Contradictions in games?
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From: quasi on 2 Aug 2010 03:19 On Sun, 01 Aug 2010 21:29:46 EDT, Robert Kaufman <Yearachmeel(a)verizon.net> wrote: >Hi, > >Quasi, you seem to be saying that since there are only a finite number >of positions all we have to do is to go through all of them to verify whether >or not we have a winning position or not. I have problem with this. It seems >that you may have confused the total number of possible positions which is definitely finite with the total number of sequences of positions following >a possibly winning position which is not finite and which is necessary to >peruse in order to see whether we truly have a winning position. But the number of forcing sequences following a winning position _is_ finite. For a position to be winning, it must be possible to both avoid a loss and prevent a draw. The 50-move rule is the key. From Wikipedia: ***************************************************************************************** The fifty-move rule in chess states that a player can claim a draw if no capture has been made and no pawn has been moved in the last fifty consecutive moves (fifty moves by each side). ***************************************************************************************** Hence, from a winning position, the player must be able to make steady progress towards a win, otherwise the opponent can claim a draw (which would mean that the claimed winning position is not really winning after all). More concretely, the 50-move rule implies that checkmate can be forced from any winning position in less that 4000 moves (a crude upper bound). quasi
From: Robert Kaufman on 2 Aug 2010 04:02 Hi, Thanks for your reply. Your example involving pawns was clear to me, but how do you show that even in a game between inexperienced or inattentive players two kings cannot check each other? What I was trying to say when I referred to multivalued functions was that in the middle of a game any piece at position (a,b) has a variety of possible moves, and this can be represented by a multivalued function e.g. f1(a,b) =( a1,b1), ... ,( an,bn) . But then once we choose a new position f1 collapses to a single valued function. Respectfully, Robert Kaufman
From: Ilmari Karonen on 2 Aug 2010 09:17 On 2010-08-02, Robert Kaufman <Yearachmeel(a)verizon.net> wrote: > > Thanks for your reply. Your example involving pawns was clear to me, > but how do you show that even in a game between inexperienced or > inattentive players two kings cannot check each other? According to the rules of chess, no valid move may place or leave the moving player's king in check. As every valid position (except the initial one) must arise as the result of a valid move, no valid position may have both kings in check. (If the players are so inexperienced or inattentive that they make invalid moves, then they're not really playing chess anymore. If you allow invalid moves, then in principle any position becomes possible. Obviously, a move which, say, added a dozen kings to the table would be guaranteed to raise eyebrows; but it would still be a possible move, just not one allowed by the rules.) -- Ilmari Karonen To reply by e-mail, please replace ".invalid" with ".net" in address.
From: Robert Kaufman on 2 Aug 2010 05:57 HI. Thank you for the information. Are there other configurations which would be impossible after valid moves had been made other than the example involving pawns previously mentioned? Respectfully, Robert Kaufman
From: James Waldby on 2 Aug 2010 10:56
On Mon, 02 Aug 2010 09:57:28 -0400, Robert Kaufman wrote: > Are there other configurations which would be impossible after valid > moves had been made other than the example involving pawns previously > mentioned? Yes. Besides the example mentioned above, [that configurations with all pawns in their initial squares and some pieces other than knights not so, are XCV] there is the well-known example that configurations with both kings in check are XCV. (In above and following, let XCV stand for the phrase "not possible in any legitimate chess game".) Besides those two examples, the vast majority of configurations that have 32 pieces on the board are XCV, as follows: The configurations that have one pawn per player per file are a tiny minority of all possible 32-piece configurations. (Pawns change files only when capturing, directly or en passant. After any capture, fewer than 32 pieces remain on the board.) You may find <http://en.wikipedia.org/wiki/Chess_composition> enlightening. -- jiw |