So far, only Glaurung 2 epsilon can find, within 21 ply

[Michael Sherwin]

As a human, I can see instantly that NxN wins. (the fastest?)

note: No table bases or bitbases used. Please do not suggest them as a valid answear to this question. I do not even know if they are warrented here.

Glaurung 2 epsilon takes 20 ply to determine this.

TogaII can not determine it, given 21 ply.

Rybka beta 1.0 can not determine it, given 21 ply!

What programming is needed to spot this in reasonable time?

8
7
6
5
4
3
2
1
	a	b	c	d	e	f	g	h

8/3nk1p1/1N3p2/P6p/8/2K5/6PP/8 w - - 0 43

[Dann Corbit]

It does not look obvious to me.

[Event "Edited position"]
[Site "DCORBIT64"]
[Date "2007.06.25"]
[Round "-"]
[White "-"]
[Black "-"]
[Result "*"]
[FEN "8/3nk1p1/1N3p2/P6p/8/2K5/6PP/8 w - - 0 1"]
[SetUp "1"]

{--------------
. . . . . . . .
. . . n k . p .
. N . . . p . .
P . . . . . . p
. . . . . . . .
. . K . . . . .
. . . . . . P P
. . . . . . . .
white to play
--------------}
1. Nxd7 Kxd7 2. Kb4 Kc7 3. Kb5 Kb7 4. a6+ Ka7
*
{giving:}

8
7
6
5
4
3
2
1
	a	b	c	d	e	f	g	h

8/k5p1/P4p2/1K5p/8/8/6PP/8 w - - 0 5

Or:
[Event "Edited position"]
[Site "DCORBIT64"]
[Date "2007.06.25"]
[Round "-"]
[White "-"]
[Black "-"]
[Result "*"]
[FEN "8/3nk1p1/1N3p2/P6p/8/2K5/6PP/8 w - - 0 1"]
[SetUp "1"]

{--------------
. . . . . . . .
. . . n k . p .
. N . . . p . .
P . . . . . . p
. . . . . . . .
. . K . . . . .
. . . . . . P P
. . . . . . . .
white to play
--------------}
1. Nxd7 Kxd7 2. a6 Kc7 3. a7 Kb7 4. a8=Q+ Kxa8
*

Giving:

8
7
6
5
4
3
2
1
	a	b	c	d	e	f	g	h

k7/6p1/5p2/7p/8/2K5/6PP/8 w - - 0 5

What is the line projected to win?

[Michael Sherwin]

Hi Dann,

Wrong direction with the white king!

White does not need to defend the QRP.

White has to be ready to take the shortest route into blacks king-side pawns when the black king is forced to yeild.

Code: Select all

Nb6xd7    Ke7xd7
Kc3d4      Kd7c6
Kd4e4      g7g6
a5a6        h5h4
a6a7        Kc6b7
Ke4d5      Kb7xa7
Kd5e6 and wins!

[Uri Blass]

The first program that I think of using is old yace that is the best in simple pawn endgames and it has no problem to find Nxd7

New game
8/3nk1p1/1N3p2/P6p/8/2K5/6PP/8 w - - 0 1

Analysis by Yace 0.99.87:

