Endgame analysis

[Arpad Rusz]

I haven't seen the (surely much more elegant) solution to this ending using triangulation. But white can also win it simply by using the king and kingside pawns to punch through in that wing. Black is helpless as was pointed out earlier.

You are missing that 1.Kf4?? is losing (1...b4! 2.cxb4 c3! -+).

[Arpad Rusz]

11.O.Bláthy, The Chess Amateur, 1921
[D]4k3/4P1p1/8/3p3b/p1pPp1pP/BpP1PpP1/1P3P1R/K2N3N w - - 0 1

White wins

[Tom Barrister]

I haven't seen the (surely much more elegant) solution to this ending using triangulation. But white can also win it simply by using the king and kingside pawns to punch through in that wing. Black is helpless as was pointed out earlier.

Your position is missing the Black pawn at c3.

[Tom Barrister]

16. Rd1 Ka6 17. Qa2 bxa2 18. b3 dxc2 19. Kxc2 a1=Q 20.bxa4! Qa2+ 21. Kc1 Qb3 22. d4 cxd3 23. Rd2 Qxa4 24. Rb2 Qc4 25. a4 Ka7 26. Kd2 Qxa4 27. Kc1 Qc4 28. Nfd2 Qc5 29. Ra2+ Kb6 30. Nf1 and white is slowly winning.

It might also win, but it seems like the long way around, compared to the other line.

[StratCat]

I haven't seen the (surely much more elegant) solution to this ending using triangulation. But white can also win it simply by using the king and kingside pawns to punch through in that wing. Black is helpless as was pointed out earlier.

You are missing that 1.Kf4?? is losing (1...b4! 2.cxb4 c3! -+).

Your position is missing the Black pawn at c3.

You are completely right, I setup the position WITHOUT the black c4 pawn ! Indeed Kf4 now looks completely losing and HIARCS plays b4 after briefly considering the position.

What a difference a pawn makes....

My apologies.

[Eelco de Groot]

Yes, that's the solution for the second puzzle. It seems like only 1.d5! wins. Stockfish has a good solving time!

This second puzzle was hard to find on a small system. I have not tried default Stockfish but I doubt I would get anywhere near that solution time with 256 Mb hashtables. Anyway, I'm getting a bit closer, but the critical variation for me is if Black decides to play 1...exd5 instead of 1...cxd5 The solution turns out to be similar but I think it takes a bit longer, especially after 2.exd5 c5. If Black plays 2... cxd5 it is more forced. I had to turn to Houdini to get the solution, I was a bit lazy too and could not work it out by myself.
It still needed 40 minutes in the 32 bits version to see an advantage for White, but that is better than my current builds.

Position after 1. d5 exd5:

[D]5k2/8/pppp1ppp/3p4/PPP1PPPP/8/8/5K2 w - -

Engine: Houdini 1.5a w32 (256 MB)
by Robert Houdart

4/09 0:00 0.00 2.cxd5 cxd5 3.exd5 Ke7 4.Ke2 (573)

5/09 0:01 +0.01 2.cxd5 c5 3.bxc5 bxc5 4.Ke2 Ke7 (882)

5/09 0:01 +0.05 2.exd5 cxd5 3.cxd5 Ke7 4.Ke2 h5 (1.044)

6/10 0:01 +0.03 2.exd5 cxd5 3.cxd5 Ke7 4.Ke2 h5
5.gxh5 gxh5 (1.503) 1

7/11 0:01 +0.05 2.exd5 c5 3.b5 axb5 4.axb5 Ke7 5.Ke2 h5 (2.708) 1

8/13 0:01 +0.07 2.exd5 c5 3.b5 axb5 4.axb5 Ke7 5.Ke2 f5
6.gxf5 gxf5 7.Kd3 (4.612) 2

9/13 0:01 +0.07 2.exd5 c5 3.b5 axb5 4.axb5 Ke7 5.Ke2 f5
6.gxf5 gxf5 7.Kd3 (6.702) 3

10/15 0:01 +0.10 2.exd5 c5 3.b5 axb5 4.axb5 Ke7 5.Ke2 f5
6.gxf5 gxf5 7.Kd3 Kf6 (11.851) 6

