Endgame study, Costeff 1996

[zullil]

Can any engine solve the following study, white to play and win? It is from Gady Costeff, 1996:

[d]5K2/p2p4/p7/4P3/P7/8/1R4pp/6nk w - - 0 1

White's first move 1. Rb1 is easy to find. But after 1...a5, White's only move is 2 Rd1! Can engines solve that?

1.Rb1 a5 2.Rd1 ( 2.Ra1 a6 3.Kf7 ( 3.Rd1 d5 4.e6 d4 5.e7 d3 6.e8=Q d2 7.Rxd2 Nf3 8.Rf2 g1=Q 9.Qe2 Qg3 10.Qd1+ Ng1 11.Qd5+ Nf3 ( 11...Qf3+ 12.Rxf3 Nxf3 13.Qg8 Ng5 14.Ke7 ) 12.Rxf3 Qxf3+ 13.Qxf3+ Kg1 ) 3...d5 4.e6 d4 5.e7 d3 6.e8=B d2 ) 2...a6 3.Ra1 d5 4.e6 d4 5.e7 d3 6.e8=B d2 7.Bh5 d1=Q 8.Bxd1 Nh3 9.Bc2+ Ng1 10.Bb1 Nf3 11.Be4+ Ng1 12.Ra2 1-0

Stockfish didn't get far.

Here's what Stockfish-1.7.1 (8 threads) shows at depth 47:

Code: Select all

info depth 47 score cp 8413 time 6726897 nodes 69592103829 nps 10345349 pv b2b1 a6a5 b1d1 a7a6 f8f7 d7d5 e5e6 d5d4 e6e7 d4d3 e7e8q d3d2 d1d2 g1f3 d2d3 g2g1q d3f3 g1a7 f7e6 a7b6 e6f5 b6b1 f5g5 b1c1 g5h5 c1b1 e8e7 b1d1 e7e4 h1g2 e4g4 g2h1 h5h4 d1d3 h4g3 d3d4 g4h5 d4g7 g3h3 g7d7 h5f5 d7f5 f3f5 h1g1 f5g5 g1h1 g5a5 h1g1 a5g5 g1f2 h3h2 f2e3 h2g3 e3d4 g5a5 d4c3 a5a6 c3c4 g3f4 c4d4 a6d6 d4c5 f4e5 c5b4 d6a6 

That's a score of +84 for White.

[BBauer]

That's a score of +84 for White.

That shows what a great study it is.
A score of +84 and perhaps wrong.
kind regards
Bernhard

[metax]

The second position is easy for ChessMind:


[D]5K2/4P3/p7/p7/P7/3p4/6pp/R5nk w - - 0 1

Analysis by ChessMind 0.82:

