2/3 of the case and stick for the rest. How about that? :) Yes, I'm now a mathematically experienced candidate. Rolf Tueschen
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