Bishop ending

[Andre]

Can an engine find the plan here?

[d]

[Date "1980.??.??"]
[White "Belokon, S."]
[Black "?"]
[Result "1-0"]
[FEN "5k2/6pB/8/4K1pP/8/8/8/8 w - - 0 1"]
[PlyCount "31"]

1. Ke4 (1. Kf5? g6+ 2. hxg6 Kg7 3. Kxg5 Kh8) 1... g4 2. Ke3! Kf7 3. Kf2 Kf6
(3... g6 4. h6 Kf6 5. Bg8 g5 6. Bh7) 4. Bg6! Kg5 5. Kg3 Kh6 6. Kf4 g3 7. Kxg3
Kg5 8. Kf3 Kf6 9. Kf4 Ke7 10. Kf5 Kf8 11. Bh7 Kf7 12. Kg5 Ke7 (12... g6 13.
h6) 13. Bg8 Kf8 14. Ba2 Ke7 15. Kg6 Kf8 16. Bb3 1-0

[kgburcham]

[d] 5k2/6pB/8/4K1pP/8/8/8/8 w - - 0 1

Modified Zappa

1.Ke4 g4 2.Ke3 Kf7 3.Kf2 Kf6 4.Bg6 Ke7 5.Kg3 Kf8 6.Bh7 g5 7.h6 Kf7 8.Kxg4 Kf6 9.Kh5 Ke5 10.Kxg5
+/= (0.51) Depth: 17/37 00:00:07 46769kN, tb=17979
1.Ke4 g4 2.Ke3 Kf7 3.Kf2 Kf6 4.Bg6 Ke7 5.Kg3 Kf8 6.Bh7 g5 7.h6 Kf7 8.Kxg4 Kf6 9.Kh5 Ke5 10.Kxg5
+/= (0.51) Depth: 17/37 00:00:08 50523kN, tb=21733
1.Ke4 g4 2.Ke3 Kf7 3.Kf2 Kf6 4.Bg6 Ke7 5.Kg3 Kf8 6.Bh7 Kf7 7.Kxg4 Kf6 8.Bg6 Ke7 9.Bh7 Kf6
+- (2.44) Depth: 18/37 00:00:08 52223kN, tb=25786
1.Ke4 g4 2.Ke3 Kf7 3.Kf2 Kf6 4.Bg6 Ke7 5.Kg3 Kf8 6.Bh7 Kf7 7.Kxg4 Kf6 8.Bg6 Ke7 9.Bh7 Kf6
+- (2.44) Depth: 18/37 00:00:09 53882kN, tb=32384
1.Ke4 g4 2.Ke3 Kf7 3.Kf2 Kf6 4.Bg6 Kg5 5.Kg3 Kh6 6.Kh4 g3 7.Kxg3 Kg5 8.Kf3 Kf6 9.Kf4 Ke7 10.Kf5 Kf8 11.Bh7 Kf7 12.Kg5 Ke8 13.Bg8 Kf8 14.Bd5 Ke8 15.Kg6 Kf8 16.Bc4 Ke8 17.Kxg7
+- (#27) Depth: 19/49 00:00:14 84242kN, tb=60549
1.Ke4 g4 2.Ke3 Kf7 3.Kf2 Kf6 4.Bg6 Kg5 5.Kg3 Kh6 6.Kh4 g3 7.Kxg3 Kg5 8.Kf3 Kf6 9.Kf4 Ke7 10.Kf5 Kf8 11.Bh7 Kf7 12.Kg5 Ke8 13.Bg8 Kf8 14.Bd5 Ke8 15.Kg6 Kf8 16.Bc4 Ke8 17.Kxg7
+- (#27) Depth: 19/49 00:00:16 97109kN, tb=71206
1.Ke4 g4 2.Ke3 Kf7 3.Kf2 Kf6 4.Bg6 Kg5 5.Kg3 Kh6 6.Kh4 g3 7.Kxg3 Kg5 8.Kf3 Kf6 9.Kf4 Ke7 10.Kf5 Kf8 11.Bh7 Kf7 12.Kg5 Ke8 13.Bg8 Kf8 14.Bd5 Ke8 15.Kg6 Kf8 16.Bc4 Ke8 17.Kxg7
+- (#27) Depth: 20/49 00:00:16 97109kN, tb=71206
1.Ke4 g4 2.Ke3 Kf7 3.Kf2 Kf6 4.Bg6 Kg5 5.Kg3 Kh6 6.Kh4 g3 7.Kxg3 Kg5 8.Kf3 Kf6 9.Kf4 Ke7 10.Kf5 Kf8 11.Bh7 Kf7 12.Kg5 Ke8 13.Bg8 Kf8 14.Bd5 Ke8 15.Kg6 Kf8 16.Bc4 Ke8 17.Kxg7
+- (#27) Depth: 20/49 00:00:18 106mN, tb=82582
