Endgame test position

[Stephen Ham]

Dear readers,

Is this position a draw?

8/5k2/R5p1/7p/3r3P/5BK1/8/8 w

All my 64-bit mp engines (i.e. Rybka 3, Stockfish 1.6.3JA, and Firebird 1.2) with 5-man tablebases are unanimous in claiming White wins.

But as a human player, I think this is a draw that exceeds the engines' horizon. Black can just shuffle his rook along the 4th rank or move his King to g7 and back, so White can't make progress. Right?

Those of you with 6-man tablebases, please let me know what your engines claim.

Thanks in advance.

All the best,
Steve

[Albert Silver]

Dear readers,

Is this position a draw?

[d]8/5k2/R5p1/7p/3r3P/5BK1/8/8 w

All my 64-bit mp engines (i.e. Rybka 3, Stockfish 1.6.3JA, and Firebird 1.2) with 5-man tablebases are unanimous in claiming White wins.

But as a human player, I think this is a draw that exceeds the engines' horizon. Black can just shuffle his rook along the 4th rank or move his King to g7 and back, so White can't make progress. Right?

Those of you with 6-man tablebases, please let me know what your engines claim.

Thanks in advance.

All the best,
Steve

What is their line?

[Marc MP]

Dear readers,

Is this position a draw?
[d]8/5k2/R5p1/7p/3r3P/5BK1/8/8 w

All my 64-bit mp engines (i.e. Rybka 3, Stockfish 1.6.3JA, and Firebird 1.2) with 5-man tablebases are unanimous in claiming White wins.

But as a human player, I think this is a draw that exceeds the engines' horizon. Black can just shuffle his rook along the 4th rank or move his King to g7 and back, so White can't make progress. Right?

Those of you with 6-man tablebases, please let me know what your engines claim.

Thanks in advance.

All the best,
Steve

At depth 31, Toga 1.4.1 SE JA with 5 men EGBB doesn't seems to find a win for white, despite showing quite a high score.

Code: Select all

New game, 120'/40+60'/20+30'
8/5k2/R5p1/7p/3r3P/5BK1/8/8 w - - 0 1

Analysis by Toga II 1.4.1SE JA:

<snip>

1.Rc6 Ra4 2.Rc7+ Ke6 3.Rc5 Kf6 4.Rg5 Rd4 5.Rb5 Ra4 6.Rb8 Kf5 7.Rf8+ Ke5 8.Rc8 Kf6 9.Rc5 Kg7 10.Bd1 Rd4 11.Bc2 Rg4+ 12.Kh3 Kf8 13.Ra5 Ke7 14.Ra7+ Kf6 15.Ra6+ Kf7 
  +-  (2.70)   Depth: 25/56   00:06:37  252mN

1.Rc6 Ra4 2.Rc7+ Ke6 3.Rc5 Kf6 4.Rg5 Rd4 5.Rb5 Ra4 6.Rb8 Kf5 7.Rf8+ Ke5 8.Rc8 Kf6 9.Rc5 Ke6 10.Rg5 Kf6 11.Rb5 Rd4 12.Rb6+ Kf5 13.Ra6 Rb4 14.Ra8 Rd4 15.Ra5+ Ke6 
  +-  (2.70)   Depth: 26/56   00:10:55  419mN

1.Ra8 Ke7 2.Rg8 Kf6 3.Rf8+ Ke5 4.Rc8 Kf5 5.Rc5+ Ke6 6.Be2 Kf6 7.Rc6+ Kf5 8.Rb6 Rd5 9.Ba6 Rd1 10.Bc4 Ke5 11.Be2 Rg1+ 12.Kf2 Rh1 13.Rb5+ Kf6 14.Kg3 Re1 15.Rb6+ Ke5 
  +-  (2.71)   Depth: 26/71   00:13:40  521mN

1.Ra8 Ke7 2.Rg8 Kf6 3.Rf8+ Ke5 4.Rc8 Kf5 5.Rc5+ Ke6 6.Be2 Kf6 7.Rc6+ Kf5 8.Rb6 Rd5 9.Ba6 Rd1 10.Rb4 Kf6 11.Bb7 Ke5 12.Bg2 Rd2 13.Bf3 Rd6 14.Rb7 Rd4 15.Rb5+ Ke6 
  +-  (2.71)   Depth: 27/71   00:15:18  576mN

