Author: Robert Hyatt
Date: 06:27:58 05/10/01
Go up one level in this thread
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. 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.
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