I am not really sure if we are talking about the same thing. What I mean is: I believe that for KBNK mating the following two criteria are sufficient, with the first having higher priority:Don wrote:Yes, it does help because the friendly king serves a big role in pushing the king to the edge and corner. Give two otherwise equal positions you are much farther from mate if the friendly king is on the other side of the board.Sven Schüle wrote:Is that third criterion necessary for mating, resp. for finding the mate faster?Don wrote:3. the friendly king closer to the center than the enemy king.
Is it absolutely necessary? No, king centralization will automatically put the friendly kind closer to the enemy king but won't make the finer distinctions that can be helpful.
With LMR and heavy pruning and other reductions you want to make the finest distinctions possible so that the moves that are good get put to the front of the list (and thus not reduced.) So the game I play when building these routines is to imagine I'm playing the ending and what moves are best - and then I ask myself if the scoring function would put these moves near the front of the list. If my king is several squares away from the king will it move toward the king or toward some random center square? They are not always the same. Sometimes a move AWAY the king is STILL equally centered or even BETTER centered such as e4 to d4 when the enemy king is on h5 so without the king heuristic there is no scoring penalty for moving in the opposite direction of the king which is obviously wrong.
I don't do this in the other basic mates, the only reason I have it for KNBK is that I specifically wrote a handler for it. I think almost any program would still mate at any reasonable level even if all you do is identify the correct corner.
1. The winning side tries to minimize the distance of the enemy king to any of the two "right" corners.
2. The winning side tries to minimize the distance between the two kings.
As I understand your first statement you favor the same 1+2 but additionally a third criterion:
3. The winning side tries to keep its own king closer to the center than the enemy king.
Now I asked whether 3. is really necessary. But your last comment is not clear to me, it still appears that you explained why 2. is needed, which is beyond any doubt.
In my opinion 3. is almost redundant when 2. is present, and might even make the application of 2. somewhat weaker.