To me that has always suggested that this eval term is more about board control than about number of moves. You would not expect Knight moves to be on the average more dangerous than Queen moves; on the contrary. But a square attacked by a Knight is interdicted to a lot more enemy pieces than a square attacked only by a Queen.PK wrote:once You count pseudo-legal moves in Your evaluation function, it makes sense to weigh them differently. Sungorus uses 4*knight mobility, 3 * bishop, 2* rook and 1* queen. It is sufficiently good for start.
Of course it could also have something to do with the urgency to have moves for withdrawing the piece, should it get into trouble. But also then, trouble is a relative notion, and what scares a Queen, could be laughed at by a protected Knight. But if this is a factor, then it suggests the first eight moves of the Queen should also be worth 4 (or even more), like the first (and only) eight moves of the Knight, and it is only the moves in excess of 16 (that even a Rook doesn't have) that count for 1. But of course the Queen would almost always have those first 8 moves, so the mobility bonus associated with them can be incorporated in the base value without much loss of accuracy.
It would be interesting to know if it would be better to have an eval term that gives points for every attacked square, 1 point if the lowest attacker is a Queen, 2 points if it is a Rook, 4 points if it is a Knight... Nearly the same as the weighted mobility, but not quite, as attacking squares that are already attacked by Knight with a Queen would be recognized as rather pointless.
So two 'saturation effects' are to be expected:
* Extra moves on a piece that already has many aren't that important
* Extra attacks on a square that already has many (or better, i.e. by less-valuable piece) aren't that important
The latter might have to be considered in relation to the number (or quality) of attacks on it by the opponent. I guess this goes a lot towards 'safe mobility'; an obvious measure for the effect achieved by all those attacks would be "what can you or the opponent move there safely, now?".