1.e8Q
+- (8.88) Depth: 11/28 00:00:00 215kN
1.e8Q
+- (8.88) Depth: 11/28 00:00:00 215kN
1.e8Q
+- (10.00 ++) Depth: 12/32 00:00:00 220kN
1.e8Q
+- (10.60 ++) Depth: 12/32 00:00:00 220kN
1.e8Q d2 2.Qb5 d1Q 3.Rxd1 axb5 4.axb5 a4 5.b6 a3 6.b7 a2
+- (10.60) Depth: 12/32 00:00:00 236kN
1.e8Q d2 2.Qb5 d1Q 3.Rxd1 axb5 4.axb5 a4 5.b6 a3 6.b7 a2
+- (10.60) Depth: 12/32 00:00:01 307kN
1.e8Q d2
+- (10.00 --) Depth: 13/32 00:00:01 312kN
1.e8Q d2
+- (8.80 --) Depth: 13/32 00:00:01 465kN
1.e8Q d2
+- (10.60 ++) Depth: 13/32 00:00:01 572kN
1.e8Q d2
+- (9.60) Depth: 13/32 00:00:01 573kN
1.e8Q d2
+- (9.60) Depth: 13/32 00:00:01 573kN
1.e8Q d2
+- (9.00 --) Depth: 14/34 00:00:02 592kN
1.e8Q d2
+- (7.80 --) Depth: 14/34 00:00:02 849kN
1.e8Q d2
+- (5.40 --) Depth: 14/34 00:00:03 1057kN
1.e8B d2 2.Bh5 d1Q 3.Bxd1 Nh3 4.Bc2+ Ng1 5.Bb1 Nf3 6.Be4+ Ng1 7.Ra2 Nf3
+- (7.48) Depth: 14/34 00:00:03 1118kN
1.e8B d2 2.Bh5 d1Q 3.Bxd1 Nh3 4.Bc2+ Ng1 5.Bb1 Nf3 6.Be4+ Ng1 7.Ra2 Nf3
+- (7.48) Depth: 14/34 00:00:03 1238kN
1.e8B d2 2.Bh5 d1Q 3.Bxd1 Nh3 4.Bc2+ Ng1 5.Bb1 Nf3 6.Be4+ Ng1 7.Ra2 Nf3 8.Bxf3 Kg1
+- (8.12 ++) Depth: 15/34 00:00:03 1238kN
1.e8B d2 2.Bh5 d1Q 3.Bxd1 Nh3 4.Bc2+ Ng1 5.Bb1 Nf3 6.Be4+ Ng1 7.Ra2 Nh3 8.Rxg2 Nf2
+- (8.31) Depth: 15/34 00:00:04 1284kN
1.e8B d2 2.Bh5 d1Q 3.Bxd1 Nh3 4.Bc2+ Ng1 5.Bb1 Nf3 6.Be4+ Ng1 7.Ra2 Nh3 8.Rxg2 Nf2
+- (8.31) Depth: 15/40 00:00:06 1972kN
1.e8B d2 2.Bh5 d1Q 3.Bxd1 Nh3 4.Bc2+ Ng1 5.Bb1 Nf3 6.Be4+ Ng1 7.Ra2 Nh3 8.Rxg2 Nf2
+- (8.61 ++) Depth: 16/40 00:00:06 1973kN
1.e8B d2 2.Bh5 d1Q 3.Bxd1 Nh3 4.Bc2+ Ng1 5.Bb1 Nf3 6.Be4+ Ng1 7.Ra2 Nh3 8.Rxg2 Nf4 9.Rg3+ Ng2
+- (8.59) Depth: 16/40 00:00:06 2101kN
1.e8B d2 2.Bh5 d1Q 3.Bxd1 Nh3 4.Bc2+ Ng1 5.Bb1 Nf3 6.Be4+ Ng1 7.Ra2 Nh3 8.Rxg2 Nf4 9.Rg3+ Ng2
+- (8.59) Depth: 16/41 00:00:09 2905kN
1.e8B d2 2.Bh5 d1Q 3.Bxd1 Nh3 4.Bc2+ Ng1 5.Bb1 Nf3 6.Be4+ Ng1 7.Ra2 Nh3 8.Rxg2 Nf4 9.Rg3+ Ng2
+- (9.21 ++) Depth: 17/41 00:00:09 2905kN
1.e8B d2 2.Bh5 d1Q 3.Bxd1 Nh3 4.Bc2+ Ng1 5.Bb1 Nf3 6.Be4+ Ng1 7.Ra2 Nh3 8.Rxg2 Nf4 9.Rg3+ Ng2 10.Bxg2+ Kg1
+- (8.70) Depth: 17/41 00:00:10 3116kN
1.e8B d2 2.Bh5 d1Q 3.Bxd1 Nh3 4.Bc2+ Ng1 5.Bb1 Nf3 6.Be4+ Ng1 7.Ra2 Nh3 8.Rxg2 Nf4 9.Rg3+ Ng2 10.Bxg2+ Kg1
+- (8.70) Depth: 17/42 00:00:16 5229kN
1.e8B d2 2.Bh5 d1Q 3.Bxd1 Nh3 4.Bc2+ Ng1 5.Bb1 Nf3 6.Be4+ Ng1 7.Ra2 Nh3 8.Rxg2 Nf4 9.Rg3+ Ng2 10.Bxg2+ Kg1
+- (9.23 ++) Depth: 18/42 00:00:16 5276kN
1.e8B d2 2.Bh5 d1Q 3.Bxd1 Nh3 4.Bc2+ Ng1 5.Bb1 Nf3 6.Be4+ Ng1 7.Ra2 Nf3 8.Bxf3 Kg1 9.Rxg2+ Kf1 10.Rxh2
+- (9.23) Depth: 18/42 00:00:18 5603kN
1.e8B d2 2.Bh5 d1Q 3.Bxd1 Nh3 4.Bc2+ Ng1 5.Bb1 Nf3 6.Be4+ Ng1 7.Ra2 Nf3 8.Bxf3 Kg1 9.Rxg2+ Kf1 10.Rxh2
+- (9.23) Depth: 18/45 00:00:38 11945kN
1.e8B d2 2.Bh5 d1Q 3.Bxd1 Nh3 4.Bc2+ Ng1 5.Bb1 Nf3 6.Be4+ Ng1 7.Ra2 Nf3 8.Bxf3 Kg1 9.Rxg2+ Kf1 10.Rxh2
+- (9.53 ++) Depth: 19/45 00:00:38 12019kN
1.e8B d2 2.Bh5 d1Q 3.Bxd1 Nh3 4.Bc2+ Ng1 5.Bb1 Nf3 6.Be4+ Ng1 7.Ra2 Nf3 8.Bxf3 Kg1 9.Rxg2+ Kf1 10.Rxh2 Kg1
+- (9.41) Depth: 19/45 00:00:40 12639kN