1.Ra8 Ke7 2.Rg8 Kf6 3.Rf8+ Ke5 4.Rc8 Kf5 5.Be2 Kf6 6.Rc6+ Kf5 7.Rb6 Ra4 8.Bd3+ Ke5 9.Bc2 Ra2 10.Rb5+ Kf6 11.Rc5 Ra3+ 12.Kg2 Ra6 13.Rg5 Kf7 14.Kf2 Ra2 15.Rc5 Ra3 16.Be4 
  +-  (2.71)   Depth: 28/71   00:17:53  666mN

1.Ra8 Ke7 2.Rg8 Kf6 3.Rf8+ Ke5 4.Rc8 Kf5 5.Rc5+ Ke6 6.Rc6+ Kf5 7.Be2 Rd5 8.Bc4 Rd4 9.Ba6 Ke5 10.Be2 Kf5 11.Rb6 Ra4 12.Bd3+ Ke5 13.Ra6 Rb4 14.Be2 Rb3+ 15.Bf3 Kf5 16.Ra4 Re3 
  +-  (2.71)   Depth: 29/77   00:22:13  814mN

1.Ra8 Ke7 2.Rg8 Kf6 3.Rf8+ Ke5 4.Rc8 Kf5 5.Rc5+ Ke6 6.Rc6+ Kf5 7.Be2 Rd5 8.Bc4 Rd4 9.Ba6 Ke5 10.Be2 Kf5 11.Rb6 Ra4 12.Bd3+ Ke5 13.Ra6 Rb4 14.Be2 Rb3+ 15.Bf3 Kf5 16.Ra4 Re3 
  +-  (2.71)   Depth: 30/77   00:31:09  1136mN

1.Ra8 Ke7 2.Rg8 Kf6 3.Rf8+ Ke5 4.Rc8 Kf5 5.Rc6 Ra4 6.Bd1 Ra3+ 7.Kg2 Ra2+ 8.Bc2+ Ke5 9.Rc5+ Kd4 10.Rc8 Ra6 11.Rd8+ Ke5 12.Re8+ Kf6 13.Rc8 Rd6 14.Rc3 Ra6 15.Kg3 Ra1 16.Kf2 Rc1 
  +-  (2.71)   Depth: 31/79   00:46:34  1704mN

[Eelco de Groot]

Hello Steve,

I think that it is a classic fortress position, and it is difficult to have general rules for those. Most programs will just display a score that reflects the material advantage for White but it will not change anymore with depth. If the advantage would be slowly growing that would be a better indicator of an actually winning advantage. I think programmers have tried to incorporate that idea of progress sometimes, Uri for instance has experimented with it but apparently it does not really help the program detect draws, it is usually too late to shift; when you would detect you're in a cul-de-sac, you can't reverse course in chess, that would be cheating

[d]8/5k2/R5p1/7p/3r3P/5BK1/8/8 w - -

Engine: Rainbow Serpent 1.6.3s(dc) Build 274 (Athlon 2009 MHz, 64 MB)
by Tord Romstad, Marco Costalba, Joona Kiiski Modifications: Dann Corbit

1.00 0:00 +3.27 1.Rb6 (162) 0

2.00 0:00 +3.47 1.Rb6 Ke7 2.Rxg6 (201) 0

3.00 0:00 +3.43 1.Rb6 Kg7 2.Re6 (14.032) 39

4.00 0:00 +3.63 1.Rb6 Kg7 2.Re6 Kf7 (18.169) 50

5.00 0:00 +3.27 1.Rb6 Kg7 2.Re6 Kf7 3.Ra6 Kg7 (20.887) 55

5.00 0:00 +3.31 1.Rc6 Kg7 2.Re6 Kf7 3.Ra6 Kg7 4.Ra7+ Kf6
5.Rc7 Ke6 6.Kh3 (167.631) 298

