Author: Reinhard Scharnagl
Date: 12:01:02 01/03/04
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Hi Ed, I agree, that the discussion on piece values is very interesting. And there are additional reasons for that, which I have not yet mentioned. >I tend to this of a piece's value to be proportional to the "density" of its >attacking destinations that can be reached compared to the size of the board. As >you add squares to a board, you dilute a piece's strength. As you remove >squares, you increase its strength. > >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. 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] >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. >>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: >> >> 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 (?) >> >Let's look at another example from the endgame in both the 10x8 board and the >8x8 board. Bishop + Knight vs. King. > >If the value of the pieces increase on the 10x8 board, you would expect this to >translate into something like being able to gain some sort of advantage. I >wouldl expect one such metric to be distance to force checkmate in certain >endings. > >The opposite is true: winning on the 10x8 board is more difficult. > >In 8x8 chess, you can only mate with N + B vs. K on one of two squares: that >being the corner square of the same color as your bishop. While it is possible >to mate with the knight, this mate cannot be forced and requires your opponent >missing a mate in 1 (or maybe 2 at the most.) > >In Gothic Chess, on the 10x8 board, I discovered that B + N vs. K can only be >forced on 1 square! That square is the same color of the bishop that is closest >in rank to the enemy king. That is, the square of the same color as the bishop >that is connected to the files (of which there are 10 across) cannot force the >king to be mated. The square which is vertically connected to the ranks (of >which there are 8) can force the mate. > >It might even be that for a 10x10 board that Bishop + Knight vs. King is a draw! >Clearly this cannot mean the B and N are "stronger" in this case. These arguments really are stronger. But they imply only, that it is harder to mate in a 10x8 Board than in an 8x8 board - not that the chess men are weaker compared to pawns. >I will compile two differenct version of Gothic Vortex and have them play a >match, if you would like. Let me know which values you want to use, and I will >hook it up. I am in doubt whether one single match would be sufficient to decide on the different piece value theorems. It will need a lot of chess games. The values I have quickly calculated surely may have some errors, but I hope they are correct, I will verify all again. The values I have published should be those, which should be tested. Regards, Reinhard.
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