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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?

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