11/16 0:01 +0.06 2.exd5 c5 3.b5 axb5 4.axb5 Ke7 5.Ke2 f5
6.gxf5 gxf5 7.Kd3 Kf6 8.h5 (17.923) 9

12/18 0:02 +0.11++ 2.exd5 (35.301) 17

12/19 0:02 +0.12 2.exd5 c5 3.b5 a5 4.f5 gxf5 5.gxf5 Ke7
6.Ke2 h5 7.Ke3 Kd7 8.Ke4 (48.015) 23

13/19 0:02 +0.12 2.exd5 cxd5 3.cxd5 Ke7 4.Ke2 f5
5.gxf5 gxf5 6.h5 Kf6 7.Ke3 Ke7 8.Kd3 b5
9.axb5 axb5 10.Kd4 (90.103) 42

14/22 0:02 +0.13 2.exd5 cxd5 3.cxd5 f5 4.gxf5 gxf5
5.h5 Kf7 6.Ke2 Kf6 7.Ke3 Ke7 8.Kd4 Kf6
9.Kc4 Ke7 (185.387) 83

15/23 0:02 +0.14 2.exd5 c5 3.b5 axb5 4.axb5 f5 5.gxf5 gxf5
6.h5 Ke7 7.Ke2 Kd7 8.Ke3 Kc8 9.Kd2 Kd7
10.Ke2 Kc8 11.Kd3 Kd7 12.Ke2 Kc8 (333.802) 139

16/25 0:02 +0.10-- 2.exd5 c5 (447.975) 178

16/27 0:02 +0.10 2.exd5 c5 3.b5 a5 4.f5 gxf5 5.gxf5 h5
6.Ke2 Kf7 7.Ke3 Ke7 8.Kd3 Kd7 9.Ke4 Kc7
10.Kf4 Kd8 (668.488) 243

17/28 0:02 +0.10 2.exd5 c5 3.b5 a5 4.f5 gxf5 5.gxf5 h5
6.Ke2 Kf7 7.Ke3 Ke8 8.Kf2 Ke7 9.Kf3 Kd7
10.Ke4 Kc7 11.Kf4 Kd8 12.Ke4 Kc7
13.Kf4 (757.564) 266

18/33 0:03 +0.10 2.exd5 c5 3.b5 a5 4.f5 gxf5 5.gxf5 h5
6.Ke2 Kf7 7.Ke3 Ke8 8.Kf2 Ke7 9.Kf3 Kd7
10.Ke4 Kc7 11.Kd3 Kd7 12.Ke4 Kc7 (1.140.961) 352

19/35 0:04 +0.08 2.exd5 c5 3.b5 a5 4.f5 Kf7 5.Ke2 g5
6.hxg5 hxg5 7.Ke3 Ke8 8.Kd3 Ke7
9.Kc3 Kd7 10.Kd2 Ke8 11.Ke3 Kd7
12.Kf3 Ke8 13.Ke3 Kd7 (1.888.575) 469

20/37 0:06 +0.08 2.exd5 c5 3.b5 a5 4.f5 Kf7 5.Ke2 g5
6.hxg5 hxg5 7.Ke3 Ke8 8.Kd3 Ke7
9.Kd2 Kd7 10.Ke2 Kd8 11.Kf2 Kd7
12.Kf3 Ke8 13.Ke3 Kd7 14.Kf3 Ke8 (4.209.840) 655

21/38 0:08 +0.08 2.exd5 c5 3.b5 a5 4.f5 Kf7 5.Ke2 g5
6.hxg5 hxg5 7.Ke3 Ke8 8.Kd3 Ke7
9.Kd2 Kd7 10.Ke2 Ke7 11.Kd3 Ke8
12.Ke3 Kd7 13.Kd2 Ke8 14.Ke3 Kd7 (6.642.229) 742

22/39 0:12 +0.08 2.exd5 c5 3.b5 a5 4.f5 Kf7 5.Ke2 g5
6.hxg5 hxg5 7.Ke3 Ke8 8.Kd3 Ke7
9.Kd2 Kd7 10.Ke2 Ke7 11.Kd1 Kd7
12.Kc2 Ke8 13.Kd2 Kd7 14.Ke2 (9.863.824) 802

