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Piece Values[Subject Thread] [Add Response]

H. G. Muller wrote on Sat, May 3, 2008 09:31 PM UTC:

Reinhard, if I understand you correct, what you basically want to introduce
in the evaluation is terms of the type w_ij*N_i*N_j, where N_i is the
number of pieces of type i of one side, and N_j is the number of pieces of
type j of the opponent, and w_ij is an tunable weight.

So that, if type i = A and type j = N, a negative w_ij would describe a
reduction of the value of each Archbishop by the presence of the enemy
Knights, through the interdiction effect. Such a term would for instance
provide an incentive to trade A in a QA vs ABNN for the QA side, as his A
is suppressed in value by the presence of the enemy N (and B), while the
opponent's A would not be similarly suppressed by our Q. On the contrary,
our Q value would be suppressed by the the opponent's A as well, so
trading A also benefits him there.

I guess it should be easy enough to measure if terms of this form have
significant values, by playing Q-BNN imbalances in the presence of 0, 1
and 2 Archbishops, and deducing from the score whose Archbishops are worth
more (i.e. add more winning probability). And similarly for 0, 1, 2
Chancellors each, or extra Queens. And then the same thing with a Q-RR
imbalance, to measure the effect of Rooks on the value of A, C or Q.

In fact, every second-order term can be measured this way. Not only for
cross products between own and enemy pieces, but also cooperative effects
between own pieces of equal or different type. With 7 piece types for each
side (14 in total) there would be 14*13/2 = 91 terms of this type possible.