1.Ke4 g4 2.Ke3 Kf7 3.Kf2 Kf6 4.Bg6 Kg5 5.Kg3 Kh6 6.Kh4 g3 7.Kxg3 Kg5 8.Kf3 Kf6 9.Kf4 Ke7 10.Kf5 Kf8 11.Bh7 Kf7 12.Kg5 Ke8 13.Bg8 Kf8 14.Bd5 Ke8 15.Kg6 Kf8 16.Bc4 Ke8 17.Kxg7
+- (#27) Depth: 21/49 00:00:21 127mN, tb=92097
1.Ke4 g4 2.Ke3 Kf7 3.Kf2 Kf6 4.Bg6 Kg5 5.Kg3 Kh6 6.Kh4 g3 7.Kxg3 Kg5 8.Kf3 Kf6 9.Kf4 Ke7 10.Kf5 Kf8 11.Bh7 Kf7 12.Kg5 Ke8 13.Bg8 Kf8 14.Bd5 Ke8 15.Kg6 Kf8 16.Bc4 Ke8 17.Kxg7
+- (#27) Depth: 21/49 00:00:24 144mN, tb=109674
1.Ke4 g4 2.Ke3 Kf7 3.Kf2 Kf6 4.Bg6 Kg5 5.Kg3 Kh6 6.Kh4 g3 7.Kxg3 Kg5 8.Kf3 Kf6 9.Kf4 Ke7 10.Kf5 Kf8 11.Bh7 Kf7 12.Kg5 Ke8 13.Bg8 Kf8 14.Bd5 Ke8 15.Kg6 Kf8 16.Bc4 Ke8 17.Kxg7
+- (#27) Depth: 22/49 00:00:34 204mN, tb=128864
1.Ke4 g4 2.Ke3 Kf7 3.Kf2 Kf6 4.Bg6 Kg5 5.Kg3 Kh6 6.Kh4 g3 7.Kxg3 Kg5 8.Kf3 Kf6 9.Kf4 Ke7 10.Kf5 Kf8 11.Bh7 Kf7 12.Kg5 Ke8 13.Bg8 Kf8 14.Bd5 Ke8 15.Kg6 Kf8 16.Bc4 Ke8 17.Kxg7
+- (#27) Depth: 22/49 00:00:41 243mN, tb=156499
1.Ke4 g4 2.Ke3 Kf7 3.Kf2 Kf6 4.Bg6 Kg5 5.Kg3 Kh6 6.Kh4 g3 7.Kxg3 Kg5 8.Kf3 Kf6 9.Kg4 Ke7 10.Kf5 Kf8 11.Bh7 Kf7 12.Kg5 Ke8 13.Bg8 Kf8 14.Bd5 Ke8 15.Kg6 Kf8 16.Bc4 Ke8 17.Kxg7
+- (#27) Depth: 23/49 00:01:07 399mN, tb=191679

[Mike S.]

It's a 6-piece position. Endgame tables, e.g. all 3/4/5-piece tables are certainly a big help here. Interesting would be if an engine can win this without any endgame tables.

Related to this position, I found:

[d]7k/7B/6P1/6K1/8/8/8/8 w - - 0 1

White cannot make progress here. From all engines I've tried (without any EGTB), only Fritz 8 and Fritz 960 (presumably a F9 version) show 0.00 immediatly. I don't have newer Fritzes. Maybe Fritz has a special algorithm for positions where the opponent has only the king left and only one free square to move to, or something like that. Although, after Kf5 Kg7 Ke6, the bK has even 3 squares (although only Kh8 holds the draw). Anyway, it's draw recognition was clearly not depth based. All other engines I tried show huge white advantages at funny depths like 40 plies or more.

(The classical "blind bishop" motif is with rook pawns and a bishop not on the color of the promotion square, not with knight pawns.)