6.00 0:00 +3.47 1.Rc6 Kg7 2.Re6 Kf7 3.Ra6 Kg7 4.Ra7+ Kf6
5.Rc7 Ke6 6.Kh3 (169.508) 301

6.00 0:00 +3.59 1.Rb6 Kg7 2.Re6 Kf7 3.Rc6 Rd7 4.Kf2 (446.154) 483

7.00 0:00 +3.27 1.Rb6 Kg7 2.Re6 Kf7 3.Rc6 Kg7 4.Rb6 Kf7
5.Ra6 Kg7 6.Rc6 Kf7 7.Ra6 (480.569) 496

8.01 0:01 +3.47 1.Rb6 Kg7 2.Re6 Kf7 3.Rc6 Kg7 4.Rb6 Kf7
5.Ra6 Kg7 6.Rc6 Kf7 7.Ra6 (538.898) 514

9.01 0:01 +3.35 1.Rb6 Kg7 2.Re6 Kf7 3.Rc6 Kg7 4.Rb6 Kf7
5.Ra6 Kg7 6.Rc6 Kf7 7.Ra6 (603.916) 529

9.02 0:01 +3.43 1.Rc6 Kg7 2.Rb6 Kf7 3.Ra6 Kg7 4.Rc6 Kf7
5.Be2 Re4 6.Bc4+ Ke7 (626.798) 542

10.01 0:01 +3.62 1.Rc6 Kg7 2.Rb6 Kf7 3.Ra6 Kg7 4.Rc6 Kh6
5.Rc7 Ra4 6.Rd7 Rb4 7.Ra7 (793.965) 577

11.01 0:01 +3.39 1.Rc6 Kg7 2.Rb6 Kf7 3.Ra6 Kg7 4.Rc6 Rb4
5.Bd1 Kf7 6.Rd6 Kg7 7.Bc2 Rg4+ 8.Kh3 Kf7
9.Bd1 Ke7 10.Ra6 Rd4 11.Bf3 Kf7
12.Rc6 Kg7 13.Be2 Kf7 14.Bf3 (1.129.359) 617

12.01 0:02 +3.39 1.Rc6 Kg7 2.Rb6 Kf7 3.Ra6 Kg7 4.Rc6 Rb4
5.Be2 Rd4 6.Rb6 Re4 7.Bd1 Rd4 8.Bc2 Rg4+
9.Kh3 Kf7 10.Bb3+ Ke7 (1.303.425) 636

13.01 0:02 +3.39 1.Rc6 Kg7 2.Rb6 Kf7 3.Ra6 Kg7 4.Rc6 Rb4
5.Be2 Rd4 6.Rb6 Re4 7.Bf3 Rd4 8.Re6 Ra4
9.Be4 Ra3+ 10.Kg2 Ra2+ 11.Kh1 Ra3 (1.667.740) 671

14.01 0:02 +3.39 1.Rc6 Kg7 2.Rb6 Kf7 3.Ra6 Kg7 4.Rc6 Rb4
5.Be2 Rd4 6.Rb6 Re4 7.Bf3 Rd4 8.Re6 Kf7
9.Rc6 (1.933.728) 687

15.01 0:03 +3.39 1.Rc6 Kg7 2.Rb6 Kf7 3.Ra6 Kg7 4.Rc6 Rb4
5.Rd6 Ra4 6.Re6 Rb4 7.Bd1 Rd4 8.Bc2 Rg4+
9.Kh3 Kf7 10.Rb6 g5 11.Bb3+ Ke7
12.Rb7+ Kf6 (2.666.813) 720

16.01 0:05 +3.26 1.Rc6 Kg7 2.Rb6 Kf7 3.Ra6 Kg7 4.Rc6 Rb4
5.Be2 Re4 6.Bd1 Rd4 7.Bc2 Rg4+ 8.Kh3 Kf7
9.Bd1 Rb4 10.Kg3 Rd4 11.Bb3+ Ke7
12.Rc7+ Kd6 13.Rb7 Rg4+ 14.Kh3 (4.078.549) 750

