Robert Shimmin wrote on Thu, Jul 10, 2003 02:46 PM UTC:
At the end of 'About the values,' Ralph mused on whether the anomalous
excess value of the queen was due to excess forking power or nonlinear
mobility; also how to account for pinning power.
I think I can account for all this in a rough way. Forking and pinning
are sort of the same thing if you think of a pin as a fork with both tines
pointing in the same direction. So let's calculate a number that's very
like crowded-board mobility, but instead of finding the average number of
squares a piece can attack, let's find the average number of two-square
combinations that a piece can simultaneously attack.
Now let's consider the practical value of a piece as a weighted sum of
mobility and this forking power. Because it gives nice results, I like
the sum PV = M + 0.043 FP. The results for a few common pieces are below.
The magic number is 0.67.
Piece Mobility Forking Practical % from
Power Value Forking
Knight 5.25 13.06 5.81 9.6
Bishop 5.72 16.38 6.42 11.0
Rook 7.72 29.23 8.98 14.0
Cardinal 10.97 62.77 13.67 19.7
Marshall 12.97 84.53 16.61 21.9
Queen 13.44 91.32 17.37 22.6
Amazon 18.69 179.95 26.43 29.3
The playtestable result from this is an amazon is worth about a queen and
a rook. Does anyone have the playtesting experience to say whether this
is too high, too low, or about right?
At the end of 'About the values,' Ralph mused on whether the anomalous excess value of the queen was due to excess forking power or nonlinear mobility; also how to account for pinning power. I think I can account for all this in a rough way. Forking and pinning are sort of the same thing if you think of a pin as a fork with both tines pointing in the same direction. So let's calculate a number that's very like crowded-board mobility, but instead of finding the average number of squares a piece can attack, let's find the average number of two-square combinations that a piece can simultaneously attack. Now let's consider the practical value of a piece as a weighted sum of mobility and this forking power. Because it gives nice results, I like the sum PV = M + 0.043 FP. The results for a few common pieces are below. The magic number is 0.67. Piece Mobility Forking Practical % from Power Value Forking Knight 5.25 13.06 5.81 9.6 Bishop 5.72 16.38 6.42 11.0 Rook 7.72 29.23 8.98 14.0 Cardinal 10.97 62.77 13.67 19.7 Marshall 12.97 84.53 16.61 21.9 Queen 13.44 91.32 17.37 22.6 Amazon 18.69 179.95 26.43 29.3 The playtestable result from this is an amazon is worth about a queen and a rook. Does anyone have the playtesting experience to say whether this is too high, too low, or about right?