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Subject: Re: A Pawn Endgame

Author: Richard Pijl

Date: 03:02:12 12/21/04

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On December 20, 2004 at 04:53:42, Peter McKenzie wrote:

>[D]8/p7/7p/4k1p/6PP/P3K3/8/8 w - -
>
>White to play and draw.
>
>I saw this one in Informator 45 (1988).
>1.a4 gxh4 2.a5! is the drawing line given.
>
>Warp doesn't get it but maybe other programs do.  Tablebases could be a big help
>here.

The Baron with 5-men tablebases (Xeon 2.8):
 12(15)&   0:00.55     66455   -0.41  h4xg5 h6xg5 Ke3-f3 Ke5-d4 Kf3-g3
                                      Kd4-e4 a3-a4 a7-a5 Kg3-g2 Ke4-f4 Kg2-h3
                                      Kf4-f3
 12(18).   0:01.50    105576   -0.41  h4xg5 h6xg5 Ke3-f3 Ke5-d4 Kf3-g3
                                      Kd4-e4 a3-a4 a7-a5 Kg3-g2 Ke4-f4 Kg2-h3
                                      Kf4-f3
 13(15)&   0:01.74    123309 -MATE28  h4xg5 h6xg5 Ke3-f3 Ke5-d4 a3-a4
                                      a7-a5 Kf3-f2 Kd4-e4 Kf2-g3 Ke4-e3 Kg3-g2
                                      Ke3-f4 (Kg2-h3) (Kf4-f3)
 13(22)&   0:06.78    577559   -2.04  a3-a4 g5xh4 a4-a5 Ke5-f6 a5-a6
                                      Kf6-e6 Ke3-f3 Ke6-d5 Kf3-g2 Kd5-c4 Kg2-h3
                                      Kc4-b5 Kh3xh4 (Kb5xa6)
 13(22).   0:06.92    600379   -2.04  a3-a4 g5xh4 a4-a5 Ke5-f6 a5-a6
                                      Kf6-e6 Ke3-f3 Ke6-d5 Kf3-g2 Kd5-c4 Kg2-h3
                                      Kc4-b5 Kh3xh4 (Kb5xa6)
 14(20)&   0:07.92    728590   -2.04  a3-a4 g5xh4 a4-a5 Ke5-f6 a5-a6
                                      Kf6-e6 Ke3-f3 Ke6-d5 Kf3-g2 Kd5-c4 Kg2-h3
                                      Kc4-b5 Kh3xh4 Kb5xa6
 14(20).   0:08.28    782176   -2.04  a3-a4 g5xh4 a4-a5 Ke5-f6 a5-a6
                                      Kf6-e6 Ke3-f3 Ke6-d5 Kf3-g2 Kd5-c4 Kg2-h3
                                      Kc4-b5 Kh3xh4 Kb5xa6
 15(23)&   0:09.55   1006608   -2.01  a3-a4 g5xh4 a4-a5 Ke5-f6 a5-a6
                                      Kf6-e6 Ke3-f2 Ke6-f7 Kf2-e3 (Kf7-g6)
(Ke3-e2)
                                      (Kg6-g7) (Ke2-f3) (Kg7-f6) (Kf3-e3) <rep>
 15(23).   0:09.88   1049584   -2.01  a3-a4 g5xh4 a4-a5 Ke5-f6 a5-a6
                                      Kf6-e6 Ke3-f2 Ke6-f7 Kf2-e3 (Kf7-g6)
(Ke3-e2)
                                      (Kg6-g7) (Ke2-f3) (Kg7-f6) (Kf3-e3) <rep>
 16(24)&   0:12.36   1438453   -2.01  a3-a4 g5xh4 a4-a5 Ke5-f6 a5-a6
                                      Kf6-e7 Ke3-f3 Ke7-f7 (Kf3-e3) (Kf7-g6)