17.01 0:39 +3.26 1.Rc6 Kg7 2.Rb6 Kf7 3.Ra6 Kg7 4.Rc6 Rb4
5.Be2 Re4 6.Bd1 Rd4 7.Bc2 Rg4+ 8.Kh3 Kf7
9.Rc5 Kf6 10.Bd3 Rg1 11.Rc6+ Ke7 (35.266.882) 901

18.01 1:02 +3.27 1.Rc6 Kg7 2.Rb6 Kf7 3.Ra6 Kg7 4.Rc6 Rb4
5.Be2 Re4 6.Bd1 Rd4 7.Bc2 Rg4+ 8.Kh3 Kf7
9.Rc5 Kf6 10.Rb5 Ke6 11.Ra5 Kf6
12.Ra6+ Kf7 13.Bd1 Re4 14.Rc6 (55.961.649) 899

19.01 1:20 +3.07-- 1.Rc6 Kg7 2.Rb6 Kf7 3.Ra6 Kg7 4.Rb6 (72.198.865) 900

20.01 2:48 +3.07 1.Rc6 Kg7 2.Rb6 Kf7 3.Ra6 Kg7 4.Kh3 Kf7
5.Ra8 Kf6 6.Ra5 Rd3 7.Kg3 Rd4 8.Rc5 Ke6
9.Rb5 Kf6 10.Rb7 Ra4 11.Rb5 Rd4 (149.689.537) 890

21.01 7:31 +3.07 1.Rc6 Kg7 2.Rb6 Kf7 3.Ra6 Kg7 4.Kh3 Kf7
5.Ra8 Kf6 6.Ra5 Rd3 7.Kg3 Rd4 8.Rc5 Kf7
9.Rc1 Kf6 10.Rc8 Ra4 11.Rc6+ Kg7
12.Rd6 Kf7 13.Be2 Re4 14.Rd2 (397.666.148) 880

22.01 15:05 +3.06 1.Rc6 Kg7 2.Rb6 Ra4 3.Rb7+ Kf6 4.Rb5 Ke7
5.Rb6 Kf7 6.Rd6 Kg7 7.Rd8 Rb4 8.Rd5 Kf6
9.Bd1 Re4 10.Ra5 Re3+ 11.Bf3 Re5
12.Rxe5 Kxe5 (784.900.414) 866

best move: Ra6-c6 time: 28:22.141 min n/s: 860.491 nodes: 1.464.570.244

[Robert Flesher]

Dear readers,

Is this position a draw?

8/5k2/R5p1/7p/3r3P/5BK1/8/8 w

All my 64-bit mp engines (i.e. Rybka 3, Stockfish 1.6.3JA, and Firebird 1.2) with 5-man tablebases are unanimous in claiming White wins.

But as a human player, I think this is a draw that exceeds the engines' horizon. Black can just shuffle his rook along the 4th rank or move his King to g7 and back, so White can't make progress. Right?

Those of you with 6-man tablebases, please let me know what your engines claim.

Thanks in advance.

All the best,
Steve

One engine seems to understand the fortress.



New game
8/5k2/R5p1/7p/3r3P/5BK1/8/8 w - - 0 1

Analysis by Junior 2010 UCI:

1.Be2 Rb4
+- (2.32) Depth: 3 00:00:00
1.Be2 Re4 2.Bd1 Re6 3.Ra1
+- (2.31) Depth: 3 00:00:00
1.Be2 Re4 2.Bd1 Re6 3.Ra1
+- (2.31) Depth: 6 00:00:00 1kN
1.Be2 Rd2 2.Bf1 Rd4 3.Bh3 Rd3+ 4.Kh2 Rd4
+- (2.20) Depth: 9 00:00:00 45kN
1.Rc6 Ra4 2.Be2 Rd4 3.Bf1
+- (2.31) Depth: 9 00:00:00 77kN
1.Rc6 Ra4 2.Be2 Ra3+ 3.Kf4 Ra4+ 4.Bc4+ Ke7 5.Kg5 Kd7 6.Bb5
+- (1.62) Depth: 12 00:00:00 171kN
1.Rc6 Rb4 2.Rd6 Kg7 3.Ra6 Rc4 4.Be2 Rd4 5.Bf1
+- (1.59) Depth: 15 00:00:00 1628kN
1.Rc6 Rb4 2.Rd6 Kg7 3.Ra6 Kf7 4.Ra5 Ke6
+- (1.41) Depth: 18 00:00:02 7754kN
1.Rc6 Rb4 2.Rd6 Kg7 3.Ra6 Kf7 4.Be2 Re4 5.Bd1 Rd4
± (1.27) Depth: 20 00:00:05 16831kN
1.Rc6 Rb4 2.Rd6 Rb5 3.Bd5+ Ke7 4.Re6+ Kd7 5.Bc4 Rc5 6.Re4 g5 7.Kg2 gxh4 8.Kf3
± (0.85) Depth: 22 00:00:28 95524kN
1.Rc6 Rb4 2.Bd5+ Ke7 3.Re6+ Kd7 4.Re1 Rg4+ 5.Kh3 Kc7 6.Bf3 Rf4 7.Be4 Rg4 8.Rc1+ Kd7 9.Bf3 Rf4
± (0.85) Depth: 23 00:01:15 248064kN
1.Rc6 Rb4 2.Bd5+ Ke7 3.Re6+ Kd7 4.Re1 Rg4+ 5.Kh3 Kc7 6.Bf3 Rf4 7.Be4 Rg4 8.Rc1+ Kd8 9.Bf3 Rf4 10.Kg3
± (0.85) Depth: 24 00:01:38 319819kN
1.Rc6 Rb4 2.Bd5+ Ke7 3.Re6+ Kf8 4.Be4 Kf7 5.Re5 Rb3+ 6.Bf3 Rb4 7.Bd5+ Kf6 8.Re6+ Kf5 9.Ra6 Rg4+ 10.Kh3
± (0.85) Depth: 25 00:02:42 517291kN
1.Rc6 Rb4 2.Rc5 Ra4 3.Be2 Rd4 4.Rc7+ Ke6 5.Rc6+ Rd6 6.Rc5 Rd2 7.Bc4+
± (0.81) Depth: 26 00:06:08 1152720kN

(, Microsoft 03.04.2010)

[michiguel]

Dear readers,

Is this position a draw?

8/5k2/R5p1/7p/3r3P/5BK1/8/8 w

All my 64-bit mp engines (i.e. Rybka 3, Stockfish 1.6.3JA, and Firebird 1.2) with 5-man tablebases are unanimous in claiming White wins.

But as a human player, I think this is a draw that exceeds the engines' horizon. Black can just shuffle his rook along the 4th rank or move his King to g7 and back, so White can't make progress. Right?

Those of you with 6-man tablebases, please let me know what your engines claim.

Thanks in advance.

All the best,
Steve

One engine seems to understand the fortress.



New game
8/5k2/R5p1/7p/3r3P/5BK1/8/8 w - - 0 1

Analysis by Junior 2010 UCI:

1.Be2 Rb4
+- (2.32) Depth: 3 00:00:00
1.Be2 Re4 2.Bd1 Re6 3.Ra1
+- (2.31) Depth: 3 00:00:00
1.Be2 Re4 2.Bd1 Re6 3.Ra1
+- (2.31) Depth: 6 00:00:00 1kN
1.Be2 Rd2 2.Bf1 Rd4 3.Bh3 Rd3+ 4.Kh2 Rd4
+- (2.20) Depth: 9 00:00:00 45kN
1.Rc6 Ra4 2.Be2 Rd4 3.Bf1
+- (2.31) Depth: 9 00:00:00 77kN
1.Rc6 Ra4 2.Be2 Ra3+ 3.Kf4 Ra4+ 4.Bc4+ Ke7 5.Kg5 Kd7 6.Bb5
+- (1.62) Depth: 12 00:00:00 171kN
1.Rc6 Rb4 2.Rd6 Kg7 3.Ra6 Rc4 4.Be2 Rd4 5.Bf1
+- (1.59) Depth: 15 00:00:00 1628kN
1.Rc6 Rb4 2.Rd6 Kg7 3.Ra6 Kf7 4.Ra5 Ke6
+- (1.41) Depth: 18 00:00:02 7754kN
1.Rc6 Rb4 2.Rd6 Kg7 3.Ra6 Kf7 4.Be2 Re4 5.Bd1 Rd4
± (1.27) Depth: 20 00:00:05 16831kN
1.Rc6 Rb4 2.Rd6 Rb5 3.Bd5+ Ke7 4.Re6+ Kd7 5.Bc4 Rc5 6.Re4 g5 7.Kg2 gxh4 8.Kf3
± (0.85) Depth: 22 00:00:28 95524kN
1.Rc6 Rb4 2.Bd5+ Ke7 3.Re6+ Kd7 4.Re1 Rg4+ 5.Kh3 Kc7 6.Bf3 Rf4 7.Be4 Rg4 8.Rc1+ Kd7 9.Bf3 Rf4
± (0.85) Depth: 23 00:01:15 248064kN
1.Rc6 Rb4 2.Bd5+ Ke7 3.Re6+ Kd7 4.Re1 Rg4+ 5.Kh3 Kc7 6.Bf3 Rf4 7.Be4 Rg4 8.Rc1+ Kd8 9.Bf3 Rf4 10.Kg3
± (0.85) Depth: 24 00:01:38 319819kN
1.Rc6 Rb4 2.Bd5+ Ke7 3.Re6+ Kf8 4.Be4 Kf7 5.Re5 Rb3+ 6.Bf3 Rb4 7.Bd5+ Kf6 8.Re6+ Kf5 9.Ra6 Rg4+ 10.Kh3
± (0.85) Depth: 25 00:02:42 517291kN
1.Rc6 Rb4 2.Rc5 Ra4 3.Be2 Rd4 4.Rc7+ Ke6 5.Rc6+ Rd6 6.Rc5 Rd2 7.Bc4+
± (0.81) Depth: 26 00:06:08 1152720kN

(, Microsoft 03.04.2010)

Actually, It does not understand the position because after 6. Rxd6+ Kxd6 7. Kf4 Black loses (that is in the PV). After exchanging the rooks, if white king reaches h6, white wins.

It is a draw because to make progress, white needs to bring the king. To do so, it needs to block the fourth rank. It cannot do it by playing Re4 because the exchange of rooks lead to a draw. It cannot block the 4th rank with the bishop, because the rook will have to be diverted to do that (Re6-e3 for instance) and Black can play Kf6-g5. Any other attempt that involved moving the bishop, will lead to Rg4+ g5.

Miguel

[Mark]

For those that don't read the Rybka forum, here's some info from a post by Dadi Johnson:

Here is what Rybka 3 says at depth 37, with 6 piece tablebases:

[+2.17] d=37 1.Rb6 Kg7 2.Re6 Ra4 3.Rc6 Rd4 4.Re6 Ra4 5.Rc6 Rd4 6.Re6 Ra4 7.Rc6 Rd4 8.Re6 Ra4 9.Rc6 Rd4 10.Re6 Ra4 11.Rc6 Rd4 12.Re6 Ra4 13.Rc6 Rd4 14.Re6 Ra4 15.Rc6 Rd4 16.Re6 (0:37:56) 451593kN

No progress here. I also analyzed the position with IDeA in Aquarium, but it showed the same pattern. The initial evaluation was similar to above and didn't change with deeper analysis.

> But as a human player, I think this is a draw that exceeds the engines' horizon. Black can just shuffle his rook along the 4th rank or move his King to g7 and back, so White can't make progress. Right?


I think so. It also helps that the bishop doesn't cover the queening square of the h4-pawn. Removing the rooks in the initial position gives a tablebase draw.

[Albert Silver]

It is a draw because to make progress, white needs to bring the king. To do so, it needs to block the fourth rank. It cannot do it by playing Re4 because the exchange of rooks lead to a draw.

True, though against a human opponent I would play it out.

[d]8/6k1/6p1/6Kp/4B2P/8/8/8 b - - 0 6

The player might become careless and think anything draws and decide to just stick his king on g8 or h8 which would lose.

Albert