23/41 0:19 +0.08 2.exd5 c5 3.b5 a5 4.f5 Kf7 5.Ke2 g5
6.hxg5 hxg5 7.Ke3 Ke8 8.Kd3 Ke7
9.Kd2 Kd7 10.Ke2 Ke7 11.Kd3 Kd7
12.Kd2 Ke7 13.Kc3 Kd7 14.Kd2 Ke7 (16.888.408) 867

24/43 0:32 +0.08 2.exd5 c5 3.b5 a5 4.f5 Kf7 5.Ke2 g5
6.hxg5 hxg5 7.Ke3 Ke8 8.Kd3 Ke7
9.Kd2 Kd7 10.Ke2 Ke7 11.Kf3 Kd7
12.Kf2 Ke7 13.Kg3 Kd7 14.Kf3 Ke8
15.Ke3 (29.596.347) 916

25/46 0:54 +0.08 2.exd5 c5 3.b5 a5 4.f5 Kf7 5.Ke2 g5
6.hxg5 hxg5 7.Ke3 Ke8 8.Kd3 Ke7
9.Kd2 Kd7 10.Ke2 Ke7 11.Kf2 Kf7
12.Kg2 Ke8 13.Kf3 Kd7 14.Kf2 Ke7
15.Kg3 (51.829.518) 949

26/48 1:47 +0.08 2.exd5 c5 3.b5 a5 4.f5 Kf7 5.Ke2 g5
6.hxg5 hxg5 7.Ke3 Ke8 8.Kd3 Ke7
9.Kd2 Kd7 10.Ke2 Ke7 11.Kf2 Kf7
12.Kg2 Ke8 13.Kg3 Kd7 14.Kf3 Kd8
15.Kf2 (104.929.108) 980

27/59 3:28 +0.08 2.exd5 c5 3.b5 a5 4.f5 Kf7 5.Ke2 g5
6.hxg5 hxg5 7.Ke3 Ke8 8.Kd3 Ke7
9.Kd2 Kd7 10.Ke2 Ke7 11.Kf2 Kf7
12.Kf3 Ke7 13.Kg3 Kd7 14.Kf2 Ke7
15.Ke1 (208.450.927) 997

28/59 5:07 +0.08 2.exd5 c5 3.b5 a5 4.f5 Kf7 5.Ke2 g5
6.hxg5 hxg5 7.Ke3 Ke8 8.Kd3 Ke7
9.Kd2 Kd7 10.Ke2 Ke7 11.Kf3 Kd7
12.Kf2 Ke7 13.Ke1 Kd7 14.Kd2 Ke7
15.Kd3 (310.046.442) 1009

29/63 11:31 +0.07 2.exd5 cxd5 3.cxd5 f5 4.gxf5 gxf5
5.h5 b5 6.a5 Ke7 7.Ke2 Kd7 8.Ke3 Ke7
9.Kf3 Kd7 10.Kf2 Kc7 11.Ke3 Kd7
12.Kd3 Ke7 13.Kd2 Kd7 14.Kc3 Kd8
15.Kc2 (720.390.352) 1042

30/63 18:53 +0.07 2.exd5 cxd5 3.cxd5 f5 4.gxf5 gxf5
5.h5 b5 6.a5 Ke7 7.Ke2 Kd7 8.Ke3 Ke7
9.Kf3 Kd7 10.Kf2 Ke7 11.Kf1 Kd7
12.Ke2 Kc7 13.Ke1 Kd7 14.Kd2 Kd8
15.Kc1 (1.194.789.062) 1054

31/66 42:59 +0.11++ 2.exd5 (2.761.392.188) 1070

31/68 58:37 +0.20++ 2.exd5 (3.770.612.977) 1072

31/70 77:11 +0.39++ 2.exd5 (4.957.891.399) 1070

31/71 99:59 +1.16++ 2.exd5 (6.392.935.785) 1065

31/74 120:58 +3.83++ 2.exd5 (7.730.500.604) 1065

31/74 228:56 +8.56 2.exd5 c5 3.a5 bxa5 4.b5 axb5 5.cxb5 Ke7
6.b6 Kd7 7.b7 Kc7 8.g5 hxg5 9.f5 gxf5
10.h5 Kxb7 11.h6 Ka6 12.h7 Kb5
13.h8Q Kc4 14.Qxf6 Kxd5 15.Qxf5+ (15.032.322.261) 1094