(Ke3-e2)
                                      (Kg6-g7) (Ke2-f2) (Kg7-g6) (Kf2-e2) <rep>
 16(24).   0:12.91   1505245   -2.01  a3-a4 g5xh4 a4-a5 Ke5-f6 a5-a6
                                      Kf6-e7 Ke3-f3 Ke7-f7 (Kf3-e3) (Kf7-g6)
(Ke3-e2)
                                      (Kg6-g7) (Ke2-f2) (Kg7-g6) (Kf2-e2) <rep>
 17(26)+   0:15.53   2144696   -1.00  a3-a4 (g5xh4) (a4-a5) (Ke5-f6) (a5-a6)
                                      (Kf6-e7) (Ke3-f3) (Ke7-f7) (Kf3-e3)
(Kf7-g6) (Ke3-e2)
                                      (Kg6-g7) (Ke2-f2) (Kg7-g6) (Kf2-e2) <rep>
 17(26)&   0:17.88   3142343   -0.31  a3-a4 g5xh4 a4-a5 Ke5-f6 a5-a6
                                      Kf6-e7 Ke3-f3 Ke7-f7 Kf3-g2 Kf7-g6 Kg2-h2
                                      Kg6-f6 Kh2-g2 Kf6-e5 Kg2-h3 Ke5-e4 Kh3xh4
 17(26).   0:18.33   3216014   -0.31  a3-a4 g5xh4 a4-a5 Ke5-f6 a5-a6
                                      Kf6-e7 Ke3-f3 Ke7-f7 Kf3-g2 Kf7-g6 Kg2-h2
                                      Kg6-f6 Kh2-g2 Kf6-e5 Kg2-h3 Ke5-e4 Kh3xh4
 18(27)&   0:23.05   4319102   -0.31  a3-a4 g5xh4 a4-a5 Ke5-f6 a5-a6
                                      Kf6-e7 Ke3-f3 Ke7-f7 Kf3-g2 Kf7-g6 Kg2-h2
                                      Kg6-f6 Kh2-g2 Kf6-e5 Kg2-h3 Ke5-e4 Kh3xh4
                                      Ke4-d4 (Kh4-h3)
 18(27).   0:23.53   4414997   -0.31  a3-a4 g5xh4 a4-a5 Ke5-f6 a5-a6
                                      Kf6-e7 Ke3-f3 Ke7-f7 Kf3-g2 Kf7-g6 Kg2-h2
                                      Kg6-f6 Kh2-g2 Kf6-e5 Kg2-h3 Ke5-e4 Kh3xh4
                                      Ke4-d4 (Kh4-h3)
 19(29)+   0:36.94   8205996   -0.01  a3-a4 (g5xh4) (a4-a5) (Ke5-f6) (a5-a6)
                                      (Kf6-e7) (Ke3-f3) (Ke7-f7) (Kf3-g2)
(Kf7-g6) (Kg2-h2)
                                      (Kg6-f6) (Kh2-g2) (Kf6-e5) (Kg2-h3)
(Ke5-e4) (Kh3xh4)
                                      (Ke4-d4) (Kh4-h3)
 19(29)&   0:42.20  10274059   +0.00  a3-a4 g5xh4 a4-a5 Ke5-f6 a5-a6
                                      Kf6-e7 Ke3-f3 Ke7-f7 Kf3-g2 Kf7-g6 Kg2-f2
                                      Kg6-f6 Kf2-e3 <rep>
 19(29).   0:42.73  10381085   +0.00  a3-a4 g5xh4 a4-a5 Ke5-f6 a5-a6
                                      Kf6-e7 Ke3-f3 Ke7-f7 Kf3-g2 Kf7-g6 Kg2-f2
                                      Kg6-f6 Kf2-e3 <rep>
 20(30)&   0:58.78  14292638   +0.00  a3-a4 g5xh4 a4-a5 Ke5-f6 a5-a6
                                      Kf6-e7 Ke3-f3 Ke7-f7 Kf3-g2 Kf7-g6 Kg2-f2
                                      Kg6-f6 Kf2-e3 <rep>

