Author: Bruce Moreland
Date: 23:49:10 10/27/98
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On October 27, 1998 at 17:46:59, Roberto Waldteufel wrote: >I think it get's even more complicated because even if you have an unstoppable >passed pawn that can queen two or three moves before an opponent could possible >promote a pawn, you could still end up with a lost position if the opponent has >a mass of advanced passed pawns where you can only delay one of them queening by >a series of checks that ultimately end, wherupon the opponent may have achieved >a winning Q+P ending with a remaining advanced passed pawn. The idea here is not to produce an evaluation function that will win a Nobel Peace Prize, the goal I think in most cases is to try to make sure that you score as many points as possible against all opposition. The number of cases where you'll have a pawn queen several moves in advance of the opponent and fail to score the point is very small. And the odds of detecting these cases in an eval function are practically zero. I think this is an important point. You can devise cases that will defeat an eval function, it will always have the potential of evaluating a lost game as won, and this is true in any phase of the game. Every eval function has tactical failings, otherwise it would be safe to do a one-ply search and just move. The question is, why is the eval function there, and what can be done to make sure that it does the job that is required of it. It is not just that too much eval returns zero benefit, but rather that it can actually harm you by slowing down the search in order to evaluate terms that don't matter. I think that K+P endings do matter in practical play, but that they don't matter a huge amount. Toward this end, it would be my goal to try to teach my program about them without slowing down the general case, and it would be my goal to try to teach my program about the situations that are apt to come up in practical play, that would be hard to resolve with search, and are apt to have a marked effect upon the score of lots of important positions. I think that an easy and obvious place where the eval function is going to fail is when there does exist an unstoppable pawn. Because the search might not be able to follow the thing all the way to queening, and whatever passed pawn bonuses that are normally in the eval function are probably not going to be big enough to see past a material sacrifice in order to create an unstoppable pawn. There are a lot of other cases, as you correctly point out. A pawn on the 4th that can run, can easily lose against the pawn structure white pawn on a2, black pawns on a3 and b4. Black will play ... b3 and queen two moves later regardless of what white does. It's a lot harder to catch this, though, and in those cases I'm hoping that you can cross your fingers and hope that when the important node is encountered, there is enough draft under it that the search can resolve it correctly. A famous example of where the square of the pawn heuristic fails is in the 1921 Reti study: 7K/8/k1P5/7p/8/8/8/8 w - - 0 1 In this study, white's king is outside the square of the pawn, yet he can draw with 1. Kg7. >Nonetheless, I think maybe the old "square of the pawn" rule might make a good >pruning heuristic at nodes in the main search close to the frontier, like you >discuss in your excellent paper on pruning techniques at frontier, pre-frontier >and pre-pre-frontier nodes. I can't help thinking that I am wasting the >potential of this easily computed test by only usig it when the opponent has a >bare king. Even if the side to move has many pawns and its king opposing a >single enemy (unpassed) pawn as well as having the unstoppable passed pawn, my >search continues to explore more plies instead of simply terminating the search >and scoring it as a win, which is what I think it ought to do, if only I could >think of a good way to weed out the exceptions. I once tried to score it as a >win only if the opponent had no passed pawn, but this also proved inadequate >because sometimes a passed pawn can be created by a breakthrough combination or >simply by a king gobbling up pawns. There are points in the tree where it is safe to terminate the search, but having a pawn that's outside the square isn't one that I'd pick. >You said you use a sophisticated K+P evaluation. I assume this understands about >passed pawns and the "square of the pawn". How does it recognise when such a >"trivial" win really is trivial, and when it is an exception? Yes, I would like to know more as well. bruce
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