31/74 349:18 +8.56 2.exd5 c5 3.a5 bxa5 4.b5 axb5 5.cxb5 Ke7
6.b6 Kd7 7.b7 Kc7 8.g5 hxg5 9.f5 gxf5
10.h5 Kxb7 11.h6 Ka6 12.h7 Kb5
13.h8Q Kc4 14.Qxf6 Kxd5 15.Qxf5+ (23.168.285.726) 1105

best move: e4xd5 time: 349:29.203 min n/s: 1.105.000 CPU 97.9% n/s(1CPU): 1.128.702 nodes: 23.168.285.726

I finally have a version of Rainbow Serpent using TT cutoffs in PV nodes and assorted other search experiments that can find White can win also on the limited hardware of the Athlon, but after the hashtables are full the Fail Highs take very very long. It is mainly because a lot of TT nodes are missing and I need a lot of Internal Iterative Deepening to be able to do the exclusion searches. Still I'm glad at least Rainbow Serpent can see this now with all the experimental changes:


5k2/8/pppp1ppp/3p4/PPP1PPPP/8/8/5K2 w - -

Engine: Rainbow Serpent 2.0 Build 066 (Athlon 2009 MHz, 256 MB)
by Romstad, Costalba, Kiiski

1/01 0:00 -0.08 2.exd5 (179) 0

2/03 0:00 -0.08 2.exd5 cxd5 3.cxd5 (200) 0

3/03 0:00 -0.08 2.exd5 cxd5 3.cxd5 (290) 0

4/04 0:00 -0.40 2.exd5 cxd5 3.cxd5 Ke7 (440) 1

5/05 0:00 -0.08 2.exd5 cxd5 3.cxd5 Ke7 4.Ke2 (701) 1

6/06 0:00 +0.04 2.exd5 cxd5 3.cxd5 Ke7 4.Ke2 Kd7 (1.015) 2

7/08 0:00 +0.04 2.exd5 cxd5 3.cxd5 Ke7 4.Ke2 f5
5.gxf5 gxf5 (1.586) 4

8/08 0:00 +0.04 2.exd5 cxd5 3.cxd5 Ke7 4.Ke2 f5
5.gxf5 gxf5 (3.073) 8

9/09 0:00 +0.08 2.exd5 cxd5 3.cxd5 Ke7 4.Ke2 f5
5.gxf5 gxf5 6.Ke3 (5.811) 15

10/11 0:00 +0.08 2.exd5 cxd5 3.cxd5 Ke7 4.Ke2 g5
5.hxg5 hxg5 6.Ke3 gxf4+ 7.Kxf4 (11.085) 28

11/11 0:00 +0.16++ 2.exd5 cxd5 3.cxd5 Ke7 4.Ke2 g5
5.hxg5 hxg5 6.Ke3 gxf4+ 7.Kxf4 (19.276) 47

11/12 0:00 +0.20 2.exd5 cxd5 3.cxd5 Ke7 4.Ke2 g5
5.hxg5 hxg5 6.Ke3 gxf4+ 7.Kxf4 Kd7 (22.091) 54

12/13 0:00 +0.20 2.exd5 cxd5 3.cxd5 Ke7 4.Ke2 g5
5.hxg5 hxg5 6.Ke3 gxf4+ 7.Kxf4 Kd7
8.Ke4 (42.080) 96

13/14 0:00 +0.20 2.exd5 cxd5 3.cxd5 Ke7 4.Ke2 g5
5.hxg5 hxg5 6.Ke3 gxf4+ 7.Kxf4 b5
8.axb5 axb5 (74.874) 154

14/15 0:00 +0.20 2.exd5 cxd5 3.cxd5 Ke7 4.Ke2 g5
5.hxg5 hxg5 6.Ke3 gxf4+ 7.Kxf4 b5
8.axb5 axb5 9.Ke4 (138.809) 240