[zullil]

More formally, Can the engines find move 3, which must be
3 Ra1 and not 3 Kf7?

Here's the position after 3 Kf7 d5:

[D] 8/5K2/p7/p2pP3/P7/8/6pp/3R2nk w - d6 0 1

Why is this not a win for White? Here's Stockfish-1.7.1 (8 threads) at depth 43:

Code: Select all

info depth 43 score cp 8904 time 7217102 nodes 74623009325 nps 10339747 pv e5e6 d5d4 e6e7 d4d3 e7e8q d3d2 d1d2 g1f3 d2d3 g2g1q d3f3 g1a7 f7e6 a7b6 e6f5 b6b1 f5g5 b1c1 g5h5 c1b1 f3f8 b1d1 h5g5 d1d5 g5f4 d5d6 f4e4 h1g2 f8g8 g2h1 e8a8 d6d5 e4e3 d5a8 g8a8 h1g2 a8g8 g2f1 g8h8 f1g2 e3d4 h2h1q h8h1 g2h1 d4c5 h1g2 c5b6 g2f3 b6a5 f3e2 a5a6 e2d3 a4a5 d3d2 a6b7 d2e2 b7c7 e2f2 a5a6 f2g3 a6a7 g3f2 a7a8q f2e3 c7d6 

[jarkkop]

FEN: 5K2/p2p4/p7/4P3/P7/8/1R4pp/6nk w - - 0 1

BobboTripleBase in use.
Seems to be drawing line.

IvanHoe999965:

30 00:16 21.379.565 1.326.000 0.00 Rb2b1 a6a5 Kf8e7 a7a6 Ke7xd7
31+ 00:18 24.150.555 1.344.000 +0.08 Rb2b1 a6a5 Kf8e7 a7a6 Ke7xd7
31+ 00:18 24.438.412 1.345.000 +0.16 Rb2b1 a6a5 Kf8e7 a7a6 Ke7xd7
31+ 04:15 374.349.068 1.467.000 +3.98 Rb2b1 a6a5 Kf8e7 a7a6 Ke7xd7
31 10:02 876.810.790 1.456.000 +4.13 Rb2b1 a6a5 Rb1e1 a7a6 Re1d1 d7d5 e5e6 d5d4 e6e7 d4d3 e7e8Q d3d2 Rd1xd2 Ng1f3 Rd2d3 g2g1Q Qe8c6 Qg1g3 Rd3xf3 Qg3xf3+ Qc6xf3+ Kh1g1 Qf3d1+ Kg1g2 Qd1c2+ Kg2g1 Qc2b1+ Kg1g2 Qb1e4+ Kg2g1 Qe4g6+ Kg1f2 Qg6h5 Kf2g1 Qh5g5+ Kg1f2 Qg5c1 Kf2g2 Qc1c6+ Kg2g1 Qc6b6+ Kg1g2 Qb6b2+ Kg2g1 Qb2a1+ Kg1g2 Qa1a2+ Kg2g1 Qa2g8+ Kg1f2 Qg8d5 Kf2g1 Qd5d4+ Kg1g2 Qd4g4+ Kg2f2 Qg4h3 Kf2g1 Qh3g3+ Kg1h1 Qg3e5 Kh1g2 Qe5g7+ Kg2f2 Qg7h6 Kf2g1 Qh6e3+ Kg1g2 Qe3d2+ Kg2g1 Qd2e1+ Kg1g2 Qe1e2+ Kg2g1 Qe2xa6 h2h1Q Qa6b6+ Kg1f1 Qb6b1+ Kf1g2 Qb1e4+ Kg2h2 Qe4f4+ Kh2g1 Qf4d4+ Kg1f1 Qd4d3+ Kf1g2 Qd3d5+ Kg2h2 Qd5e5+ Kh2h3 Qe5h5+ Kh3g2 Qh5g6+ Kg2f2 Qg6c2+ Kf2g3 Qc2c7+ Kg3g4 Qc7d7+ Kg4g5 Qd7e7+ Kg5f4 Qe7c7+ Kf4g5 Qc7g3+ Kg5f6 Qg3d6+ Kf6g5 Qd6e7+