1.Nb6xd7 Ke7xd7
² (0.58) Depth: 1 00:00:00
1.Nb6xd7 Ke7xd7
² (0.58) Depth: 1 00:00:00
1.Nb6xd7 Ke7xd7 2.a5-a6
± (0.93) Depth: 2 00:00:00
1.Nb6xd7 Ke7xd7 2.a5-a6
± (0.93) Depth: 2 00:00:00
1.Nb6xd7 Ke7xd7 2.a5-a6 Kd7-c6 3.Kc3-d4 g7-g5
± (0.96) Depth: 3 00:00:00
1.Nb6xd7 Ke7xd7 2.a5-a6 Kd7-c6 3.Kc3-d4 g7-g5
± (0.96) Depth: 3 00:00:00
1.Nb6xd7 Ke7xd7 2.g2-g3 Kd7-c6 3.Kc3-c4 g7-g5 4.a5-a6 f6-f5
± (0.78) Depth: 4 00:00:00
1.Nb6xd7 Ke7xd7 2.g2-g3 Kd7-c6 3.Kc3-c4 g7-g5 4.a5-a6 f6-f5
± (0.78) Depth: 4 00:00:00
1.Nb6xd7 Ke7xd7 2.Kc3-c4 Kd7-c6 3.Kc4-b4 g7-g5 4.Kb4-c4 f6-f5 5.h2-h3 Kc6-c7 6.Kc4-d5 f5-f4
² (0.61) Depth: 5 00:00:00
1.Nb6-d5+ Ke7-e6 2.Nd5-f4+ Ke6-f7
² (0.64) Depth: 5 00:00:00
1.Nb6-d5+ Ke7-d6 2.Nd5-f4 h5-h4 3.Nf4-g6 h4-h3
± (0.71) Depth: 5 00:00:00
1.Nb6-d5+ Ke7-d6 2.Nd5-f4 h5-h4 3.Nf4-g6 h4-h3
± (0.71) Depth: 5 00:00:00
1.Nb6-d5+ Ke7-d6 2.Nd5-f4 h5-h4 3.a5-a6 Nd7-b6 4.a6-a7 Nb6-a8
± (0.93) Depth: 6/18 00:00:00 150kN
1.Nb6-d5+ Ke7-d6 2.Nd5-f4 h5-h4 3.a5-a6 Nd7-b6 4.a6-a7 Nb6-a8
± (0.93) Depth: 6/21 00:00:00 304kN
1.Nb6-d5+ Ke7-d6 2.Nd5-f4 h5-h4 3.a5-a6 Kd6-c6 4.Nf4-e6 g7-g6
² (0.61) Depth: 7/21 00:00:00 330kN
1.Nb6xd7 Ke7xd7 2.Kc3-c4 Kd7-c6 3.g2-g3 g7-g5 4.Kc4-d4 g5-g4 5.Kd4-c4 Kc6-b7 6.Kc4-b5 f6-f5 7.a5-a6+ Kb7-b8 8.Kb5-a5 Kb8-c7
² (0.62) Depth: 7/21 00:00:00 1023kN
1.Nb6xd7 Ke7xd7 2.g2-g3 Kd7-c6 3.Kc3-c4 Kc6-b7 4.Kc4-b5 g7-g5 5.a5-a6+ Kb7-a7 6.h2-h3 f6-f5 7.h3-h4 f5-f4 8.g3xf4 g5xh4
± (0.72) Depth: 7/25 00:00:01 1943kN
1.Nb6xd7 Ke7xd7 2.g2-g3 Kd7-c6 3.Kc3-c4 Kc6-b7 4.Kc4-b5 g7-g5 5.a5-a6+ Kb7-a7 6.h2-h3 f6-f5 7.h3-h4 f5-f4 8.g3xf4 g5xh4
± (0.72) Depth: 7/25 00:00:01 2047kN
1.Nb6xd7 Ke7xd7 2.h2-h4 Kd7-c6 3.Kc3-d4 g7-g6 4.a5-a6 Kc6-b6 5.Kd4-d5 Kb6xa6 6.Kd5-e6 Ka6-b5 7.Ke6xf6 Kb5-c4 8.Kf6xg6 Kc4-b4 9.g2-g3 Kb4-b3 10.Kg6-g7 Kb3-c4 11.Kg7-f6 Kc4-d4 12.Kf6-g5 Kd4-d5
± (1.12) Depth: 8/26 00:00:03 4820kN
1.Nb6xd7 Ke7xd7 2.h2-h4 Kd7-c6 3.Kc3-d4 Kc6-b5 4.Kd4-e4 Kb5xa5 5.Ke4-f5 Ka5-b5 6.Kf5-g6 f6-f5 7.Kg6xg7 f5-f4 8.Kg7-g6 Kb5-c4 9.Kg6xh5
+- (1.68) Depth: 8/27 00:00:03 5191kN
1.Nb6xd7 Ke7xd7 2.h2-h4 Kd7-c6 3.Kc3-d4 Kc6-b5 4.Kd4-e4 Kb5xa5 5.Ke4-f5 Ka5-b5 6.Kf5-g6 f6-f5 7.Kg6xg7 f5-f4 8.Kg7-g6 Kb5-c4 9.Kg6xh5
+- (1.68) Depth: 8/27 00:00:04 5597kN
1.Nb6xd7 Ke7xd7 2.h2-h4 Kd7-c6 3.Kc3-c4 g7-g6 4.a5-a6 f6-f5 5.Kc4-d4 Kc6-b6 6.Kd4-e5 Kb6xa6 7.Ke5-f6 Ka6-a7 8.Kf6xg6 Ka7-b6 9.Kg6xh5 Kb6-b7 10.Kh5-h6 Kb7-c6 11.g2-g3 f5-f4 12.g3xf4 Kc6-d6
+- (1.78) Depth: 9/28 00:00:05 8435kN
1.Nb6xd7 Ke7xd7 2.h2-h4 Kd7-c6 3.Kc3-c4 g7-g6 4.a5-a6 f6-f5 5.Kc4-d4 Kc6-b6 6.Kd4-e5 Kb6xa6 7.Ke5-f6 Ka6-a7 8.Kf6xg6 Ka7-b6 9.Kg6xh5 Kb6-b7 10.Kh5-h6 Kb7-c6 11.g2-g3 f5-f4 12.g3xf4 Kc6-d6
+- (1.78) Depth: 9/30 00:00:08 12565kN
1.Nb6xd7 Ke7xd7 2.h2-h4 Kd7-c6 3.Kc3-c4 g7-g6 4.Kc4-d4 Kc6-b5 5.Kd4-d5 Kb5xa5 6.Kd5-e6 f6-f5 7.Ke6-f6 Ka5-b5 8.Kf6xg6 Kb5-c5 9.Kg6xh5 Kc5-d4
+- (1.86) Depth: 10/30 00:00:11 17210kN
1.Nb6xd7 Ke7xd7 2.h2-h4 Kd7-c6 3.Kc3-c4 g7-g6 4.Kc4-d4 Kc6-b5 5.Kd4-d5 Kb5xa5 6.Kd5-e6 f6-f5 7.Ke6-f6 Ka5-b5 8.Kf6xg6 Kb5-c5 9.Kg6xh5 Kc5-d4
+- (1.86) Depth: 10/31 00:00:15 23003kN
1.Nb6xd7 Ke7xd7 2.g2-g3 Kd7-c6 3.Kc3-c4 g7-g6 4.a5-a6 Kc6-b6 5.Kc4-d5 Kb6xa6 6.Kd5-e6 f6-f5 7.Ke6-f6 Ka6-b5 8.Kf6xg6 Kb5-c6 9.Kg6xf5 Kc6-d6 10.Kf5-f6 Kd6-d7 11.h2-h3 Kd7-e8 12.g3-g4 Ke8-d7 13.g4-g5 Kd7-c7 14.g5-g6 h5-h4 15.Kf6-g5 Kc7-b7 16.Kg5xh4 Kb7-c7
+- (1.88) Depth: 11/33 00:00:23 35143kN
1.Nb6xd7 Ke7xd7 2.g2-g3 Kd7-c6 3.Kc3-c4 g7-g6 4.a5-a6 Kc6-b6 5.Kc4-d5 Kb6xa6 6.Kd5-e6 f6-f5 7.Ke6-f6 Ka6-b5 8.Kf6xg6 Kb5-c6 9.Kg6xf5 Kc6-d6 10.Kf5-f6 Kd6-d7 11.h2-h3 Kd7-e8 12.g3-g4 Ke8-d7 13.g4-g5 Kd7-c7 14.g5-g6 h5-h4 15.Kf6-g5 Kc7-b7 16.Kg5xh4 Kb7-c7
+- (1.88) Depth: 11/33 00:00:28 44102kN
1.Nb6xd7 Ke7xd7 2.Kc3-d4 Kd7-c6 3.Kd4-e4 g7-g6 4.h2-h4 Kc6-b5 5.Ke4-d5 f6-f5 6.Kd5-e6 Kb5-c5 7.Ke6-f6 g6-g5 8.h4xg5 Kc5-b4 9.Kf6xf5 h5-h4 10.g5-g6 Kb4-c3 11.g6-g7 h4-h3 12.g7-g8Q Kc3-d3
+- (2.28) Depth: 12/34 00:00:37 56960kN
1.Nb6xd7 Ke7xd7 2.Kc3-d4 Kd7-c6 3.Kd4-e4 g7-g6 4.h2-h4 Kc6-b5 5.Ke4-d5 f6-f5 6.Kd5-e6 Kb5-c5 7.Ke6-f6 f5-f4 8.Kf6xg6 Kc5-b5 9.a5-a6 Kb5-b4 10.a6-a7 f4-f3 11.a7-a8Q f3-f2 12.Kg6xh5 f2-f1Q 13.g2-g4
+- (3.28) Depth: 12/35 00:00:38 58671kN
1.Nb6xd7 Ke7xd7 2.Kc3-d4 Kd7-c6 3.Kd4-e4 g7-g6 4.h2-h4 Kc6-b5 5.Ke4-d5 Kb5xa5 6.Kd5-e6 Ka5-b4 7.Ke6-f7 Kb4-c5 8.Kf7xg6 Kc5-d6 9.Kg6xh5 Kd6-e7 10.Kh5-g6 Ke7-f8 11.h4-h5 Kf8-g8 12.h5-h6 Kg8-h8 13.h6-h7 f6-f5 14.Kg6-f6
+- (3.45) Depth: 12/35 00:00:39 61230kN