Without tablebases it takes a little longer:
 16(22)&   0:00.72    562112   -2.43  h4xg5 h6xg5 Ke3-f3 Ke5-d4 a3-a4
                                      a7-a5 Kf3-f2 Kd4-c3 Kf2-e3 Kc3-b3 Ke3-d3
                                      Kb3xa4 Kd3-c4 Ka4-a3 Kc4-c3 a5-a4
 16(26).   0:00.92    717385   -2.43  h4xg5 h6xg5 Ke3-f3 Ke5-d4 a3-a4
                                      a7-a5 Kf3-f2 Kd4-c3 Kf2-e3 Kc3-b3 Ke3-d3
                                      Kb3xa4 Kd3-c4 Ka4-a3 Kc4-c3 a5-a4
 17(22)&   0:01.02    802124   -2.43  h4xg5 h6xg5 Ke3-f3 Ke5-d4 a3-a4
                                      a7-a5 Kf3-f2 Kd4-c3 Kf2-e3 Kc3-b3 Ke3-d3
                                      Kb3xa4 Kd3-c4 Ka4-a3 Kc4-c3 a5-a4 Kc3-c4
                                      (Ka3-a2)
 17(29).   0:01.27    997186   -2.43  h4xg5 h6xg5 Ke3-f3 Ke5-d4 a3-a4
                                      a7-a5 Kf3-f2 Kd4-c3 Kf2-e3 Kc3-b3 Ke3-d3
                                      Kb3xa4 Kd3-c4 Ka4-a3 Kc4-c3 a5-a4 Kc3-c4
                                      (Ka3-a2)
 18(24)&   0:02.11   1758316   -2.71  h4xg5 h6xg5 Ke3-f3 Ke5-d4 a3-a4
                                      a7-a5 Kf3-f2 Kd4-c3 Kf2-e3 Kc3-b3 Ke3-d3
                                      Kb3xa4 Kd3-c3 Ka4-b5 Kc3-b3 a5-a4 Kb3-a3
                                      Kb5-a5 Ka3-b2
 18(29).   0:02.70   2203279   -2.71  h4xg5 h6xg5 Ke3-f3 Ke5-d4 a3-a4
                                      a7-a5 Kf3-f2 Kd4-c3 Kf2-e3 Kc3-b3 Ke3-d3
                                      Kb3xa4 Kd3-c3 Ka4-b5 Kc3-b3 a5-a4 Kb3-a3
                                      Kb5-a5 Ka3-b2
 19(25)&   0:03.48   2965368   -3.07  h4xg5 h6xg5 Ke3-f3 Ke5-d4 a3-a4
                                      a7-a5 Kf3-f2 Kd4-e4 Kf2-g3 Ke4-e3 Kg3-g2
                                      Ke3-f4 Kg2-h2 Kf4xg4 Kh2-g2 Kg4-f4 Kg2-f2
                                      g5-g4 Kf2-g2 (g4-g3)
 19(30).   0:04.75   3964638   -3.07  h4xg5 h6xg5 Ke3-f3 Ke5-d4 a3-a4
                                      a7-a5 Kf3-f2 Kd4-e4 Kf2-g3 Ke4-e3 Kg3-g2
                                      Ke3-f4 Kg2-h2 Kf4xg4 Kh2-g2 Kg4-f4 Kg2-f2
                                      g5-g4 Kf2-g2 (g4-g3)
 20(26)&   0:07.63   6886991   -3.35  h4xg5 h6xg5 Ke3-f3 Ke5-d4 a3-a4
                                      a7-a5 Kf3-f2 Kd4-c3 Kf2-e3 Kc3-b3 Ke3-d3
                                      Kb3xa4 Kd3-c3 Ka4-a3 Kc3-c4 a5-a4 Kc4-c3
                                      Ka3-a2 Kc3-b4 a4-a3 Kb4-c4 (Ka2-b2)
 20(33).   0:09.52   8385690   -3.35  h4xg5 h6xg5 Ke3-f3 Ke5-d4 a3-a4
                                      a7-a5 Kf3-f2 Kd4-c3 Kf2-e3 Kc3-b3 Ke3-d3
                                      Kb3xa4 Kd3-c3 Ka4-a3 Kc3-c4 a5-a4 Kc4-c3
                                      Ka3-a2 Kc3-b4 a4-a3 Kb4-c4 (Ka2-b2)
 21(28)&   0:12.73  11460184   -3.56  h4xg5 h6xg5 Ke3-f3 Ke5-d4 a3-a4
                                      a7-a5 Kf3-f2 Kd4-c3 Kf2-e3 Kc3-b3 Ke3-d3
                                      Kb3xa4 Kd3-d2 Ka4-b4 Kd2-c2 a5-a4 Kc2-b2
                                      a4-a3 Kb2-a2 Kb4-a4 Ka2-b1 Ka4-b5 (Kb1-a1)