[afzzq]

Let me explain in human terms what is happening in the endgame study (one of my favorites).

(1) If white promotes to a queen, the position is drawn. E.g., after move 13 in the variation with 3 Rd1, even though white wins a queen and a knight for a rook, it is drawn:
[d]5K2/8/p7/p7/P7/5Q2/7p/7k b - - 0 1
draw.
All White can do is keep checking, as soon as white stops, either black is in stalemate or black promotes the pawn.

(2) White's problem here is that he wants his rook on a1 when the black pawn promotes, so that the white bishop can eventually come to b1. But doing so at once fails: the position after 1Rb1 a5 2Ra1? a6!

[d]5K2/3p4/p7/p3P3/P7/8/6pp/R5nk w - - 0 1

is mutual zugzwang. White to play draws, black to play loses. White has no way to lose a move in this position though (if he moves his King to the g file, black promotes with check; if he moves his King to f7, it blocks the bishop; if to the e file, it blocks his own pawn).

That is why White must reach the same position with Black to move, which he does by 2 Rd1!, losing a move, and then 3 Ra1!

So I like the study not only because it is hard but because once a human sees the logic, its answer becomes completely clear and logical. Yet computers seem to have trouble with it.

[zullil]

[D]4Q3/5K2/p7/p7/P7/3R1n2/7p/6qk w - - 0 8

What will happen here?

[afzzq]

4Q3/5K2/p7/p7/P7/3R1n2/7p/6qk w - - 0 8

What will happen here?

That position never arises, black just doesn't play Qg2-g1, in the line you give, but instead sacs the queen for the rook on f3. If you play out a bit deeper the engines get the idea.

[zullil]

4Q3/5K2/p7/p7/P7/3R1n2/7p/6qk w - - 0 8

What will happen here?

That position never arises, black just doesn't play Qg2-g1, in the line you give, but instead sacs the queen for the rook on f3. If you play out a bit deeper the engines get the idea.

I'm still missing something. What should be different in what follows?

[D]5K2/p2p4/p7/4P3/P7/8/1R4pp/6nk w - - 0 1

Code: Select all

[Event "?"]
[Site "?"]
[Date "2010.05.14"]
[Round "?"]
[White "?"]
[Black "?"]
[Result "*"]
[SetUp "1"]
[FEN "5K2/p2p4/p7/4P3/P7/8/1R4pp/6nk w - - 0 1"]

1. Rb1 a5 2. Rd1 a6 3. Kf7 d5 4. e6 d4 5. e7 d3 6. e8=Q d2 7. Rxd2 Nf3 8. Rd3
g1=Q *

[afzzq]

I'm still missing something. What should be different in what follows?

5K2/p2p4/p7/4P3/P7/8/1R4pp/6nk w - - 0 1

Code: Select all

[Event "?"]
[Site "?"]
[Date "2010.05.14"]
[Round "?"]
[White "?"]
[Black "?"]
[Result "*"]
[SetUp "1"]
[FEN "5K2/p2p4/p7/4P3/P7/8/1R4pp/6nk w - - 0 1"]

1. Rb1 a5 2. Rd1 a6 3. Kf7 d5 4. e6 d4 5. e7 d3 6. e8=Q d2 7. Rxd2 Nf3 8. Rd3
g1=Q *

I see your point now. That is a difficult line. Say 9 R:f3 Qa7+ and it looks dangerous. Perhaps someone with large tablebases can shed more light.