(, 26.06.2007)

[Uri Blass]

I also tried latest rybka and it has no problem to find it at depth 19

New game
8/3nk1p1/1N3p2/P6p/8/2K5/6PP/8 w - - 0 1

Analysis by Rybka 2.3.2a 32-bit :

1.Nb6xd7 Ke7xd7 2.g2-g3
+- (1.63) Depth: 5 00:00:00
1.Nb6xd7 Ke7xd7 2.g2-g3 Kd7-c6
+- (1.65) Depth: 6 00:00:00 1kN
1.Nb6xd7 Ke7xd7 2.g2-g3 Kd7-c6 3.Kc3-c4
+- (1.63) Depth: 7 00:00:00 2kN
1.Nb6xd7 Ke7xd7 2.g2-g3 Kd7-c6 3.Kc3-c4 g7-g5
+- (1.59) Depth: 8 00:00:00 3kN
1.Nb6xd7 Ke7xd7 2.Kc3-c4 Kd7-c6 3.h2-h4 g7-g5 4.h4xg5
± (1.31) Depth: 9 00:00:00 6kN
1.Kc3-b4 Nd7-b8 2.Kb4-b5 Ke7-d6 3.a5-a6 Nb8xa6 4.Kb5xa6 Kd6-c5
+- (1.74) Depth: 9 00:00:00 12kN
1.Kc3-b4 Nd7-b8 2.Kb4-b5 Ke7-d6 3.a5-a6 Nb8xa6 4.Kb5xa6 Kd6-c6 5.Ka6-a5
+- (1.75) Depth: 10 00:00:00 15kN
1.Kc3-b4 Nd7-b8 2.Kb4-b5 Ke7-d6 3.a5-a6 Nb8xa6 4.Kb5xa6 Kd6-c6 5.Ka6-a5 f6-f5
+- (1.74) Depth: 11 00:00:00 18kN
1.Kc3-b4 Nd7-b8 2.Kb4-b5 Ke7-d6 3.a5-a6 Nb8xa6 4.Kb5xa6 Kd6-c6 5.Ka6-a5 f6-f5 6.Nb6-a4
+- (1.74) Depth: 12 00:00:00 24kN
1.Kc3-b4 Nd7-b8 2.Kb4-b5 Ke7-d6 3.a5-a6 Nb8xa6 4.Kb5xa6 Kd6-c6 5.Ka6-a5 f6-f5 6.Nb6-c8 Kc6-d7
+- (1.77) Depth: 13 00:00:01 34kN
1.Kc3-b4 Nd7xb6 2.a5xb6 Ke7-d7 3.Kb4-b5 Kd7-c8 4.Kb5-a6 Kc8-b8 5.b6-b7 g7-g5 6.h2-h3 f6-f5 7.Ka6-b6
+- (1.70) Depth: 14 00:00:01 58kN
1.Kc3-c4 Nd7-b8 2.Kc4-b5 Ke7-d6 3.a5-a6 Nb8xa6 4.Kb5xa6 Kd6-c6 5.Nb6-a4 f6-f5 6.Na4-c3 h5-h4 7.Nc3-e2
+- (1.79) Depth: 14 00:00:01 92kN
1.Kc3-c4 Nd7-b8 2.Kc4-b5 Ke7-d6 3.a5-a6 Nb8xa6 4.Kb5xa6 Kd6-c6 5.Nb6-a4 h5-h4 6.Na4-c3 Kc6-c5 7.Nc3-e4+ Kc5-d5
+- (1.78) Depth: 15 00:00:01 116kN
1.Kc3-c4 Nd7-b8 2.Kc4-b5 Ke7-d6 3.a5-a6 Nb8xa6 4.Kb5xa6 Kd6-c6 5.Nb6-a4 h5-h4 6.Na4-c3 Kc6-c5 7.Nc3-e4+ Kc5-d5
+- (1.81) Depth: 16 00:00:02 167kN
1.Kc3-c4 Nd7-b8 2.Kc4-b5 Ke7-d6 3.a5-a6 Nb8xa6 4.Kb5xa6 Kd6-c6 5.Nb6-c8 g7-g5 6.Nc8-e7+ Kc6-d6 7.Ne7-f5+ Kd6-e5
+- (1.84) Depth: 17 00:00:02 257kN
1.Kc3-c4 Nd7-b8 2.Kc4-b5 Ke7-d6 3.a5-a6 Nb8xa6 4.Kb5xa6 Kd6-c6 5.Nb6-c8 g7-g5 6.Ka6-a5 Kc6-d5 7.Ka5-b4 f6-f5
+- (1.83) Depth: 18 00:00:04 405kN
1.Kc3-c4 Nd7-b8 2.Kc4-b5 Ke7-d6 3.a5-a6 Nb8xa6 4.Kb5xa6 Kd6-c6 5.Nb6-c8 g7-g5 6.Ka6-a5 Kc6-c5 7.Nc8-e7 Kc5-d6
+- (1.82) Depth: 19 00:00:08 825kN
1.Nb6xd7 Ke7xd7 2.Kc3-d4 Kd7-c6 3.h2-h4 Kc6-b5 4.Kd4-e4 g7-g6 5.Ke4-d5 Kb5xa5 6.Kd5-e6 g6-g5 7.Ke6xf6 g5xh4
+- (3.01) Depth: 19 00:00:10 1034kN
1.Nb6xd7 Ke7xd7 2.Kc3-d4 Kd7-c6 3.h2-h3 g7-g6 4.a5-a6 h5-h4 5.a6-a7 Kc6-b7 6.Kd4-d5 Kb7xa7 7.Kd5-e6 f6-f5
+- (5.01) Depth: 20 00:00:12 1206kN
1.Nb6xd7 Ke7xd7 2.Kc3-d4 Kd7-c6 3.h2-h3 h5-h4 4.Kd4-e4 g7-g6 5.a5-a6 Kc6-b6 6.Ke4-d5 Kb6xa6 7.Kd5-e6 f6-f5
+- (5.01) Depth: 21 00:00:20 1755kN
1.Nb6xd7 Ke7xd7 2.Kc3-d4 Kd7-c6 3.h2-h3 Kc6-d6 4.a5-a6 Kd6-c6 5.Kd4-e4 g7-g6 6.Ke4-d4 h5-h4 7.a6-a7 Kc6-b7
+- (5.01) Depth: 22 00:00:45 3499kN

