Author: Robert Hyatt
Date: 14:56:23 12/23/00
Go up one level in this thread
On December 23, 2000 at 14:41:37, Uri Blass wrote: >On December 23, 2000 at 12:44:52, Robert Hyatt wrote: > >>On December 23, 2000 at 12:25:18, Uri Blass wrote: >> >>>On December 23, 2000 at 09:01:29, Joshua Lee wrote: >>> >>>>this is over a google and even if your program could search at 5 trillion nodes >>>>per second it wouldn't solve chess in your lifetime. >>>> >>>> 64^64 is one number that comes to mind 3.9402006196394479212279040100144e+115 >>> >>>The number of leagl positions is clearly smaller than 64^64. >>> >>>I do not understand why do you think about 64^64. >>> >>>Uri >> >> >>I still think 10^120 is a reasonable estimate, because a position is not just >>made up of the pieces on the board. > >In order to find if chess is a win for one side or a draw you need only >tablebases for all the positions in the board when the position is made only of >the pieces on the board. > That isn't true. If you do that, you will draw won positions, because you will follow a path that is a mate in N, but it repeats the position for the third time before you get to move N. Ditto for 50 move draws on deep mates. To do this _right_ the history has to be included. And when you include the history as part of a "position" the number becomes huge. IE how many different pathways are there just to reach the _starting_ position? Just let the knights get out, roam around, then return home. There are a huge number of different pathways to get to the same position, but each would have different 50-move and 3-fold repetition issues associated with them. > It _also_ includes the game history up to >>that position, because of 50 move and repetition considerations. > > >Repetition consideration is not relevant unless you want to analyze positions >when there is a history of repetition and you need to be careful to avoid a >third repetition. The question was how many legal positions are there. I believe that to answer this question _correctly_ you can't just determine how many raw positions there are, you also have to figure in the 50-move and 3-fold repetition conditions as well. > >In other cases if one side can win this side can do it also without repeating >the same position 3 times. not if you don't know what was done before you reached _this_ position. > >You can ignore the number of plies without captures for playing. > >The program can evaluate a position as a draw only if it is a draw assuming that >the last move is a capture. > >When the program evaluates a position as a win for one side it can play the move >that reduce the distance for conversion to the minimal value so it will never >miss a win. > >Uri Aha... distance to conversion is what I am talking about. Except that conversion has to be modified to not only include captures and pawn pushes, but also has to include 50-move counter and repetitions.
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