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KQKP and KRKP endgames
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Sven Schüle



Joined: 15 May 2008
Posts: 2246
Location: Berlin, Germany
PostPost subject: Re: KQKP and KRKP endgames    Posted: Sat Jun 23, 2012 12:08 pm Reply to topic Reply with quote
lucasart wrote:
Sven Schüle wrote:
lucasart wrote:
I don't want to use a table base, just to programmatically detect some general cases where such an endgame is a known draw. I google it and couldn't find anything useful. But surely there must be some theory on that, right ?

I think KQKP can be important: typically it raises from a KPKP which becomes a pawn race, one side queens, but that doesn't always guarantee a win. Obviously my stupid eval will return pretty much the material difference, which could lead to blunders (ie. choosing to simplify to obtain an apparently winning KQKP that is in fact a draw, when another choice could have won).

KRKP should be relatively similar, I suppose.

KQKP can be solved statically for many cases, even though it is not always "trivial". In general, assuming a white queen and a quiet position with white to move, the position is a known draw, beneath possible other cases, if

a) the pawn is on the 2nd rank, and
b) the pawn is on the a-, c-, f-, or h-file, and
c) the pawn's promotion square is not occupied by a white piece, and
d) the pawn's promotion square can't be safely occupied by a white piece in the next move, and
e) the bK defends the pawn OR we have one of the patterns like Ka1/Pc2, Kc1/Pa2 (not sure about the latter!) where a distance of 2 squares between bK and pawn can be sufficient for a draw, and
f) the wK is "far enough" away from the pawn.

Conditions a)-e) are exact while in f) the term "far enough" depends on the position of all other pieces. There are distinct zones where the wK must be inside to win.

EDIT: Of course the second part of e) is also not "exact" ...

There are also rare exceptions with pawns on the 3rd rank which are drawn.

For KRKP the rules seem to be slightly more complex, and I can't give you any rules here. I don't think it is very similar to KQKP.

Sven

Thanks for the link. It appears to be much more complex than I initially envisaged. What I was basically hoping for is:
1/ determine simple rules when it's a known draw, if the pawn is on the 7th rank
2/ any other drawish position should not be more than a few good moves away from 1/, so a bit of search combined with 1/ should more or less do the trick

However, rule 1/ must tolerate no exceptions, even "rare" ones, or else it's a disaster and I'm better off without it. I thought a 7th rank pawn with the king at distance 1 and attacking king at distance >=2 for example was a sufficiant condition, but even that seems to be wrong...

"attacking king at distance >= 2" is obviously wrong in many cases but you can try to find a better value instead of "2" for each interesting class of bP-bK positions by writing a program (or adding code to your engine) that enumerates all legal, non-terminal, quiet, white-to-move positions for a given bP-bK position class (restricted to Pa2/c2/a3/c3 based on symmetry and other knowledge), looks up their true values in a tablebase/bitbase, and determines the smallest wK-bP distance for which the position is always a draw for all positions of the same class, and maybe also the largest wK-bP distance for which the position is always won (the latter only if you want to get safe predictions for "always won" positions as well). That should not be too difficult. (Here I assume that the wK-bP distance is the relevant number, which I am not 100% sure about: it might also be the distance of the wK to the promotion square.)

A suitable definition of "quiet" could be: wK not in check and no safe capture of bP possible in one ply. My conditions c) and d) above would have to be considered, too, since occupying the promotion square would make all wK-bP distance calculations obsolete. So you might extend the term "quiet" by "promotion square not occupied by white and can't be safely occupied in one ply".

Maybe someone has already done something similar.

The result would be interesting, even though I am not sure whether the overall effort would really pay off when considering that KQKP is quite a special case.