15/17 0:00 +0.20 2.exd5 cxd5 3.cxd5 Ke7 4.Ke2 Kf7
5.Ke3 f5 6.gxf5 gxf5 7.Kd4 b5 8.axb5 axb5
9.Ke3 Ke7 10.Kd4 (231.990) 330

16/15 0:01 +0.20 2.exd5 cxd5 3.cxd5 Ke7 4.Ke2 Kf7
5.Ke3 f5 6.gxf5 gxf5 7.Kd4 Ke7 8.a5 bxa5
9.bxa5 (514.389) 491

17/20 0:01 +0.12-- 2.exd5 c5 3.b5 a5 4.f5 Kf7 5.Ke2 g5
6.h5 Ke7 7.Ke3 Kd7 8.Ke4 Ke7 9.Kd3 Kd7
10.Ke3 Ke8 11.Ke4 Ke7 (817.947) 569

17/20 0:01 +0.08 2.exd5 c5 3.b5 a5 4.f5 Kf7 5.Ke2 g5
6.hxg5 hxg5 7.Ke3 Ke7 8.Ke4 Kf7
9.Kd3 Ke7 10.Ke3 Kf8 11.Ke4 Kf7 (979.518) 591

18/17 0:01 +0.20++ 2.exd5 c5 3.b5 a5 4.Kf2 f5 5.gxf5 gxf5
6.Ke2 Ke7 7.Ke3 h5 8.Kd3 Kf7 9.Kd2 Ke7
10.Kd3 (1.186.934) 617

18/17 0:02 +0.20 2.exd5 c5 3.b5 a5 4.Kf2 f5 5.gxf5 gxf5
6.Ke2 Ke7 7.h5 Ke8 8.Kd2 Kf7 9.Kd3 Ke7
10.Ke2 (1.315.864) 633

19/21 0:02 +0.08 2.exd5 c5 3.bxc5 bxc5 4.f5 gxf5
5.gxf5 a5 6.Ke2 Ke7 7.Ke3 Kd7 8.Kd3 Ke7
9.h5 Kd7 10.Ke3 Ke7 11.Ke4 Kd7
12.Ke3 (1.872.811) 688

20/21 0:03 +0.08 2.exd5 c5 3.bxc5 bxc5 4.f5 gxf5
5.gxf5 a5 6.Ke2 Ke7 7.Ke3 Kd7 8.Kd3 Ke7
9.h5 Kd7 10.Ke3 Ke7 11.Ke4 Kd7
12.Ke3 (2.491.411) 699

21/19 0:05 +0.08 2.exd5 c5 3.bxc5 bxc5 4.f5 gxf5
5.gxf5 a5 6.Ke2 Ke7 7.h5 Kd7 8.Ke3 Ke7
9.Ke4 Kf7 10.Kd3 Ke7 11.Ke2 (3.682.901) 716

22/25 0:07 +0.08 2.exd5 c5 3.bxc5 bxc5 4.f5 gxf5
5.gxf5 a5 6.h5 Ke7 7.Ke2 Kd8 8.Kf3 Kd7
9.Kf4 Ke7 10.Kg3 Ke8 11.Kf3 Ke7
12.Ke3 Kd7 13.Ke4 Kd8 14.Kf3 (5.474.257) 731

23/18 0:11 0.00-- 2.exd5 c5 3.bxc5 bxc5 4.f5 gxf5
5.gxf5 h5 6.a5 Ke7 7.Kf2 Ke8 8.Kf3 Kd7
9.Ke3 Kc7 10.Kf3 Kd7 (8.435.983) 749

23/23 0:14 0.00 2.exd5 c5 3.bxc5 bxc5 4.f5 gxf5
5.gxf5 h5 6.a5 Ke7 7.Kf2 Ke8 8.Kf3 Kd7
9.Ke3 Ke8 10.Kd3 Kd8 11.Ke2 Ke7
12.Kd3 Kd7 13.Ke3 (11.065.705) 738

24/24 0:18 0.00 2.exd5 c5 3.bxc5 bxc5 4.f5 gxf5
5.gxf5 h5 6.a5 Ke7 7.Kf2 Ke8 8.Kf3 Kd7
9.Ke3 Kc7 10.Ke4 Kd7 11.Kd3 Ke8
12.Ke4 Kf7 13.Kd3 Ke8 (13.985.708) 737

