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Piece Values[Subject Thread] [Add Response]
Peter Hatch wrote on 2002-04-12 UTC
Various and sundry ideas about calculating the value of chess pieces. First off, it is quite interesting to instead of picking a magic number as the chance of a square being empty, calculate the value for everything between 32 pieces on the board and 3 pieces on the board. Currently I'm then just averaging all the numbers, and it gives me numbers slightly higher than using 0.7 as the magic number (for Runners - Knights and other single step pieces are of course the same). One advantage of it is that it becomes easier to adjust to other starting setups - for Grand Chess I can calculate everything between 40 pieces on the board and 3, and it should work. With a magic number I'd have to guess what the new value should be, as it would probably be higher since the board starts emptier. One disadvantage is that I have no idea whether or not the numbers suck. :) Interesting embellishments could be added - social and anti-social characteristics could modify the values before they are averaged, and graphs of the values would be interesting. It would be interesting to compare the official armies from Chess with Different Armies at the final average and at each particular value. It might be possible to do something besides averaging based on the shape of the graph - the simplest idea would be if a piece declines in power, subtract a little from it's value but ignore the ending part, assuming that it will be traded off before the endgame. Secondly, I'm not sure what to do with the numbers, but it is interesting to calculate the average number of moves it takes a piece to get from one square to another, by putting the piece on each square in turn and then calculate the number of moves it takes to get for there to every other square. So for example a Rook (regardless of it's position on the board) can get to 15 squares in 1 move, 48 squares in 2 moves, and 1 square in 0 move (which I included for simplicity, but which should probably be left out) so the average would be 1.75. I've got some old numbers for this on my computer which are probably accurate, but I no longer know how I got them. Here's a sampling: Knight: 2.83 Bishop: 1.66 (can't get to half the squares) Rook: 1.75 Queen: 1.61 King: 3.69 Wazir: 5.25 Ferz: 3.65 (can't get to half the squares) This concept seems to be directly related to distance. Perhaps some method of weighting the squares could make it account for forwardness as well. Finally, on the value of Kings. They are generally considered to have infinite value, as losing them costs you the game. But what if you assume that the standard method is to lose when you have lost all your pieces, and that kings have the special disadvantage that losing it loses you the game? I first assumed this would make the value fairly negative, but preliminary testing in Zillions seems to indicate it is somewhere around zero. If it is zero, that would be very nifty, but I'll leave it to someone much better than me at chess to figure out it's true value.