Author: KarinsDad
Date: 11:33:25 04/16/99
Go up one level in this thread
On April 16, 1999 at 13:16:19, Bruce Moreland wrote: > >This kind of thing sounds good in principle, but it has a hard time getting past >basic realities. It is certainly possible and useful to quickly recognize some >endings. Sometimes you can return an accurate draw score (KN vs K), and other >times you can return a heuristic score (KR vs KR). > >But there are problems with even simple 4-man cases: > > a b c d e f g h a b c d e f g h > +---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+ >8 | |///| |///| |/R/| |///| 8 | |///| |///| |///| |///| 8 > +---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+ >7 |///| |///| |///| |///| | 7 |///| |///| |///| R |///| | 7 > +---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+ >6 | |///| |///| |///| |///| 6 | |///| |///| |///| |///| 6 > +---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+ >5 |///| |///| |///| |///| | 5 |///| |///| |///| |///| | 5 > +---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+ >4 | |///| |///| |///| |///| 4 | |///| |///| |///| |///| 4 > +---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+ >3 |/k/| |///| |///| |///| | 3 |/k/| |///| |///| |///| | 3 > +---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+ >2 | |///| |///| n |///| |///| 2 | |///| |///| n |///| |///| 2 > +---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+ >1 |///| |/K/| |///| |///| | 1 |///| |/K/| |///| |///| | 1 > +---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+ > a b c d e f g h a b c d e f g h > >White to move in both cases. The position on the left is won, the position on >the right is drawn (you can also put the rook on g8, that's drawn as well). > >I think it would be pretty hard to statically evaluate these KR vs KN positions. > And this is only a 4-man class, it would have to be even harder to do stuff >like KRP vs KR. > >If you do manage to make a rule-base for an ending, it would be trivial to check >that it can do either of the following: > >1) Distinguish with accuracy between drawn and won cases. >2) Make progress in won cases. > >I believe that Marsland did KP vs K, which is the easiest non-trivial case. I >think people have tried KR vs KN, but I've never seen anything that would >indicate that anyone succeeded. > >bruce Bruce, You are absolutely correct. This is where the difficulty comes in. However, some years back I came up with my own technique for "long range" opposition. Due to this technique, I am able to immediately make the proper king move in certain types of KPP vs. KPP and other types of similar endings. The difficulty here lies in knowing whether you want to have opposition or not. Once that is determined, the rest of the moves in these types of endings are almost self evident (there are special cases as kings get near the edge of the board or near pawns). I believe (or at least I hope) that similar types of techniques can be used in KN vs. KR or other endings, the solution (or algorithm) just has to be found. If the possibilities could be broken down into certain subsets of mini-positions, then it may be possible to determine a solution. However, you are right that for some of the non-trivial cases, this will take a lot of work (and of course it was easier to write a program to exhaustively search all of the possibilities and put that result into a tablebase than it is to dissect these endings into their basic components). To me, this seems to be a complex math problem where the "equations" have not yet been created due to the fact that the mathematics of chess is totally alien to any real world phenomenom (knights, castling, en passant and pawn promotion throw real monkey wrenches into the system), therefore, we have not been trained to think properly when it comes to "solving the problem". One of the reason I post messages of this type is to get people to attempt to get beyond their normal thought processes. Finally, some of these cases (especially many of those with knights in them) may be TOO difficult to resolve via an algorithm. And those might just be better served with a normal tablebase. KarinsDad :)
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