H. G. Muller wrote on Fri, Jul 11, 2008 08:41 PM UTC:
Indeed,this is a known problem with Smirf. Because the underlying piece-value model is linear in the average piece mobility, the piece values become additive, and a the value of Q becomes that of R+B, and that of A that of B+N. For A this is more disastrously wrong than for Q, but trading Q for R+B is still quite bad (like blundering away a Pawn).
For the short-range leapers I found a clear non-linearity in the relation between (maximum) number of target squares N and piece value V:
V = (30+5/8*N)*N (centiPawn).
The methodology of basing piece values on board-averaged mobilities seems flawed to me: it overestimates the impact of bad squares where the moblity is low. In practical play you avoid putting the piece on such squares. e.g. take a few thousand positions randomly chosen from grandmaster games, and count how many of those had a Knight on a corner square. It seems a safe bet that this will be FAR LESS than 4/64 = 6%, and in fact I would be really surprised if it is more than 0.6%.
It would be interesting to observe the frequencies with which pieces visit each board square in grandmaster games, and determine how this correlates with the mobility of the piece.