25/20 0:34 0.00 2.exd5 c5 3.bxc5 bxc5 4.f5 gxf5
5.gxf5 h5 6.a5 Ke7 7.Kf2 Ke8 8.Kf3 Kd7
9.Ke3 Ke7 10.Ke4 Ke8 11.Ke3 Ke7 (24.929.435) 726

26/16 0:57 0.00 2.exd5 c5 3.bxc5 bxc5 4.f5 gxf5
5.gxf5 h5 6.a5 Ke7 7.Kf2 Ke8 8.Kf3 Kd7
9.Ke3 Ke7 (41.576.220) 726

27/18 1:32 0.00 2.exd5 c5 3.bxc5 bxc5 4.f5 gxf5
5.gxf5 h5 6.a5 Ke7 7.Kf2 Ke8 8.Kf3 Kd7
9.Ke3 Ke8 10.Ke4 Ke7 (66.931.873) 722

28/15 2:17 0.00 2.exd5 c5 3.bxc5 bxc5 4.f5 gxf5
5.gxf5 h5 6.a5 Ke7 7.Kf2 Ke8 8.Kf3 Kd7
9.Ke3 (99.094.313) 719

29/18 3:26 0.00 2.exd5 c5 3.bxc5 bxc5 4.f5 gxf5
5.gxf5 h5 6.a5 Ke7 7.Kf2 Ke8 8.Kf3 Kd7
9.Ke3 Ke8 10.Ke2 Ke7 (148.241.068) 717

30/15 7:06 0.00 2.exd5 c5 3.bxc5 bxc5 4.f5 gxf5
5.gxf5 h5 6.a5 Ke7 7.Kf2 Ke8 8.Kf3 Kd7
9.Ke3 (307.941.579) 721

31/15 11:47 0.00 2.exd5 c5 3.bxc5 bxc5 4.f5 gxf5
5.gxf5 h5 6.a5 Ke7 7.Kf2 Ke8 8.Kf3 Kd7
9.Ke3 (512.190.362) 724

32/15 23:00 0.00 2.exd5 c5 3.bxc5 bxc5 4.f5 gxf5
5.gxf5 h5 6.a5 Ke7 7.Kf2 Ke8 8.Kf3 Kd7
9.Ke3 (1.003.386.247) 726

33/15 37:27 0.00 2.exd5 c5 3.bxc5 bxc5 4.f5 gxf5
5.gxf5 h5 6.a5 Ke7 7.Kf2 Ke8 8.Kf3 Kd7
9.Ke3 (1.637.297.393) 728

34/02 129:44 +0.08++ {Yes!} 2.exd5 c5 (5.893.146.238) 757

34/01 195:32 +0.16++ {Yes!} 2.exd5 (8.907.286.151) 759

34/01 369:14 +0.32++ 2.exd5 (16.960.216.607) 765

34/01 470:00 +0.64++ 2.exd5 (21.553.133.658) 764

34/01 650:28 +1.29++ 2.exd5 (29.811.010.707) 763

34/01 780:29 +2.58++ 2.exd5 (35.638.667.309) 761

best move: e4xd5 time: 798:17.937 min n/s: 760.173 nodes: 36.410.658.417

Eelco

[Tom Barrister]

[D]n3K3/Pp6/2p4k/7P/8/8/8/8 w - - 0 1


To understand this position, we have to look ahead to this position:

[D]n7/P7/2K4k/7P/1p6/8/8/8 b - - 0 3

In this position, if White moves, he loses. If Black moves, it's a draw.

Look at it from the vantage point of White moving first:

1 Kb7

White has no waiting moves if he's to get to a8 in time.

1 ... b3
2 Kxa8 b2
3 Ka7

Unfortunately, White now has to move out of the safe haven and into Black's upcoming check.

3 ... b1=Q+
4 Kc8 Qf5+
5 Kc7 Qc5+
6 Kb7 Qb5+
7 Kc7 Qa6
8 Kb8 Qb6+
9 Ka8 Kg5
10 h6 Qc7
11 h7 Qc8#

Now we look at it with Black to move first:

1 ... b3

If 1 ... Kg5, 2 Ka7! and Black has to capture the pawn and can't win the Queen vs RP ending.

