Author: Robert Hyatt
Date: 20:40:29 12/23/00
Go up one level in this thread
On December 23, 2000 at 21:42:55, Vincent Vega wrote: >On December 23, 2000 at 17:56:23, Robert Hyatt wrote: > >>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. >> > >This is clearly wrong. Chess has a well defined starting position, so you don't >need to be able to figure out the best move in every possible position with its >associated history to find out if chess is 1-0, 0-1, or 1/2-1/2. If you are doing a tablebase, you are right. But that isn't the question being asked. It was "how many positions are there?" And for that, my answer is correct. Because a position X that was reached one way is _not_ the same as the same position X reached via another sequence of moves. All according to the normal rules of chess. > >Adding 50-move and 3-fold repetition conditions has no effect whatsoever on >whether computer will be able to play perfect chess. If you play the game >perfectly from the beginning, and there is a win for one side, there won't ever >be any repetitions of positions. You are aware that tablebases do _not_ handle this case at present? Distance to mate is going to fail when the mate can't be done with the 50 move rule. Distance to conversion isn't any better at present, as the 50 move rule isn't considered a "conversion" and they fail in the same way... It is _essential_ to include this information or any tablebase with 32 pieces will simply be useless unless the rules of chess are changed from their present state. And if you follow the algorithm that chooses >the next move by finding the minimum distance to resetting the 50-move counter >among all moves that lower the distance to mate, you won't need to know the game >history at all. That won't work for reasons that are well-known and often discussed. There is no "resetting the 50-move-counter" factored in to current tablebases. And unless a new 'standard' is created (using both DTM _and_ DTC) the problem is insolvable. (and of course, conversion has to include 50 moves as a factor.) > >I don't find figuring out when computer will be able to play perfectly from any >possible position nearly as important as knowing when a computer will play >perfectly from the only position that really counts - starting position. First, that will _never_ happen. Unless you consider a time-span long enough for the sun to burn out, for starters. But as to the number of different positions in the game, it is _far_ larger than most realize... due to the rules we have to play under.
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