(, 26.06.2007)

[Guetti]

Hiarcs11 finds it within 18 ply (without tablebases):

Code: Select all

polyglot hiarcs11.ini
PolyGlot 1.4 by Fabien Letouzey
new
post
setboard 8/3nk1p1/1N3p2/P6p/8/2K5/6PP/8 w - - 0 43
analyze
12 +118 58 338217 Kc4 Nxb6+ axb6 Kd8 Kc5 Kc8 Kc6 h4 b7+ Kb8 Kb6 h3 gxh3 g6
12 +131 62 363574 Kc4 Nxb6+ axb6 Kd7 Kd5 h4 Kc5 Kc8 Kc6 g6 g3 h3 Kc5 Kb7
13 +113 99 599986 Kc4 Nxb6+ axb6 Kd7 Kb5 Kc8 Kc6 Kb8 b7 g5
14 +138 202 1241787 Kc4
14 +138 207 1270221 Kc4 Nxb6+ axb6 Kd7 Kc5 h4 Kd5 Kc8 Ke6 Kb7 Kf7 Kxb6 Kxg7 f5 Kf6 h3 Kxf5
15 +163 336 2073808 Kc4
15 +163 350 2158763 Kc4 Nxb6+ axb6 Kd7 Kc5 h4 Kd5 h3
16 +188 571 3553056 Kc4
16 +208 1819 10113781 Kc4 Nb8 Kb5 Kd6 a6 Nxa6 Kxa6 Kc6 Ka5 f5 Nc4 Kd5 Kb4 g5 Kc3 Ke4 Nd6+ Ke5
17 +208 2156 12137161 Kc4 Nb8 Kb5 Kd6 a6 Nxa6 Kxa6 Kc6 g3 f5 Nc4 Kd5 Nd2 Ke6 Nf3 Kf6 Kb5 g5 Nd4 Kg6
18 +208 2835 16037241 Kc4 Nb8 Kb5 Kd6 a6 Nxa6 Kxa6 Kc6 g3 g5 Nc4 Kc5 Nd2 Kd6 Kb5 Kd5 Nc4 f5
18 +209 2953 16804246 Nxd7
18 +233 3004 17203795 Nxd7
18 +251 3224 18850344 Nxd7 Kxd7 Kd4 Kd6 h4
19 +276 3667 21568699 Nxd7
19 +348 4341 25300158 Nxd7 Kxd7 g3 Kc6 Kc4 h4 gxh4 g6 h5 gxh5 h4 f5 Kd4 f4 Ke4 f3 Kxf3 Kb7 Ke4 Ka7
20 +373 5442 32070619 Nxd7
20 +804 16541 104767171 Nxd7 Kxd7 h4 Kc6 Kc4 g6 a6 Kb6 Kd5 Kxa6 Ke6 f5 Kf6 Kb6 Kxg6 Kc5 Kxh5 Kd6 Kg6 Ke7 Kxf5
21 +789 27186 175123021 Nxd7 Kxd7 Kd4 Kc6 h4 Kb5 Ke4 g6 Kd5 Kxa5 Ke6 f5 Kf6 Kb6 Kxg6 Kc7 Kxh5 Kd8 Kg6 Ke7 Kxf5 Kf7

[Tord Romstad]

As a human, I can see instantly that NxN wins. (the fastest?)

note: No table bases or bitbases used. Please do not suggest them as a valid answear to this question. I do not even know if they are warrented here.