2 Kb7 a2
3 Kxa8 Kg5

Of course 3 ... b1=Q/R is stalemate. 3 ... Kg7, 4 h6+ Kh7 5 Kb8 b1=Q+ leads to the same basic position as the main line.

4 h6 b1=Q+
5 h7 Qe5+
6 Kb8 Qb4+
7 Kc7 Qb5+
8 Kb8

White saves a few moves to illustrate the final position.

8 ... Qb6+
9 Ka8

And Black has no time to play Qc7, as White will promote and stop Qc8#

Knowing the key position, it's easy for White to formulate his plan:

[D]n3K3/Pp6/2p4k/7P/8/8/8/8 w - - 0 1

1 Kd7 b5

Or 1 ... c5, 2 Kc8 c4, 3 Kxb7 c3, 4 Kxa8 c2, 5 Kc7 c1=Q, 6 a8=Q draws.

2 Kd6! b4
3 Kxc6

And the key position is reached with Black to move.

[Tom Barrister]

Here's one I took from Chess.com. The author is unknown to me; I couldn't find it in any of the online databases.

[D]6b1/5p2/1p3Bp1/1P3pP1/5P2/pp1BK3/pr4P1/k7 w - - 0 1

White to move and mate in 21.

The conventional engines I tried had problems with it. Chest, configured correctly, solved it in a a few seconds.

[Dann Corbit]

What were the parameters you chose and what was the solution?

[Tom Barrister]

What were the parameters you chose and what was the solution?

AutoTurbo and "XPK".

The solution (which I found before trying engines), is easy, once the goals are determined.

[D]6b1/5p2/1p3Bp1/1P3pP1/5P2/pp1BK3/pr4P1/k7 w - - 0 1

White has Black in a stalemate position, with the exception of the Bishop. Analysis shows that White can't breakthrough with the pawns. This will free Black's Bishop and allow it to head straight for c4 to drive White's Bishop off of the diagonal or, if pawns are gone, follow it to either force it off the diagonal or gain a draw by repetition.

White also can't move his white-square Bishop because it will free Black's King. He can't move the black-square Bishop, either, because it will allow Black to free himself by f6.

All this leaves is the King. Ideally, the King would like to get to a3. However, there's no safe route to get there. The only access square is d4, and moving the King there breaks the pin in the Rook, which can then escape, followed by the pawn's move to b2.

Therefore, White has to figure out another way to get in. It would be nice to be able to move the Bishop from c3 so that the King could access it, but this isn't possible, as the other squares on the b1-h7 diagonal are covered by Black. Trying g4 to remove the pawn on f5 won't work, because Black will simply refuse to take it. For example, 1 g4 Bh7, 2 Kf3 Bg8, 3 gxf5 gxf5, 4 Bxf5 Bh7, and White must take the Bishop and stalemate Black.

However, White has another way to go about it, one that involves a two King tours, sandwiched around a short Bishop tour.

1 Kf3 Bh7

There's no sense in listing Black's moves, as they'll all be moving the Bishop back and forth from g8 to h7.

2 Kg3 Bg8
3 Kh2

The reason for the pawn at g2---and the reason for not moving it!

3 ... Bh7
4 Kg1 Bg8
5 Kf1 Bh7
6 Ke1 Bg8
7 Kd1 Bh7
8 Kc1 Bg8

The first tour is ended, and now White's King keeps Black's King from moving, freeing the Bishop for other duties.

9 Bc4 Bh7
10 Bxb3 Bg8
11 Bc2 Bh7

The Bishop now shields the King, as well as relieving His Majesty of the duties of guarding b8, so that he can begin his second tour.

12 Kd2 Bg8
13 Kd3 Bh7

Now that this square is open, White can safely pick his way through without unpinning Black's Rook.

14 Kc4 Bg8
15 Kd5 Bh7
16 Kc6 Bg8
17 Kxb6 Bh7
18 Ka5 Bg8
19 Ka4 Bh7
20 Kxa3
At long last, the King's journeys end at the desired square.

20 ... Bg8

By now, the Bishop must be rather tired of shuffling back and forth in the corner and will probably happy to be shortly getting to take a nap before the next game.

21 Bxb2#