Endgame: Is this a draw?

[govert]

From an engine tournament of mine. I adjudicated it as 1/2-1/2, but I don't trust my judgement.

[d] 5n2/1R5p/8/5K2/3k4/2b5/6B1/8 b - - 21 77


Is there any software out there that can prove this position?

[skoony]

hi martin,
i loaded rybka2.2n2 in winboard,time control
20 moves in 3 minutes.
by move 43 it was king and bishop v king and rook.
i stopped the game and loaded it into scid.
using crafty with 4 megtb crafty says draw
starting with rook b8.

regards,
mike

[Event "Computer chess game"]
[Site "LAPTOP1"]
[Date "2010.02.12"]
[Round "-"]
[White "Rybka 2.2n2 mp 32-bit"]
[Black "Rybka 2.2n2 mp 32-bit"]
[Result "*"]
[TimeControl "20/180"]
[SetUp "1"]
[FEN "5n2/1R5p/8/5K2/3k4/2b5/6B1/8 b - - 0 1"]

1...Be1 2.Bf1 Bd2 3.Re7 Bb4 4.Re4+ Kc3 5.Re3+ Kb2 6.Bc4 Bd2 7.Re7 Kc3 8.
Bg8 h5 9.Re4 Nd7 10.Rh4 Be1 11.Rxh5 Nc5 12.Rh2 Nb7 13.Rh3+ Kd2 14.Bb3 Bf2
15.Bd5 Nd6+ 16.Kf6 Bd4+ 17.Kg6 Be5 18.Rh5 Bf4 19.Be6 Ne8 20.Rd5+ Ke3 21.
Bf5 Kf2 22.Ra5 Be3 23.Ra2+ Kg3 24.Be4 Nd6 25.Bc6 Nc4 26.Rg2+ Kf4 27.Kh5
Ne5 28.Bb7 Bc5 29.Ra2 Nd7 30.Ra4+ Ke5 31.Bc6 Kd6 32.Bxd7 Kxd7 33.Rg4 Kc6
34.Rg3 Kb5 35.Rg2 Ba3 36.Rg5+ Kc4 37.Rg4+ Kb5 38.Re4 Bd6 39.Re1 Kb4 40.
Rb1+ Kc4 41.Rc1+ Kb3 42.Ra1 Bc5 43.Rb1+ Kc2 44.Rb8 *

[Trahald]

If there is an engine that can access 6 piece tablebases in search, I guess that could give you a definite answer, but I'm not sure if such an engine exists.

In practice though I guess most engines would lose this with Black. For example Rybka 3 Human with 5 piece TB's evaluates this position as 0.27 at d29 and starts with the moves 1... Ng6 2.Rxh7, this gives a position which is actually a tablebase win for White in 72 moves! Maybe even then Black could hold with perfect defense by the 50 move rule, I haven't followed that line to see where the next capture occurs.

At least if Rybka 3 can make such a dubious choice as Black on move 1, then I would say that White has enough chances to play on.

[zamar]

Hmmm...

From 6 pieces tablebases we see that KRB vs. KBN (opposite color bishops) is usually won, so it comes down to the question whether or not white can capture black's extra pawn. Black's knight is so badly placed, that this might be possible...

[govert]

A 6-men DTC online tablebase would also be nice, but I don't suppose there is one is there?

[Jim Walker]

Why adjudicate this game? It should be played to it's conclusion. Anything else is pure speculation as to what would have happened. It doesn't matter what a 7 man tablebase says.
Jim

[alpha123]

Shredder with 6-piece Nalimov TBs should give you the result.

Or Freezer, which is a special endgame tool.

Peter

[Eelco de Groot]

Hmmm...

From 6 pieces tablebases we see that KRB vs. KBN (opposite color bishops) is usually won, so it comes down to the question whether or not white can capture black's extra pawn. Black's knight is so badly placed, that this might be possible...

Amazingly this might indeed be the case, just running the given position, this is no proof of course but in the last two mainlines White actually wins the h-pawn and then it would possibly be a technical win. Stockfish and Rainbow Serpent do not know that the KRB vs. KBN opposite with color bishops is won here though so they think the loss of the pawn does not change much in the eval. Maybe Black can defend better and force an exchange of pieces, and then I think White can no longer win?. If you could prove that the pawn is always purely lost without a further piece exchange then you could classify the resulting 6 men endgames. The 50 move rule would make this a draw though, after the capture of the pawn it takes White more than 50 moves, at least in the given line it would still appear to be a '50 moves rule' draw.


