Author: Gerrit Reubold
Date: 13:17:02 09/27/02
Go up one level in this thread
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
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