                                      (Kb5-c5) (Ka1-a2) (Kc5-b4)
 21(32).   0:20.33  17267957   -3.56  h4xg5 h6xg5 Ke3-f3 Ke5-d4 a3-a4
                                      a7-a5 Kf3-f2 Kd4-c3 Kf2-e3 Kc3-b3 Ke3-d3
                                      Kb3xa4 Kd3-d2 Ka4-b4 Kd2-c2 a5-a4 Kc2-b2
                                      a4-a3 Kb2-a2 Kb4-a4 Ka2-b1 Ka4-b5 (Kb1-a1)

                                      (Kb5-c5) (Ka1-a2) (Kc5-b4)
 22(30)&   0:25.91  22962139   -3.64  h4xg5 h6xg5 Ke3-f3 Ke5-d4 a3-a4
                                      a7-a5 Kf3-f2 Kd4-e4 Kf2-g3 Ke4-e3 Kg3-g2
                                      Ke3-f4 Kg2-h1 Kf4xg4 Kh1-h2 Kg4-f3 Kh2-h3
                                      Kf3-f4 Kh3-h2 g5-g4 Kh2-g2 g4-g3 Kg2-f1
                                      (Kf4-g5)
 22(43)&   4:03.37 143248517   -3.45  a3-a4 g5xh4 a4-a5 h4-h3 Ke3-f3
                                      h3-h2 Kf3-g2 Ke5-f4 Kg2xh2 Kf4xg4 a5-a6
                                      h6-h5 Kh2-g2 h5-h4 Kg2-f2 h4-h3 Kf2-g1
                                      Kg4-g5 Kg1-f1 Kg5-f5 Kf1-g1 Kf5-g4 Kg1-f2
                                      Kg4-f4
 22(43).   4:04.64 143910961   -3.45  a3-a4 g5xh4 a4-a5 h4-h3 Ke3-f3
                                      h3-h2 Kf3-g2 Ke5-f4 Kg2xh2 Kf4xg4 a5-a6
                                      h6-h5 Kh2-g2 h5-h4 Kg2-f2 h4-h3 Kf2-g1
                                      Kg4-g5 Kg1-f1 Kg5-f5 Kf1-g1 Kf5-g4 Kg1-f2
                                      Kg4-f4
 23(44)&   5:24.98 188681540   -3.43  a3-a4 g5xh4 a4-a5 h4-h3 Ke3-f3
                                      h3-h2 Kf3-g2 Ke5-f4 Kg2xh2 Kf4xg4 a5-a6
                                      h6-h5 Kh2-g2 h5-h4 Kg2-f2 h4-h3 Kf2-g1
                                      Kg4-g5 Kg1-f1 Kg5-f5 Kf1-g1 Kf5-g4 Kg1-h2
                                      Kg4-h4 Kh2-g1 (Kh4-g5) <rep>
 23(44).   5:27.04 189801214   -3.43  a3-a4 g5xh4 a4-a5 h4-h3 Ke3-f3
                                      h3-h2 Kf3-g2 Ke5-f4 Kg2xh2 Kf4xg4 a5-a6
                                      h6-h5 Kh2-g2 h5-h4 Kg2-f2 h4-h3 Kf2-g1
                                      Kg4-g5 Kg1-f1 Kg5-f5 Kf1-g1 Kf5-g4 Kg1-h2
                                      Kg4-h4 Kh2-g1 (Kh4-g5) <rep>
 24(46)&  19:03.70 603892043   -3.28  a3-a4 g5xh4 a4-a5 h4-h3 Ke3-f3
                                      h3-h2 Kf3-g2 Ke5-f4 Kg2xh2 Kf4xg4 a5-a6
                                      h6-h5 Kh2-g2 h5-h4 Kg2-f2 h4-h3 Kf2-g1
                                      Kg4-g5 Kg1-f1 Kg5-f5 Kf1-g1 Kf5-g4 Kg1-h2
                                      Kg4-h4 Kh2-g1 Kh4-h5 (Kg1-f2)
 24(46).  19:06.70 605589127   -3.28  a3-a4 g5xh4 a4-a5 h4-h3 Ke3-f3
                                      h3-h2 Kf3-g2 Ke5-f4 Kg2xh2 Kf4xg4 a5-a6
                                      h6-h5 Kh2-g2 h5-h4 Kg2-f2 h4-h3 Kf2-g1
                                      Kg4-g5 Kg1-f1 Kg5-f5 Kf1-g1 Kf5-g4 Kg1-h2
                                      Kg4-h4 Kh2-g1 Kh4-h5 (Kg1-f2)



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