[d]5n2/1R5p/8/5K2/3k4/2b5/6B1/8 b - -

Engine: Rainbow Serpent 1.6.3s(dc) Build 102 (Athlon 2009 MHz, 64 MB)
by Tord Romstad, Marco Costalba, Joona Kiiski Modifications: Dann Corbit

10.00 0:00 -0.52 1...Bd2 2.Be4 Bc3 3.Rc7 h5 4.Rc8 Bb4
5.Rd8+ Kc4 6.Bd3+ Kc3 7.Be4 (75.889) 167

11.00 0:00 -0.52 1...Bd2 2.Be4 Bc3 3.Rb6 Ke3 4.Rd6 Bd4
5.Rh6 Bc3 6.Rh3+ Kd4 7.Rd3+ Kc4 (161.497) 234

12.00 0:00 -0.52 1...Bd2 2.Be4 Bc3 3.Rb6 Ke3 4.Rd6 Bd4
5.Rh6 Bc3 6.Rh3+ Kd4 7.Rd3+ Kc4
8.Rh3 (233.773) 257

13.00 0:01 -0.52 1...Bd2 2.Be4 Bc3 3.Rb6 Ke3 4.Rd6 Bd4
5.Rh6 Bc3 6.Rh3+ Kd4 7.Rd3+ Kc4
8.Rd6 Bb4 9.Bd5+ Kc5 (401.884) 302

14.01 0:02 -0.52 1...Bd2 2.Be4 Bc3 3.Rb6 Ke3 4.Rd6 Bd4
5.Rh6 Bc3 6.Rh3+ Kd4 7.Rd3+ Kc4
8.Rd6 Bb4 9.Bd5+ Kc5 (671.732) 333

15.01 0:02 -0.52 1...Bd2 2.Be4 Bc3 3.Rb6 Ke3 4.Rd6 Bd4
5.Rh6 Bc3 6.Rh3+ Kd4 7.Rd3+ Kc4
8.Rd1 Ng6 9.Rd7 Ne5 10.Rxh7 Kd4
11.Rc7 (1.026.188) 360

16.01 0:05 -0.52 1...Bd2 2.Be4 Bc3 3.Rb6 Ke3 4.Rd6 Bd4
5.Rh6 Bc3 6.Rh3+ Kd4 7.Rd3+ Kc4
8.Rd1 Kc5 9.Rd8 Ng6 10.Rd5+ Kc4
11.Rd7 Ne5 12.Rxh7 Kd4 13.Rc7 Bb4 (2.137.709) 384

17.01 0:10 -0.52 1...Bd2 2.Be4 Bc3 3.Rb6 Ke3 4.Rd6 Bd4
5.Rh6 Bc3 6.Rh3+ Kd4 7.Rd3+ Kc4
8.Rd1 Kc5 9.Rd8 Ng6 10.Rd5+ Kc4
11.Rd7 Ne5 12.Rxh7 Kd4 13.Rh1 (4.343.424) 395

18.01 0:13 -0.52 1...Bd2 2.Be4 Bc3 3.Rb6 Ke3 4.Rd6 Bd4
5.Rh6 Bc3 6.Rh3+ Kd4 7.Rd3+ Kc4
8.Rd1 Kc5 9.Rd8 Bg7 10.Rd2 Kc4
11.Rh2 Kc5 12.Rh1 (5.321.453) 398

19.01 0:18 -0.52 1...Bd2 2.Be4 Bc3 3.Rb6 Ke3 4.Rd6 Bd4
5.Rh6 Bc3 6.Rh3+ Kd4 7.Rd3+ Kc4
8.Rd1 Kc5 9.Rd8 Bg7 10.Rd2 Kc4
11.Rh2 Kc5 12.Rh1 Kd6 (7.393.122) 399

20.01 0:24 -0.52 1...Bd2 2.Be4 Bc3 3.Rb6 Ke3 4.Rd6 Bd4
5.Rh6 Bc3 6.Rh3+ Kd4 7.Rd3+ Kc4
8.Rd1 Kc5 9.Rd8 Bg7 10.Rd2 Kc4
11.Rh2 Kc5 12.Rh1 Kc4 13.Rd1 h6
14.Rh1 (9.834.009) 404

