Single Comment

Ideal Values and Practical Values (part 3). More on the value of Chess pieces.[All Comments] [Add Comment or Rating]

Robert Shimmin wrote on Thu, Jul 10, 2003 09:23 PM UTC:

I once tried to take the levelling effect into account via the following
scheme: a piece can neither occupy nor attack a square where it is either
left en prise or attacked by a weaker piece.  The result is that the minor
pieces can more easily occupy the center, where they are more easily
defended, and the major pieces must occupy the edge, where they most
easily avoid attack.

The numbers I got for levelled crowded board mobility were (I forget the
magic number, but it was somewhere between 0.6 and 0.7):

Knight: 3.71
Bishop: 4.31
Rook:   5.56
Queen:  8.98

Aside from giving a slightly overstrength bishop and a decidedly
understrength queen, the calculation was a great deal of hassle.  In
short, it was rather disappointing because the results were no better than
a straight-out mobility calculation, even though they took into account
something the mobility calculation neglects.  Which may mean the mobility
calculation works as well as it does because a lot of its errors very
nearly cancel out.

I would love to think of a better way to include a levelling effect, but
haven't come up with one yet.  One note though: the levelling effect is
not inherent in a piece's strength, but in the strength of pieces that
are less valuable than it.  So if the amazon is the strongest piece on the
board, then all other things remaining equal, it suffers from levelling no
worse than the queen would if it were the strongest piece, because the
ability of the other pieces to harass it remains the same.