Author: Uri Blass
Date: 07:10:59 05/10/01
Go up one level in this thread
On May 10, 2001 at 09:27:58, Robert Hyatt wrote: >On May 10, 2001 at 00:35:50, Uri Blass wrote: > >>On May 09, 2001 at 22:01:31, Robert Hyatt wrote: >> >>>On May 09, 2001 at 19:20:18, Uri Blass wrote: >>> >>>>On May 09, 2001 at 18:41:43, Robert Hyatt wrote: >>>> >>>>>On May 09, 2001 at 13:33:21, Uri Blass wrote: >>>>> >>>>>> >>>>>>The rules of chess say that the if a game takes more than 9999 half moves both >>>>>>sides can ask for a draw by the 50 move rule. >>>>>> >>>>>>If you do not assume that both opponents are stupid in your calculation then it >>>>>>is clear that one of them will ask for the draw so you can assume for practical >>>>>>purpose that it is a draw. >>>>> >>>>> >>>>>Suppose it is a game, for "winner takes all" where if it is drawn, nobody >>>>>gets a cent? Will you claim the 50-move draw there or will you keep trying >>>>>to win the pot of gold? >>>>> >>>>>Then you see why I say that unless someone proves that chess is won for white >>>>>or black, which is not going to happen for a few thousand centuries, then I >>>>>will keep playing. Until the end of time if needed, hoping for my opponent to >>>>>make a mistake... >>>>> >>>>> >>>>>> >>>>>>I can prove for a bigger constant that there is not. >>>>>>The shortest mate is of less than 10^100 plies because every game of 10^100 >>>>>>plies include repetitions and if there is a mate there is a shorter mate with no >>>>>>repetitions. >>>>>> >>>>>>Uri >>>>> >>>>> >>>>>That doesn't make the length of all possible games finite however. >>>> >>>>It is totally irrelevant. >>>>The point is that even without the 50 move rule after enough plies searching >>>>deeper is not going to give better results. >>>> >>>>If you find a forced mate for one of the sides it is clear that searching deeper >>>>is not going to help. >>>> >>>>If you do not find a forced mate for one side then it is clear that the position >>>>is drawn and searching deeper is not going to help(programs do not assume that >>>>the opponent will do a mistake in their search). >>>> >>>>Uri >>> >>> >>>Please prove that KQQQ vs KQQQ is drawn or won for each case. Note that we >>>declare the 50-move rule is not in use. How do you decide when to declare a >>>position drawn? No captures in 50 moves? I'll be happy to show you a 5 piece >>>position where a forced mate happens _well_ beyond the 50 move rule. So how >>>do you stop? >> >>10^50 is an upper bound of the number of the legal positions(2 positions are the >>same if the pieces are in the same places and both sides have the same right to >>castle and the same rights to capture by the en passant rule). >>After less than 10^50 moves the same position happens twice >> >>If you can mate in 10^50 moves the game contains a repetition of the same >>position twice. >>If you can win with repetition you have a shorter win without repetition. >> >>It means that the problem of finding if a position is a draw or a forced mate is >>solvable in a finite time even without the 50 move rule >> >>Uri > > >Actually 10^50 simply means chess will never be solved. I did not talk about chess but about chess without the 50 move rule that is not exactly the same game. I claimed that even chess without the 50 move rule can be solved in finite time. The finite time is of course not practical with today's hardware. With the 50 move rule things are even more easy because searching 5000 plies forward is enough. That is getting very >close to the number of atoms in the universe. How are you going to store that >information? > >and I am not convinced 10^50 is the right number. There are positions and there >are positions... the history (or move path) to a position is just as important >to its identity as is the location of each of the pieces. Because without this, >repetitions and 50-move rule won't work at all. Repetitions are irrelevant for solving chess and you can ignore them because if white can win the game with repetition then white can win the game also without repetition. It is relevant for analysing games when the sides did mistakes but not for finding if chess is a draw or a win for white. With the 50 move rule it is enough to search 12600 plies forward in order to find if chess is a draw or not after the right moves because if you find no forced mate after 12600 plies then you can find no forced mate in more plies because in every line of more than 12600 plies the loser can claim a draw by the 50 move rule. I get the number 12600 by the fact that there are at most 96 pawns moves and there are at most 30 captures. In every 100 plies there must be at least 1 capture or 1 pawn move otherwise the result is a draw from theoretical point of view and the case when both sides do not want a draw is not relevant because it is clear that at least one of the sides cannot get more than it and the search algorithm of programs do not continue to analyze positions after 100 quiet moves. It means that in 12600 plies there must be 30 captures and it means that it is a draw because only kings are in the board. Practically the number is even smaller than it because if you assume 96 pawn moves at least 4 of the pawn moves are captures and it is possible to prove that even 12200 is enough. Uri
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