Glaurung 2 epsilon takes 20 ply to determine this.

TogaII can not determine it, given 21 ply.

Rybka beta 1.0 can not determine it, given 21 ply!

What programming is needed to spot this in reasonable time?

In the case of Glaurung, it's nothing more than blind luck. I have no special search and evaluation tricks which help to solve this position.

Here is the analysis of Glaurung 2 - &949;/5, (2 GHz Core Duo, 512 MB hash):

Code: Select all

12     +1.35   00:00   241366 Nc8+ Kd8 Nd6 Nc5 Kc4 Na6 Nf5 g6 Nh4 g5 Nf5 Kd7
                              Kd4
13     +1.33   00:00   443808 Nc8+ Kd8 Nd6 Nb8 Nf5 g6 Nh4 g5 Nf5 Nc6 a6 Kd7 Kc4
                              Ne5+ Kd4
13     +1.41   00:00   658656 Nc4 Nc5 Kb4 Na6+ Kb5 Nc7+ Kc6 Kd8 Nd6 Na6 Nf5 g6
                              Nh4 g5 Nf5
14     +1.37   00:00    1592k Nc4 Kd8 Kd4 Nb8 Kd5 Kc7 Nd6 Kd7 Ne4 Na6 Nc5+ Nxc5
                              Kxc5 Kc7 a6 g6
15     +1.37   00:01    2209k Nc4 Kd8 Kd4 Nb8 Kd5 Kd7 Kc5 Kc7 Nb6 Na6+ Kb5 Kb7
                              Nd5 h4 Kc4 Kc6
16     +1.37   00:01    3000k Nc4 Kd8 Kd4 Nb8 Kd5 Kd7 Kc5 Kc7 Nb6 Na6+ Kb5 Kb7
                              Nd5 h4 Kc4 Kc6 Kd4
17     +1.35   00:02    4915k Nc4 Kd8 Kd4 Nb8 Kd5 Kd7 Kc5 Kc7 g3 Nd7+ Kb5 Kb7
                              a6+ Ka7 Nd6 g6 Nc8+ Kb8 a7+ Kb7 h3
18     +1.39   00:03    8226k Nc4 Kd8 Kd4 Nb8 Kd5 Kd7 Nb6+ Ke7 Na4 Na6 Nc5 Nb4+
                              Kc4 Nc6 a6 Kd6 Ne4+ Ke5 Kc5 f5 Nd6
19     +1.39   00:06   14980k Nc4 Kd8 Kd4 Nf8 Kd5 Kd7 g3 Ne6 Nb6+ Ke7 Kc4 Nc7
                              Nd5+ Kd6 Nxc7 Kxc7 Kd5 Kb7 Ke6 Kc6 Kf7 h4 Kxg7
                              hxg3 hxg3
20     +1.53   00:10   22383k Nc4 Kd8 Kd4 Nf8 Kd5 Kd7 g3 Ne6 Nb6+ Ke7 Kc4 Nc7
                              Nd5+ Nxd5 Kxd5 Kd7 a6 Kc7 Kc5 g5 Kb5 f5 a7
20     +1.76   00:12   27739k Nxd7 Kxd7 Kd4 Kc6 h4 Kb5 Ke4 Kxa5 Kf5 Kb6 Kg6 Kc7
                              Kxh5 Kd6 Kg6 Ke5 Kxg7 f5 h5 f4
21     +2.20   00:13   29719k Nxd7 Kxd7 Kd4 Kc6 h4 Kb5 Ke4 Kxa5 Kf5 Kb6 Kg6 Kc7
                              Kxh5 Kd6 Kg6 Ke5 Kxg7 f5 h5 f4 h6
22     +2.71   00:16   36571k Nxd7 Kxd7 Kd4 Kc6 h4 Kb5 Ke4 Kxa5 Kf5 Kb6 Kg6 Kc6
                              Kxh5 Kd6 Kg6 f5 Kxg7 f4 h5 f3 gxf3 Ke5
23     +3.08   00:20   44828k Nxd7 Kxd7 Kd4 Kc6 h4 Kb5 Ke4 g6 Kd5 Kxa5 Ke6 f5
                              Kf7 Kb6 Kxg6 f4 Kxh5 f3 gxf3 Kc6 Kg5 Kd5 h5
24     +3.24   00:25   57125k Nxd7 Kxd7 Kd4 Kc6 h4 Kb5 Ke4 g6 Kd5 Kxa5 Ke6 f5
                              Kf7 Kb6 Kxg6 f4 Kxh5 f3 gxf3 Kc6 Kg5 Kd5 h5 Ke6
25     +3.59   00:34   76251k Nxd7 Kxd7 Kd4 Kc6 h4 Kb5 Ke4 g6 Kd5 Kxa5 Ke6 f5
                              Kf7 Kb6 Kxg6 f4 Kxh5 f3 gxf3 Kc6 Kg5 Kd5 h5 Ke6
                              h6
26     +4.14   01:17  169315k Nxd7 Kxd7 h4 Kc6 Kc4 g6 a6 Kb6 Kd5 Kxa6 Ke6 f5
                              Kf6 Kb6 Kxg6 f4 Kxh5 f3 gxf3 Kc6 Kg6 Kd6 h5 Ke7
                              h6 Kf8
27     +4.57   01:40  218288k Nxd7 Kxd7 h4 Kc6 Kc4 g6 a6 Kb6 Kd5 Kxa6 Ke6 f5
                              Kf6 Kb6 Kxg6 f4 Kxh5 f3 gxf3 Kc6 Kg6 Kd6 h5 Ke7
                              h6 Kf8 h7
28    +12.02   04:32  571712k Nxd7 Kxd7 h4 Kc6 Kc4 Kb7 Kd5 Ka6 Ke6 Kxa5 Kf7 Kb5
                              Kxg7 Kc6 Kg6 Kd7 Kxh5 Ke6 Kg6 f5 h5 f4 h6 Kd5 h7
                              Kc5 h8=Q Kc4
29    +12.18   08:30    1064M Nxd7 Kxd7 h4 Kc6 Kc4 Kb7 Kd5 Ka6 Ke6 Kxa5 Kf7 Kb5
                              Kxg7 Kc6 Kg6 Kd7 Kxh5 Ke6 Kg6 f5 h5 f4 h6 Kd5 h7
                              Kc5 h8=Q Kd5 Qd8+ Ke5 Qg5+ Ke4
Nodes: 1945104030
Nodes/second: 2048627
Best move: Nxd7

