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End-game evaluation
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H.G.Muller



Joined: 10 Mar 2006
Posts: 12903
Location: Amsterdam
PostPost subject: Re: End-game evaluation    Posted: Tue Nov 08, 2011 8:16 pm Reply to topic Reply with quote
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).
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Subject Author Date/Time
End-game evaluation H.G.Muller Tue Oct 04, 2011 11:44 am
      Re: End-game evaluation Evert Glebbeek Tue Oct 04, 2011 1:02 pm
            Re: End-game evaluation H.G.Muller Tue Oct 04, 2011 2:20 pm
      Re: End-game evaluation Oliver Uwira Tue Oct 04, 2011 1:59 pm
      Re: End-game evaluation Jon Dart Tue Oct 04, 2011 2:10 pm
            Re: End-game evaluation Jon Dart Tue Oct 04, 2011 2:13 pm
      Re: End-game evaluation Kevin Hearn Tue Oct 04, 2011 8:19 pm
            Re: End-game evaluation Pawel Koziol Wed Oct 05, 2011 10:46 am
      Re: End-game evaluation H.G.Muller Mon Oct 10, 2011 8:09 am
            Re: End-game evaluation H.G.Muller Mon Oct 10, 2011 9:00 am
                  Re: End-game evaluation Evert Glebbeek Mon Oct 10, 2011 1:04 pm
                  Re: End-game evaluation Ed Schroder Mon Nov 07, 2011 10:15 pm
            Re: End-game evaluation H.G.Muller Wed Oct 19, 2011 10:16 am
                  Re: End-game evaluation Michael Hoffmann Wed Oct 19, 2011 11:48 am
                        Re: End-game evaluation H.G.Muller Wed Oct 19, 2011 1:24 pm
                              Re: End-game evaluation Michael Hoffmann Wed Oct 19, 2011 2:53 pm
                                    Re: End-game evaluation Volker Annuss Wed Oct 19, 2011 4:53 pm
                                    Re: End-game evaluation H.G.Muller Wed Oct 19, 2011 4:54 pm
                                          Re: End-game evaluation H.G.Muller Sat Oct 22, 2011 5:29 pm
                                                Re: End-game evaluation H.G.Muller Mon Nov 07, 2011 7:28 pm
                                                      Re: End-game evaluation Evert Glebbeek Mon Nov 07, 2011 8:33 pm
                                                            Re: End-game evaluation Evert Glebbeek Mon Nov 07, 2011 9:02 pm
                                                                  Re: End-game evaluation H.G.Muller Mon Nov 07, 2011 9:40 pm
                                                            Re: End-game evaluation H.G.Muller Tue Nov 08, 2011 11:16 am
                                                                  Re: End-game evaluation Evert Glebbeek Tue Nov 08, 2011 5:50 pm
                                                                        Re: End-game evaluation H.G.Muller Tue Nov 08, 2011 8:16 pm
                                                                              Re: End-game evaluation Evert Glebbeek Tue Nov 08, 2011 8:52 pm
                                                                                    Re: End-game evaluation H.G.Muller Tue Nov 08, 2011 10:14 pm
                                                      Re: End-game evaluation Karlo Bala Jr. Mon Nov 07, 2011 11:59 pm
                                                            Re: End-game evaluation H.G.Muller Tue Nov 08, 2011 7:30 am
                                                                  Re: End-game evaluation Kevin Hearn Tue Nov 08, 2011 9:58 am
                                                                        Re: End-game evaluation H.G.Muller Tue Nov 08, 2011 12:40 pm
                                                                              Re: End-game evaluation Evert Glebbeek Tue Nov 08, 2011 5:53 pm
      Re: End-game evaluation Mark Lefler Mon Oct 10, 2011 4:08 pm
            Re: End-game evaluation H.G.Muller Mon Oct 10, 2011 9:09 pm
                  Re: End-game evaluation H.G.Muller Mon Oct 10, 2011 9:58 pm
                  Re: End-game evaluation H.G.Muller Tue Oct 11, 2011 8:50 am
                        Re: End-game evaluation H.G.Muller Tue Oct 18, 2011 6:36 pm
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