Author: Uri Blass
Date: 14:56:26 09/27/02
Go up one level in this thread
On September 27, 2002 at 17:30:11, Gerrit Reubold wrote: >On September 27, 2002 at 17:07:57, Uri Blass wrote: > >>On September 27, 2002 at 16:17:02, Gerrit Reubold wrote: >> >>>On September 27, 2002 at 16:04:45, Uri Blass wrote: >>> >>>>On September 27, 2002 at 15:40:07, Gerrit Reubold wrote: >>>> >>>>>On September 27, 2002 at 15:04:26, Uri Blass wrote: >>>>> >>>>>>On September 27, 2002 at 14:40:09, Gerrit Reubold wrote: >>>>>> >>>>>>>Uri, >>>>>>> >>>>>>>I think your model of the game is not a model of the situation which I am >>>>>>>discussing. >>>>>>> >>>>>>>Suppose you and me are playing the following game (f.ex. by email). >>>>>>> >>>>>>>1. I, the host, take an empty chessboard and put a single king one one of the >>>>>>>squares. Trust me that I don't cheat. You send me your guess which square this >>>>>>>might be. >>>>>>> >>>>>>>2. I assume you, the candidate, guess it is a1. >>>>>>> >>>>>>>3. I give you a hint: >>>>>>>The square is not one of >>>>>>> b1 c1 d1 e1 f1 g1 h1 >>>>>>>a2 b2 c2 d2 e2 f2 g2 h2 >>>>>>>a3 b3 c3 d3 e3 f3 g3 h3 >>>>>>>a4 b4 c4 d4 e4 f4 g4 h4 >>>>>>>a5 b5 c5 d5 e5 f5 h5 >>>>>>>a6 b6 c6 d6 e6 f6 g6 h6 >>>>>>>a7 b7 c7 d7 e7 f7 g7 h7 >>>>>>>a8 b8 c8 d8 e8 f8 g8 h8 >>>>>>> >>>>>>>(Note that it is no difference if I suddenly forgot on which square the king >>>>>>>stands, I decide to look only on the given 62 squares and, surprise, all of them >>>>>>>are empty.) >>>>>> >>>>>>It is important if you know where the king is. >>>>> >>>>>No. >>>>> >>>>>> >>>>>>Suppose for the discussion that you also do not know where the king is >>>>>>so you always expose all the squares except a1 g5 after >>>>>>I choose a1. >>>>> >>>>>No. I look at 62 random squares, excluding a1. >>>>> >>>>>> >>>>>>Suppose that we start to play 64000 games(most of them are >>>>>>not played because you discover the king >>>>>>in one of the 62 squares). >>>>> >>>>>No. We play only this single game. We might play again and my hint will likely >>>>>be different, maybe all squares except a1 and f8. >>>>> >>>>>Do you think it is a difference whether I forgot where the king is (I would have >>>>>told you "game over" if I accidently looked at a square with the king on it) or >>>>>whether I know the square of the king. >>>> >>>>Yes >>>>Suppose you do not know the square of the king. >>>> >>>>Suppose that for every square x(not a1) we play 64000 games when you choose >>>>square x. >>>>In these games the king is in square y in 1000 games for every square y. >>>> >>>>I claim that I can expect 62000 games out of every 64000 games to be canceled >>>>because the king is exposed(not in x and not in a1). >>>> >>>>I expect to win 1000 games out of 64000 games(the 1000 games when the king is in >>>>a1) and I expect to lose 1000 games out of 64000(the 1000 games when the king is >>>>in square x). >>>> >>>>The same hapen for everyone of the 63 squares that you can choose and I expect >>>>to win 63000 games and to lose 63000 games. >>>> >>>>Uri >>> >>>One question: >>> >>>Do you agree: If the host knows the solution (the door with the car, the >>>position of the king, ...), the candidate should switch? >>> >>>Greetings, >>>Gerrit >> >>Yes > >If (_only if_, and this is the only situation which I discuss) the situation >arises, that the host opened all the wrong doors, what should the candidate do: >should he switch or not? He can't read the mind of the host, maybe the host >knows the winning square/door, maybe it was just good luck. How should the >candidate seperate these cases: I think it is not possible and he should switch. Maybe the host knows that the candidate was right in the first choice and he tries to confuse the candidate so the candidate should not switch. If you assume no knowledge of the candidate about the host strategy then it is not clear what to do. Uri Uri
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