Tord

[BBauer]

This is what I got whith glaurung2-epsilon/5
running on a Xeon box 3GHz, 4 threads

Code: Select all

PolyGlot 1.4 by Fabien Letouzey
setboard 8/3nk1p1/1N3p2/P6p/8/2K5/6PP/8 w - - 0 1
post
analyze
15 +131 58 1264810 Kc4 Nxb6+ axb6 Kd8 Kb5 Kc8 Kc6 g5
16 +96 76 1946192 Kc4 Nxb6+ axb6 Kd8 Kb5 Kc8 Kc6 g5
16 +129 123 3903043 Nc4 Kd8 Kd4 Nb8 Kd5 Kd7 Kc5 Kc7
17 +129 163 5500437 Nc4 Kd8 Kd4 Nb8 Kd5 Kd7 Nb6+ Ke7
18 +133 237 8497559 Nc4 Kd8 Kd4 Nf8 Kd5 Kd7 Nb2 Ne6
19 +135 332 12291315 Nc4 Kd8 Kd4 Nf8 Kd5 Kd7 g3 Ne6
20 +149 570 22160959 Nc4 Nb8 Kb4 Kd7 Kb5 Kc7 a6 Nc6
21 +152 888 35396529 Nc4 Kd8 Kd4 Nf8 Kd5 Kd7 a6 Kc7
21 +229 1144 45777032 Kc4 Nxb6+ axb6 Kd7 Kd5 h4 h3 g6
22 +239 1700 68677282 Kc4 Nxb6+ axb6 Kd7 Kd5 h4 h3 g6
22 +272 1825 73610536 Nxd7 Kxd7 Kd4 Kc6 h4 g6 a6 Kb6 Kd5
23 +307 1877 75596310 Nxd7 Kxd7 Kd4 Kc6 h4 g6 a6 Kb6 Kd5
24 +323 2079 83710294 Nxd7 Kxd7 Kd4 Kc6 h4 g6 a6 Kb6 Kd5
25 +358 2404 96758813 Nxd7 Kxd7 Kd4 Kc6 h4 g6 a6 Kb6 Kd5
26 +413 2906 116903669 Nxd7 Kxd7 Kd4 Kc6 h4 g6 a6 Kb6 Kd5
27 +456 3834 154429986 Nxd7 Kxd7 Kd4 Kc6 h4 g6 a6 Kb6 Kd5
28 +1203 15901 632259944 Nxd7 Kxd7 h4 Kc6 Kc4 g6 a6 g5 Kd4 quit

kind regards
Bernhard

[Eelco de Groot]

As a human, I can see instantly that NxN wins. (the fastest?)

note: No table bases or bitbases used. Please do not suggest them as a valid answear to this question. I do not even know if they are warrented here.

Glaurung 2 epsilon takes 20 ply to determine this.

TogaII can not determine it, given 21 ply.

Rybka beta 1.0 can not determine it, given 21 ply!

What programming is needed to spot this in reasonable time?

[d]8/3nk1p1/1N3p2/P6p/8/2K5/6PP/8 w - - 0 43

I do not know what programming is needed but for instance Pro Deo 1.5 Test13 has no problems finding the move:

8
7
6
5
4
3
2
1
	a	b	c	d	e	f	g	h

8/3nk1p1/1N3p2/P6p/8/2K5/6PP/8 w - -

Engine: ProDeo 1.5 wb2uci (256 MB, Athlon 2009 MHz)
gemaakt door Ed Schröder

11.00 0:00 +0.87 1.Kb4 Pxb6 2.axb6 Kd8 3.Kb5 Kc8
4.Ka6 Kb8 5.h4 f5 6.b7 g6 7.Kb6 (1.339.387) 1339387

12.01 0:01 +0.86 1.Kb4 Pxb6 2.axb6 Kd8 3.Kb5 Kc8
4.Ka6 Kb8 5.h4 g6 6.b7 g5 7.hxg5 fxg5
8.Kb6 g4 9.Kc6 h4 (2.198.682) 2198

13.01 0:02 +0.86 1.Kb4 Pxb6 2.axb6 Kd8 3.Kb5 Kc8
4.Ka6 Kb8 5.h4 g6 6.b7 g5 7.hxg5 fxg5
8.Kb6 g4 9.Kc6 h4 (4.230.600) 2115

14.01 0:04 +0.80 1.Kb4 Pxb6 2.axb6 Kd8 3.Kb5 Kc8
4.Ka6 Kb8 5.h3 h4 6.b7 g6 7.Kb6 f5
8.Ka6 g5 9.Kb6 g4 10.hxg4 fxg4
11.Ka6 Kc7 12.Ka7 (7.696.461) 1924

14.03 0:06 +0.89 1.Kc4 Pxb6+ 2.axb6 Kd7 3.Kd5 h4 4.g4 g6
5.h3 f5 6.gxf5 gxf5 7.Ke5 Kc6 8.Kxf5 Kxb6
9.Kg5 Kc5 10.Kxh4 (11.576.826) 1929

15.01 0:10 +0.89 1.Kc4 Pxb6+ 2.axb6 Kd7 3.Kd5 h4 4.g4 g6
5.h3 f5 6.gxf5 gxf5 7.Ke5 Kc6 8.Kxf5 Kxb6
9.Kg5 Kc5 10.Kxh4 (18.005.759) 1800