Sven
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Subject Author Date/Time
KQKP and KRKP endgames Lucas Braesch Fri Jun 22, 2012 2:30 pm
      Re: KQKP and KRKP endgames Mincho Georgiev Fri Jun 22, 2012 4:10 pm
      Re: KQKP and KRKP endgames Sven Schüle Fri Jun 22, 2012 4:11 pm
            Re: KQKP and KRKP endgames Lucas Braesch Sat Jun 23, 2012 7:12 am
                  Re: KQKP and KRKP endgames Kevin Hearn Sat Jun 23, 2012 8:45 am
                  Re: KQKP and KRKP endgames Sven Schüle Sat Jun 23, 2012 12:08 pm
                        Re: KQKP and KRKP endgames Sven Schüle Sat Jun 23, 2012 12:24 pm
                              Re: KQKP and KRKP endgames Lucas Braesch Sat Jun 23, 2012 12:36 pm
                                    Re: KQKP and KRKP endgames Sven Schüle Sat Jun 23, 2012 3:19 pm
                              Re: KQKP and KRKP endgames Ronald de Man Sat Jun 23, 2012 1:49 pm
                                    Re: KQKP and KRKP endgames Miguel A. Ballicora Sat Jun 23, 2012 2:45 pm
                                          Re: KQKP and KRKP endgames Ronald de Man Sat Jun 23, 2012 4:05 pm
                                                Re: KQKP and KRKP endgames Sven Schüle Sat Jun 23, 2012 4:19 pm
                                                      Re: KQKP and KRKP endgames Ronald de Man Sat Jun 23, 2012 5:11 pm
                                                            Re: KQKP and KRKP endgames Miguel A. Ballicora Sat Jun 23, 2012 5:37 pm
                                                                  Re: KQKP and KRKP endgames Michel Van den Bergh Sat Jun 23, 2012 6:09 pm
                                                                        Re: KQKP and KRKP endgames Joona Kiiski Sat Jun 23, 2012 6:16 pm
                                                                              Re: KQKP and KRKP endgames Daniel Shawul Sat Jun 23, 2012 6:27 pm
                                                                                    Re: KQKP and KRKP endgames Tord Romstad Sun Jun 24, 2012 6:32 pm
                                                                                          Re: KQKP and KRKP endgames Daniel Shawul Sun Jun 24, 2012 11:17 pm
                                                                                          Re: KQKP and KRKP endgames Robert Hyatt Mon Jun 25, 2012 12:21 am
                                                                  Re: KQKP and KRKP endgames Ronald de Man Sat Jun 23, 2012 6:21 pm
                                                                        Re: KQKP and KRKP endgames Miguel A. Ballicora Sun Jun 24, 2012 7:19 pm
                                                                              Re: KQKP and KRKP endgames Robert Hyatt Mon Jun 25, 2012 12:32 am
                                                                  Re: KQKP and KRKP endgames Robert Hyatt Mon Jun 25, 2012 12:17 am
                                          Re: KQKP and KRKP endgames Thomas Petzke Sat Jun 23, 2012 4:21 pm
      Re: KQKP and KRKP endgames Joona Kiiski Sat Jun 23, 2012 4:44 pm
            Re: KQKP and KRKP endgames Lucas Braesch Sun Jun 24, 2012 3:14 am
            Re: KQKP and KRKP endgames Sven Schüle Sun Jun 24, 2012 10:14 am
                  Re: KQKP and KRKP endgames Ronald de Man Sun Jun 24, 2012 11:05 am
                        Re: KQKP and KRKP endgames Sven Schüle Sun Jun 24, 2012 11:51 am
                              Re: KQKP and KRKP endgames Ronald de Man Sun Jun 24, 2012 12:39 pm
                                    Re: KQKP and KRKP endgames Sven Schüle Sun Jun 24, 2012 2:15 pm
                                          Re: KQKP and KRKP endgames Ronald de Man Sun Jun 24, 2012 2:24 pm
                  Re: KQKP and KRKP endgames Uri Blass Sun Jun 24, 2012 1:24 pm
                        Re: KQKP and KRKP endgames Sven Schüle Sun Jun 24, 2012 1:46 pm
            Re: KQKP and KRKP endgames Uri Blass Sun Jun 24, 2012 1:30 pm
                  Re: KQKP and KRKP endgames Thomas Petzke Mon Jun 25, 2012 7:27 am
            Re: KQKP and KRKP endgames Joona Kiiski Sun Jun 24, 2012 5:13 pm
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