I also added some algorithms how the concept could be used in chess engines. Obviously it is a very complex topic and some points are not discussed in detail:
* definition of critical squares
* non-blocked pawn positions
* etc.
anyway, I would appreciate some feedback on the algorithm posted (possible weaknesses, improvements, etc) and some comments on what you think about the use of corresponding squares in computer chess.
Just briefly my personal thoughts: Pawn endgames are a topic very weakly understood by chess engines, the increased risk of zugzwang positions makes it hard for them to apply any sensible pruning, still a very deep search is required to get a proper feedback on the actual outcome. Indeed Transposition tables prove very valuable. Anyway, at the point of deciding whether it is wise to simplify to a certain pawn endgame or not, the positions usually do not allow a >20ply search like would be necessary to solve fine #70 for example. So I think some further research on this approach that can solve certain positions at ply 1 would definitely help the endgame play of computer chess engines.
I skimmed over your article and filed it for future reference. I'm very interested in the topic, of K&P endgames, but have to build my knowledge a bit before I tackle the algorithm.
Just a general thought about K&P endgames. I can certainly see why deep and precise analysis is required. What do you think of the following idea:
In endgames I often try to visualize the position I'd like to achieve, the decide if it is possible to reach it. It occurs to me that a similar approach might work with a computer. based on the material on the board, the program might be able to know the position it wants to reach before it actually engages in a search. It might know this based on an endgame "book", or tablebase.
just a thought. I'm really not sure if it is practical.
also, there is a book Secrets of Pawn Endgames by Lamprecht & Muller, which makes extensive use of computer analysis. They have quite a lengthy chapter on Critical Squares, if that interests you.
Fguy64 wrote:In endgames I often try to visualize the position I'd like to achieve, the decide if it is possible to reach it. It occurs to me that a similar approach might work with a computer. based on the material on the board, the program might be able to know the position it wants to reach before it actually engages in a search. It might know this based on an endgame "book", or tablebase.
just a thought. I'm really not sure if it is practical.
I think the algorithm I describe is something similar to what you mention. You start by defining the final position you want to reach and later on figure out whether you can force to reach this position. Anyway this only works because the mobility is very restricted in such endgames.
For other types of positions it would have to be solved differently as the possibilities of the attacker as well as the ones of the defender are much broader. Anyways you mustn't forget that the general Alpha-Beta framework doesn't work so much differently than what you describe. First a Principal Variation is set (the moves to reach a certain aim) then the defending side tries to refute the plan (All nodes) and the attacking side just has to refute all tries of the defender to stop the plan (Cut nodes). Anyway what I am doing for pawn endgames (finding the result by calculation on the first ply) doesn't work generally because there are no easy ways to estimate the attacking / defending potential.
Fguy64 wrote:
also, there is a book Secrets of Pawn Endgames by Lamprecht & Muller, which makes extensive use of computer analysis. They have quite a lengthy chapter on Critical Squares, if that interests you.