16.01 0:29 +1.62 1.Kc4 Pb8 2.Kb5 Kd6 3.a6 Pxa6 4.Kxa6 Ke5
5.Kb5 h4 6.Kc5 g5 7.Pc4+ Ke4 8.g3 f5 (52.258.171) 1802

16.03 0:37 +1.62 1.Pxd7 (64.485.940) 1742

16.03 0:39 +1.86 1.Pxd7 Kxd7 2.Kd3 Kc6 3.Ke4 g6 (69.267.740) 1776

17.01 0:54 +2.38 1.Pxd7 Kxd7 2.Kd3 Kc6 3.Ke4 g6 (96.442.939) 1785

18.01 1:12 +2.38 1.Pxd7 Kxd7 2.Kd3 Kc6 3.Ke4 g6 (132.037.462) 1833

19.01 2:32 +2.70 1.Pxd7 Kxd7 2.Kd3 g6 (279.633.658) 1839

20.01 8:48 +3.85 1.Pxd7 Kxd7 2.Kd4 Kc6 3.h4 Kb5 4.Ke4 g6
5.Kd5 Kxa5 6.Ke6 f5 7.g3 Kb6 8.Kd7 Kc5
9.Ke7 Kd4 10.Ke6 Ke3 (990.893.008) 1876

Pro Deo 1.5 Test16 is faster, needing 9 seconds to find Nxd7:


8/3nk1p1/1N3p2/P6p/8/2K5/6PP/8 w - -

Engine: ProDeo 1.5 wb2uci (0 MB)
gemaakt door Ed Schröder

10.00 0:00 +0.85 1.Kb4 Pxb6 2.axb6 Kd8 3.Kb5 Kc8
4.Ka6 Kb8 5.h4 f5 6.b7 g6 7.Kb6 f4
8.Kc6 (448.542) 448542

10.00 0:00 +0.92 1.Pd5+ Kd6 2.Pf4 Kc5 3.Pe6+ Kb5
4.Pxg7 h4 5.Pf5 Pe5 6.Kd4 Kxa5
7.Pxh4 (631.274) 631274

11.00 0:00 +0.63 1.Pd5+ Kd6 2.Pf4 g5 3.Pxh5 Kc5 4.h4 gxh4
5.a6 Kb6 (1.296.910) 1296910

11.00 0:00 +0.85 1.Kb4 Pxb6 2.axb6 Kd8 3.Kb5 Kc8
4.Ka6 Kb8 5.h4 f5 6.b7 g6 7.Kb6 f4
8.Kc6 (1.376.044) 1376044

12.01 0:01 +0.83 1.Kb4 Pxb6 2.axb6 Kd8 3.Kb5 Kc8
4.Ka6 Kb8 5.h4 g5 6.hxg5 fxg5 7.b7 g4
8.Kb6 h4 9.Kc6 (2.133.495) 2133

12.04 0:01 +0.83 1.Kc4 (2.780.295) 2780

12.04 0:01 +1.00 1.Kc4 Pxb6+ 2.axb6 Kd8 3.Kd5 Kd7
4.h4 Kc8 5.Kc6 Kb8 6.b7 g6 7.Kb6 g5
8.hxg5 fxg5 9.Kc6 Ka7 (3.071.434) 3071

13.01 0:02 +1.00 1.Kc4 Pxb6+ 2.axb6 Kd8 3.Kd5 Kd7
4.h4 Kc8 5.Kc6 Kb8 6.b7 g6 7.Kb6 g5
8.hxg5 fxg5 9.Kc6 Ka7 (3.860.585) 1930

14.01 0:05 +0.89 1.Kc4 Pxb6+ 2.axb6 Kd8 3.Kd5 Kd7
4.g3 h4 5.gxh4 g6 6.Kc5 f5 7.Kd5 Kc8
8.h3 Kb7 9.Kc5 (9.337.172) 1867

14.07 0:09 +1.12 1.Pxd7 Kxd7 2.Kd3 Kc6 3.g3 g6 4.Ke4 h4
5.gxh4 Kb5 6.h3 Kxa5 7.h5 gxh5 8.Kf5 Kb5
9.Kxf6 Kc5 10.Kg5 Kd5 11.h4 Ke4
12.Kxh5 (15.879.038) 1764

15.01 0:10 +1.12 1.Pxd7 Kxd7 2.Kd3 Kc6 3.Ke4 g6 4.h4 Kb5
5.Kd5 Kxa5 6.g3 g5 7.Ke6 Kb6 8.Kxf6 gxh4
9.gxh4 Kc5 10.Kg5 Kd5 11.Kxh5 (17.714.947) 1771

16.01 0:24 +1.66 1.Pxd7 Kxd7 2.Kd4 Kc6 3.a6 h4 4.h3 Kb6
5.Ke4 Kxa6 6.Kf5 Ka7 7.Kg6 f5 8.Kxf5 Kb6
9.Kg6 Kc5 10.Kxg7 Kd6 (42.122.123) 1755

17.01 0:38 +1.66 1.Pxd7 Kxd7 2.Kd4 Kc6 3.a6 h4 4.a7 Kb7
5.g3 Kxa7 6.gxh4 Kb6 7.Ke4 g6 8.Kd5 f5
9.h5 gxh5 10.Ke5 Kc5 11.Kxf5 Kd5 (68.488.300) 1802

18.01 1:26 +2.61 1.Pxd7 Kxd7 2.Kd4 Kc6 3.a6 Kb6 4.Ke4 Kxa6
5.Kf5 Kb6 6.Kg6 f5 7.Kxg7 f4 8.h4 Kc5
9.Kg6 Kd5 10.Kxh5 Ke5 11.Kg5 Ke4
12.h5 (155.841.155) 1812

