Author: Ed Trice
Date: 14:33:22 01/03/04
Go up one level in this thread
Hi Reinhard, >>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. 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. >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. >>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. 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). >>>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. 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. 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. 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. 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. 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.) I will send you the entire match results. A very interesting topic! --Ed
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