[BBauer]

Hi,
Stockfish finds it in 48 sec on an AMD X2 5200+ running at 2.6GHZ

Stockfish 1.4:
30 00:17 63.296.471 3.609.104 +7,29 Ke5f5 g7g6+ h5xg6 Kf8g7
31 00:22 83.348.151 3.632.044 +6,04 Ke5f5 g7g6+ h5xg6 Kf8g7
32 00:37 137.569.599 3.665.297 +5,83 Ke5f5 g7g6+ h5xg6 Kf8g7
32 00:48 180.314.239 3.716.976 +9,35 Ke5d4
33 01:00 222.567.456 3.682.635 +12,88 Ke5d4 g5g4 Kd4e3 Kf8f7
34 01:09 254.652.814 3.661.171 +14,86 Ke5d4 g5g4 Kd4e3 Kf8f7
35 01:13 269.029.291 3.649.933 +19,05 Ke5d4
36 01:14 270.673.671 3.648.581 +77,08 Ke5d4
37 01:59 422.442.211 3.527.053 +93,26 Ke5d4 g5g4 Kd4e3 Kf8f7
38 03:00 620.855.171 3.431.219 +93,26 Ke5d4 g5g4 Kd4e3 Kf8f7

Kind regards
Bernhard

[AdminX]

Here is Stockfish running on a Intel Q9000 Core2Quad 2Ghz laptop
5k2/6pB/8/4K1pP/8/8/8/8 w - - 0 1

Analysis by Stockfish 1.4 JA 64bit:

1.Kf5 g6+ 2.hxg6 Kg7 3.Kxg5 Kh8 4.Kg4 Kg7 5.Kf4 Kh8 6.Kg5 Kg7 7.Kf5 Kh8 8.Ke4 Kg7 9.Ke5 Kh8 10.Kf5 Kg7 11.Ke6 Kh8 12.Ke5 Kg7 13.Kd5
+- (4.96) Depth: 6 00:00:01 1kN
+- (5.73) Depth: 24 00:00:05 14011kN

1.Ke4 g4 2.Ke3 Kf7 3.Kf2 Kf6 4.Bg6 Kg5 5.Kg3 Kh6 6.Kh4 g3 7.Kxg3 Kg5 8.Kf3 Kf6 9.Kg4 Ke7 10.Kf5 Kf8 11.Bh7 Kf7 12.Kg5 Ke7 13.Bd3 Kf7 14.Bc4+ Ke7 15.Kg6 Kd6 16.Kxg7 Kc5 17.h6 Kxc4 18.h7 Kd4 19.h8Q Kc4 20.Qg8+ Kc5 21.Kf6 Kb4
+- (6.04) Depth: 24 00:00:06 19041kN
+- (89.04) Depth: 36 00:02:07 601mN

And here is Deep Fritz 11 output running on same hardware as above:

Analysis by Deep Fritz 11:

1.Ke4 g4 2.Ke3 Kf7 3.Kf2 Ke6 4.Bg6 Kf6 5.Kg2 Ke7 6.Kg3 Kf8 7.Bh7 Ke7 8.Kxg4
+- (3.28) Depth: 8/12 00:00:00 23kN, tb=31
+- (#28) Depth: 20/31 00:00:17 3104kN, tb=27963

Lastly here is output from Bright, again same hardware as above:

Analysis by Bright-0.4a:

1.Kf5 g6+ 2.Ke5 gxh5 3.Be4 Kg7 4.Bf3
= (0.08) Depth: 6/17 00:00:00 5kN

1.Kd5 g4 2.Ke4 g6 3.hxg6 Kg7
+- (2.85) Depth: 6/17 00:00:00 8kN

1.Kd4 g6 2.h6 Kf7 3.Ke5 g4 4.Kf4
+- (2.90) Depth: 6/17 00:00:00 9kN
+- (2.90) Depth: 7/17 00:00:00 10kN

1.Kd5 g4 2.Ke4 g6 3.hxg6 g3 4.Kf5
+- (2.92) Depth: 7/22 00:00:00 15kN

1.Ke4 g4 2.Ke3 Kf7 3.Kf2 g6 4.h6 Kf6 5.Bg8 g3+ 6.Kxg3 Kf5 7.Kh4 g5+ 8.Kh5
+- (2.94) Depth: 7/22 00:00:00 19kN
+- (51.99) Depth: 24/64 00:00:49 188mN

[towforce]

Can an engine find the plan here?

[d]

Using the online 6 piece tablebase at http://www.k4it.de/index.php?topic=egtb&lang=en was very instructive for being shown why the obvious moves don't work.