19.01 2:20 +2.61 1.Pxd7 Kxd7 2.Kd4 Kc6 3.Ke4 g6 4.h3 Kc5
5.g3 Kb5 6.Kd4 Kxa5 7.Kd5 f5 8.Kc6 f4
9.gxf4 Kb4 10.h4 Ka4 (255.681.072) 1826

20.01 8:51 +3.08 1.Pxd7 Kxd7 2.Kd4 Kc6 3.h4 Kb5 4.Ke4 g6
5.Kd5 g5 6.hxg5 fxg5 7.Ke5 Kc6 8.Ke4 Kc7
9.Kf5 g4 10.Kg5 g3 (994.674.045) 1873


Both have
[Pruning = MISC_37] * Hash Table extension (-18%) OFF
by the way, so the PV extension from Ed is switched off, but other extensions are switched on so that is the main reason I think why this extension seemed to bring not much extra, in most Test.eng personality files this is switched off but in most Singular Checks is kept on, at least I think with the following switches incorporated three other extensions are switched on at the moment;

[Pruning = MISC_30] * Extend singular checks
[Pruning = MISC_11] * Allow Botvinnik-Markoff Extension
[Pruning = MISC_36] * Extend double attacks (W6) at the leafs


Pro Deo 1.5 Default:


8/3nk1p1/1N3p2/P6p/8/2K5/6PP/8 w - -

Engine: ProDeo 1.5 wb2uci (256 MB)
gemaakt door Ed Schröder

11.00 0:01 +0.62 1.Pd5+ Kd6 2.Pf4 g5 3.Pd3 Kc6 4.Kb4 Kb7
5.Kb5 f5 6.g3 (2.052.469) 2052

11.02 0:01 +0.87 1.Pc8+ Kd8 2.Pd6 Pb8 3.Kb4 Kd7 4.Pe4 Pc6+
5.Kb5 Kc7 6.Ka6 h4 7.g4 hxg3 8.hxg3 (2.338.520) 2338

12.01 0:03 +0.83 1.Pc8+ Kd8 2.Pd6 Pb8 3.Kc4 Kd7 4.Pb7 Pc6
5.Kb5 Kc7 6.Ka6 Pb4+ 7.Ka7 Pc6+
8.Ka8 Pb4 9.Ka7 Pc6+ 10.Ka8 Pb4 (5.329.153) 1776

12.05 0:04 +0.83 1.Kc4 (7.888.368) 1972

12.05 0:05 +1.46 1.Kc4 Pxb6+ 2.axb6 Kd8 3.Kd5 Kd7
4.Ke4 h4 5.Kf5 Kc6 6.Kg6 f5 7.Kxf5 Kxb6
8.Kg5 h3 9.gxh3 Kc5 (9.299.156) 1859

13.01 0:06 +1.46 1.Kc4 Pxb6+ 2.axb6 Kd8 3.Kd5 Kd7
4.Ke4 h4 5.Kf5 Kc6 6.Kg6 f5 7.Kxf5 Kxb6
8.Kg5 h3 9.gxh3 Kc5 (11.524.853) 1920

14.01 0:15 +1.80 1.Kc4 Pxb6+ 2.axb6 Kd8 3.Kd5 Kd7
4.Ke4 g6 5.Kd5 h4 6.h3 Kc8 7.Ke6 f5
8.Kf6 f4 9.Kxg6 Kb7 10.Kf6 Kxb6
11.Kg5 Kc5 12.Kxh4 Kd5 (28.390.938) 1892

15.01 0:24 +1.80 1.Kc4 Pxb6+ 2.axb6 Kd8 3.Kd5 Kd7
4.Ke4 g6 5.Kd5 h4 6.h3 Kc8 7.Ke6 f5
8.Kf6 f4 9.Kxg6 Kb7 10.Kf6 Kxb6
11.Kg5 Kc5 12.Kxf4 Kd5 (44.045.227) 1835

15.16 0:42 +1.80 1.Pxd7 (78.598.622) 1871

15.16 0:44 +2.29 1.Pxd7 Kxd7 2.Kd4 Kc6 3.h3 g6 4.a6 h4
5.a7 Kb7 6.Kd5 f5 7.Ke5 Kxa7 8.Kf6 f4
9.Kxg6 Kb7 10.Kg5 f3 11.gxf3 Kc6
12.Kxh4 Kd5 (83.011.916) 1886

16.01 0:46 +2.29 1.Pxd7 Kxd7 2.Kd4 Kc6 3.h3 g6 4.a6 h4
5.a7 Kb7 6.Kd5 f5 7.Ke5 Kxa7 8.Kf6 f4
9.Kxg6 Kb7 10.Kg5 f3 11.gxf3 Kc6
12.Kxh4 Kd5 (86.172.746) 1873

17.01 1:50 +3.12 1.Pxd7 Kxd7 2.Kd4 Kc6 3.h3 g6 4.a6 h4
5.a7 Kb7 6.Kd5 f5 7.Kd4 g5 8.Ke3 f4+ (205.218.922) 1865

18.01 4:42 +3.11 1.Pxd7 Kxd7 2.g3 Kc6 3.Kd4 h4 4.a6 h3
5.Kc4 g6 6.a7 Kb7 (523.436.798) 1856


Eelco

[mjlef]

As a human, I can see instantly that NxN wins. (the fastest?)

note: No table bases or bitbases used. Please do not suggest them as a valid answear to this question. I do not even know if they are warrented here.

Glaurung 2 epsilon takes 20 ply to determine this.

TogaII can not determine it, given 21 ply.

Rybka beta 1.0 can not determine it, given 21 ply!

What programming is needed to spot this in reasonable time?

[d]8/3nk1p1/1N3p2/P6p/8/2K5/6PP/8 w - - 0 43

NOW even from back in 1990 gets this in one ply. But only because I have probably terribly flawed outside passed pawn and King much closer to all pawns on one side of the board scoring. It gives about a +2.5 pawn score after a couple of ply, but creeps up with more ply. The actualy win is a bit over 20 ply.

Mark