Author: Reinhard Scharnagl
Date: 16:40:35 01/03/04
Go up one level in this thread
Hi Ed, first: you still have not answered on [http://www.talkchess.com/forums/1/message.html?339794]. >>>Imagine a Queen on a 6x6 board for example. There are only 36 squares, but when >>>placed in the center of an open board, the Queen has 5 legal vertical moves, 5 >>>legal horizontal moves, and 10 legal moves diagonally. So, the Queen can control >>>up to 20/36 = 5/9ths of the board! More than half of the board is acccessible to >>>the Queen. >> >>First you have to make this calculations for pawns too, then calculate the >>relative strength of a queen. >> > >OK but consider this: your values show an increase in value for the pieces for >an increase in board size, and presumable a decrease is value for a decrease in >board size. > >I maintain the inverse is true. Why do your piece values of Archbishop and Chancellor increase then? And - to also show an anti-trend-behaviour - the Smirf value of the king slightly decreases. >If you are correct, then that means the metric you use, the pawn value, would >have to change in direct proportion to the area of the board. My values change >linearly (a function of one dimension since the ratio of areas are divided) and >your values change as a function of some power of 2. Such a scaling would tend >to skew results I would imagine. My method is really simple. It is shown with numerical graphics. >>Second a sliding piece can thread only one enemy piece in each direction. This >>is in average growing with the size of the board. You can read more arguments on >>that at my homesite. [http://www.rescon.de/Compu/schachansatz1_e.html] >> > >OK I will look at this some more, as I have not as of yet. I hope the simpleness of my approach will make it easy to read and understand it. >>>On a board that is 100x100, the Queen would have 99 vertical moves, 99 >>>hortizonal moves, and 198 diagonal moves. There are 396 moves total for the >>>Queen, but there are 10,000 squares! Needless to say, 396/10000 is a small >>>number. >> >>Well I see that we have different approaches. The strength is not defined >>relative to the board size but relative to the pawns strength. > >I still think you should normalize the pawns to a basline of 1.0 for each >board size, so that you have something to directly compare values with. There is such a normalisation in that model. >As far as I know, every piece has always been expressed in terms of its pawn >value based on enumerating 1 pawn as being worth 1.0 -- and likewise, since a >King cannot be exchanged, computing a pawn value for it must indicate something >else (that is why I have no King value in Gothic). Within the positional fine evaluation (which depends on the inverse piece values) influences of the king also have to be registered. Therefore it is important to fix a value for the king, too. Most theoreticians miss that, because the king will be exchanged "very rarely". It is not right to specify it to the maximum value ever possible to forth the minimax to avoid being mated. This is a tactical missuse of his piece value, only needed when pseudolegal moves would be generated, what at best should be completely avoided. >>>>May be my method of calculating piece values is simpler than Taylors "safe >>>>check" method, but I think the Smirf method produces more realistic values >>>>especially for traditional chess and its pieces: > >Taylor's idea gave us a ballpark figure to work with, and master play has >adjusted it as needed. (Taylor never claimed "exactness", but he did provide a >good mathematical basis for understanding the relative values of pieces.) > >For example, look at your value for 2 knights in 8x8 chess. > >>>> >>>> 8x10 8x8 >>>>Piece SMIRF Vortex SMIRF Taylor >>>>-------------------------------------------- >>>>Pawn 1.00 1.00 1.000 1.00 >>>>Knight 3.06 2.50 (!) 3.000 2.50 (?) >>>>Bishop 3.60 3.00 (!) 3.375 3.03 >>>>King 3.72 ---- 3.750 ---- >>>>Rook 5.43 4.75 (!) 5.000 5.67 (?) >>>>Archbishop 6.65 6.50 6.375 5.53 >>>>Chancellor 8.49 8.25 8.000 8.17 >>>>Queen 9.03 8.75 8.375 8.70 (?) >>>> > >You have 2 Knights = 6.0 and the Rook = 5.0. This means your program will >prefer 2 knights to having a Rook. 2 knights cannot force checkmate, but a Rook >can. This is a tactical implication. See the fairychess piece amazone, which acts like a sliding knight. This piece is for sure worth more than 3, but as far as I know, two of them cannot mate either. You cannot conclude from a mating impotence to a weaker piece value for an average game. A pawn can be promoted to a queen, which then can mate a single king. But that would not increase the value of a pawn. >You have bishop + knight = 6.375, but look how hard it is to mate with bishop >and knight when compare to how easy it is for a rook (both pitted against the >sole enemy king.) > >You have a queen = 8.375 which is exactly equal to your Rook + Bishop. A queen >is not merely the sum of its components pieces, it is worth more than this. Why? >The queen can effect the same strength as the Bishop and Rook, but it needs only >1 square to do this, while the other pieces require 2. We are talking about average exchange values. But in evaluating a concrete position you have to overlay positional evaluating. And because of its depending on inverse piece values a combined figure has weaker threats that each of its components would own. The difference therefore can be found in the detail evaluation. >I have looked at the "problem" of computing piece values very extensively, and >where you are with your current research I once was as well. Well, may be the discussion is really academic or philosophical. >Your numbers tell me you still need to keep working for the reasons I mentioned. >Most chess masters would say the same thing, I am more than failry certain. > >But it is a fun project, just keep at it. I think this is a stuff, which cannot be objectivied by masters. See at my homesite, how their values for a queen is differing: [http://www.rescon.de/Compu/schachwert4_e.html]. >And tell me what values you want me to plug into Gothic Vortex and I will. I >will let the engines play each other with no opening book at varying time >controls. I will impose different starting postions that are balanced and let >them play from these positions as well. Take the one from my page: [http://www.rescon.de/Compu/schachveri1_e.html]. >Let me know how many games you want in the match, how many of each time control >(like maybe 10 games at 10 seconds/move, 10 games at 20 seconds/move, 10 games >at 30 seconds/move, etc.) Until it will become significant or about e.g. 100 games or you are convinced having invested too much time. >I will send you the entire match results. I would like to see what practice is like. >A very interesting topic! I fully agree. Regards, Reinhard.
This page took 0 seconds to execute
Last modified: Thu, 15 Apr 21 08:11:13 -0700
Current Computer Chess Club Forums at Talkchess. This site by Sean Mintz.