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End-game evaluation
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H.G.Muller



Joined: 10 Mar 2006
Posts: 12762
Location: Amsterdam
PostPost subject: Re: End-game evaluation    Posted: Tue Nov 08, 2011 11:16 am Reply to topic Reply with quote
Evert wrote:
So far I've come up with different piece properties to look at, colour bound being an obvious one. Another one is the ability to perform a tempo-move, which I suspect is needed to be able to mate a lone king (hence why you can't with two knights), but I don't know how valid such generatlisations are (I'd need a tablebase to test).


Well, you could use the tablebase generator I released last week. Building a 4-men EGT typically takes less than half a minute, so testing pairs of minors for mating potential should be easy. Testing a single piece for mating potential is a sub-second job.

The problem with NN is not so much tempo-moves, as well as the inability of the Knight to switch in one move from attacking c1 (so that checking the bare King on b1 would force him to step into the corner) to attacking a1 to perform the checkmate. And you must do that in a single move, or you would stalemate him. Tempo is not a problem (like it would be in 8/8/8/8/8/p7/k1K1N3/8 w - - 0 1), because the King can 'triangulate', by playing Kb3-c2 when the bare King is on a1, effectively null-moving because the new positions is symemtry-equivalent to the old one. So the real problem is stalemate, and when stalemate would be a win, as in Xiangqi, two Knights would win easily.

Any color-alternator would have that problem, but also color-bound simple leapers like Ferz (which is a 'higher-order' color-alternator). Dababba could do it, but is too weak to be of use in driving the bare King towards the corner exactly for the high-order color-biding that makes the mating move possible. So the color of the deadly corner seems to be not so much determined by color-binding, as well as the ability to step from c1 to a1 in 3 moves. The (color-bound) Bishop can do that, but the equally color-bound Ferz ((1,1) leaper) can not. The piece that plays the role of Knight in the Clobbers army of Chess with Different Armies (a (1,0) + (2,2) compound leaper) can do it. To force checkmate with that plus a color-bound (2,2) + (3,3) leaper compound (a sub-set of the Bishop!), you have to do it in the corner of opposite color of the latter. Because with (2,2) + (3,3) jumps you can not go from c1 to a1 in 3 moves, like you would have to do in your 'own corner', and neither can the piece cover a1 and c1 at the same time, as would be needed for an edge mate on b1. (Also note the piece can lose a tempo in 5 moves!)

For divergent pieces the '3-moves rule' must be replaced by '2 captures + 1 non-capture'. A pair of (1,0) capturers + (1,1) non-capturers can thus force a corner mate, while (1,1) capturers + (1,0) non-capturers can force an edge mate (cover a1 and c1 at once, while the other switches from c1 to b1 in 2 captures +1 non-capture).
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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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