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Tuesday, January 29, 2013

Two Knight Ending

      The endgame with a K+2Ns versus K+P is unusual because the by possessing extra P the K cannot be stalemated (provided the blockade on the P is lifted at the proper moment, of course) and therefore the stronger side can often force mate. There are technical requirements to win this ending known as the "Troitzky line" and it may require up to 115 moves. That’s theoretically speaking of course. Andor Lilienthal failed to win it twice in a six-year period in Norman-Lilienthal and against Smyslov. However, it has been won.  Jakob Seitz (1898-1970) the German–Argentine master once won this ending against Znosko-Borovsky. View that game.
      For several days now I have been messing around with this ending and discovered the following position in which White also has a P.   I found it is quite difficult, there being only one first move that allows White to force the win.  I also discovered a couple of other positions where there is only one move leading to a win.

White to move and win

This is the only move that will allow White to force the win. If, for example, 1.a4 f3! The only move to draw 2.a5 f2 3.a6 f1Q 4.Nc7! On any other move, White loses. 4...Qe1 5.Kd6 Qd1 6.Kc6 Qc1+ 7.Kb7 Qb1+ 8.Nab5 Qa1 9.a7 drawn.
It does not help Black to go after the P with 1...Kc3 2.Nb6 f3 3.Na4+ Kc2 4.Nb4+ Kd2 5.Nc5!  (This is the only winning move.) 5...f2 6.Ne4+ Ke2 7.Nxf2 and wins.
Again, the only winning move.
2…Kc3 3.Ng4
Capturing the P by 3.Nxc3 only draws: 3…Kb4! This is the only drawing move because now the P is lost.
3…Kb4 4.Nf2!
The only winning move.
No better is 4...Ka3 5.Nb6 Kxa2 (5...Kb4 6.Kc6 Kc3 7.Nd5+ Kc2 8.a4 wins) 6.Kc4 Kb2 7.Kb4 Ka2 8.Nc4 Kb1 9.Kc3 Ka2 10.Kc2 Ka1 11.Kb3 Kb1 12.Nd3 f2 13.Na3+ Ka1 14.Nb4 f1Q 15.Nbc2#
5.Nc7+ Kb4 6.Kd4 Ka3 7.Na6 Kxa2 8.Kc3 Ka3 9.Nc5 Ka2 10.Ncd3 Ka3 11.Nb2 Ka2 12.Nc4 Kb1 13.Kd2 Ka2 14.Kc2 Ka1 15.Kb3 Kb1 16.Nd3 f2 17.Na3+ Ka1 18.Nb4 f1Q 19.Nbc2#

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