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H.G.Muller

Joined: 10 Mar 2006
Posts: 12903
Location: Amsterdam

Post subject: Re: End-game evaluation    Posted: Tue Nov 08, 2011 8:16 pm

 Evert wrote: Hmm... my thinking was that you'd want to be able to make a waiting move so that the defending king has to yield terrain and walk into the corner. You can always do that in KRK (and KQK, but that's not interesting), KBBK and KBNK, but not in KNNK (except with the king, as you pointed out, but then your own king may be giving up terrain that you need to controlled; the correct statement would have been that I expect you want two pieces that can triangulate). Of course it's always good to have the ability to triangulate in case you need it, without saying that you do need it. Should be easy to test though whether it makes a difference: just allow the side with the knights to null-move and see whether it can do it. I might try that at some point just for fun.

That triangulation is not needed can already be seen from the fact that there are many pairs of non-triagulating pieces that can force mate. In fact, simple leapers (i.e. with only a single step vector, like (1,2) for N, symmetrized to all directions) can never triangulate: they are either color alternatorsorcolor-bound, and when they are color-bound you can consider their color as a 45-degrees rotated grid checkered by meta-colors, and then they have to be meta-color alternating ormeta-color-bound, and so on, untilin the end evry piece is meta-(meta-...)colr alternating.

But almost any combination of (an inhomogeneous pair of) Ferz (1,1), Wazir (1,0), Knight (1,2), Camel (1,3) and Zebra (2,3) can force checkmate, except F+W, F+N and another that I forgot (F+C, because they are both color-bound?). Even N+W can do it. W and F with only 4 moves are significantly weaker than the others, which have 8 moves, but even an 8-move plus a 4-move piece have little trouble driving a King into the corner.

Another indication is that there are no mate-in-2 positions at all in KNNK, not even when the King is already trapped on a1-b1 by Kb3 + Ne2, while the other Knightis free to roam the board to get in position. And that KNNKX with X slow and far away usually has longer mates (I think that KNNKN has some mate-in-6 positions, and KNNKW even much longer), beause the X breaks the stalemate. And apparently you don't even need zugzwang. When the piece can be blocked until needed, you can even have >50-move wins (KNNKP).
 Display posts from previous: All Posts1 Day7 Days2 Weeks1 Month3 Months6 Months1 Year Oldest FirstNewest First
Subject Author Date/Time
H.G.Muller Tue Oct 04, 2011 11:44 am
Evert Glebbeek Tue Oct 04, 2011 1:02 pm
H.G.Muller Tue Oct 04, 2011 2:20 pm
Oliver Uwira Tue Oct 04, 2011 1:59 pm
Jon Dart Tue Oct 04, 2011 2:10 pm
Jon Dart Tue Oct 04, 2011 2:13 pm
Kevin Hearn Tue Oct 04, 2011 8:19 pm
Pawel Koziol Wed Oct 05, 2011 10:46 am
H.G.Muller Mon Oct 10, 2011 8:09 am
H.G.Muller Mon Oct 10, 2011 9:00 am
Evert Glebbeek Mon Oct 10, 2011 1:04 pm
Ed Schroder Mon Nov 07, 2011 10:15 pm
H.G.Muller Wed Oct 19, 2011 10:16 am
Michael Hoffmann Wed Oct 19, 2011 11:48 am
H.G.Muller Wed Oct 19, 2011 1:24 pm
Michael Hoffmann Wed Oct 19, 2011 2:53 pm
Volker Annuss Wed Oct 19, 2011 4:53 pm
H.G.Muller Wed Oct 19, 2011 4:54 pm
H.G.Muller Sat Oct 22, 2011 5:29 pm
H.G.Muller Mon Nov 07, 2011 7:28 pm
Evert Glebbeek Mon Nov 07, 2011 8:33 pm
Evert Glebbeek Mon Nov 07, 2011 9:02 pm
H.G.Muller Mon Nov 07, 2011 9:40 pm
H.G.Muller Tue Nov 08, 2011 11:16 am
Evert Glebbeek Tue Nov 08, 2011 5:50 pm
Re: End-game evaluation H.G.Muller Tue Nov 08, 2011 8:16 pm
Evert Glebbeek Tue Nov 08, 2011 8:52 pm
H.G.Muller Tue Nov 08, 2011 10:14 pm
Karlo Bala Jr. Mon Nov 07, 2011 11:59 pm
H.G.Muller Tue Nov 08, 2011 7:30 am
Kevin Hearn Tue Nov 08, 2011 9:58 am
H.G.Muller Tue Nov 08, 2011 12:40 pm
Evert Glebbeek Tue Nov 08, 2011 5:53 pm
Mark Lefler Mon Oct 10, 2011 4:08 pm
H.G.Muller Mon Oct 10, 2011 9:09 pm
H.G.Muller Mon Oct 10, 2011 9:58 pm
H.G.Muller Tue Oct 11, 2011 8:50 am
H.G.Muller Tue Oct 18, 2011 6:36 pm

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