21.01 0:32 -0.52 1...Bd2 2.Be4 Bc3 3.Rb6 Ke3 4.Rd6 Bd4
5.Rh6 Bc3 6.Rh3+ Kd4 7.Rd3+ Kc4
8.Rd1 Kc5 9.Rd8 Bg7 10.Rd2 Kc4
11.Rh2 Kc5 12.Rh1 Kc4 13.Rd1 h6
14.Rh1 (13.333.788) 408

22.01 0:39 -0.52 1...Bd2 2.Be4 Bc3 3.Rb6 Ke3 4.Rd6 Bd4
5.Rh6 Bc3 6.Rh3+ Kd4 7.Rd3+ Kc4
8.Rd1 Kc5 9.Rd8 Bg7 10.Rd2 Kc4
11.Rh2 Kc5 12.Rh1 Kc4 13.Rd1 h6
14.Rh1 (16.432.728) 414

23.01 0:54 -0.52 1...Bd2 2.Be4 Bc3 3.Rb6 Ke3 4.Rd6 Bd4
5.Rh6 Bc3 6.Rh3+ Kd4 7.Rd3+ Kc4
8.Rd1 Kc5 9.Rd8 Bg7 10.Rd2 Kc4
11.Rh2 Kc5 12.Rh1 Kc4 13.Rd1 h6
14.Rd8 h5 (22.649.533) 418

24.01 1:16 -0.52 1...Bd2 2.Be4 Bc3 3.Rb6 Ke3 4.Rd6 Bd4
5.Rh6 Bc3 6.Rh3+ Kd4 7.Rd3+ Kc4
8.Rd1 Kc5 9.Rd8 Bg7 10.Rd2 Kc4
11.Rh2 Kc5 12.Rh1 Kc4 13.Rd1 h6
14.Rd8 h5 (32.233.543) 421

25.01 2:00 -0.52 1...Bd2 2.Be4 Bc3 3.Rb6 Ke3 4.Rd6 Bd4
5.Rh6 Bc3 6.Rh3+ Kd4 7.Rd3+ Kc4
8.Rd1 Kc5 9.Rd8 Bg7 10.Rd2 Kc4
11.Rh2 Kc5 12.Rh1 Kc4 13.Rd1 h6
14.Rd8 h5 (50.537.470) 418

26.01 3:52 -0.52 1...Bd2 2.Be4 Bc3 3.Rb6 Ke3 4.Rd6 Bd4
5.Rh6 Bc3 6.Rh3+ Kd4 7.Rd3+ Kc4
8.Rd1 Kc5 9.Rd8 Bg7 10.Rd2 Kc4
11.Rh2 Kc5 12.Rh1 Kc4 13.Rd1 h6
14.Rd8 h5 (96.171.494) 413

27.01 17:14 -0.52 1...Bd2 2.Be4 Be1 3.Rb1 Bc3 4.Rd1+ Kc4
5.Rd8 Ng6 6.Rd7 Nf8 7.Bd3+ Kc5
8.Rc7+ Kd4 9.Be2 Be1 10.Rc4+ Kd5
11.Rc1 Bb4 12.Rh1 Kd4 13.Rh4+ Kc3
14.Rc4+ Kd2 (409.327.142) 395

28.01 32:49 -0.56 1...Bd2 2.Be4 Be1 3.Rb8 Ng6 4.Rd8+ Kc4
5.Bd3+ Kc3 6.Bb1 Ne7+ 7.Kg5 Ng6
8.Rd7 Nf8 9.Rf7 Ne6+ 10.Kf6 Nd4
11.Rxh7 {This is technically won but takes more
than 50 moves, diagram below}
11...Kc4 12.Be4 Bg3 13.Rd7 Bh4+
14.Kg6 Kc5 (776.523.397) 394

29.01 54:07 -0.56 1...Bd2 2.Be4 Be1 3.Rb8 Ng6 4.Rd8+ Kc4
5.Bd3+ Kc3 6.Bb1 Ne7+ 7.Kg5 Ng6
8.Rd7 Nf8 9.Rf7 Ne6+ 10.Kf6 Nd4
11.Rxh7 Kc4 12.Be4 Bg3 13.Rd7 Bh4+
14.Kg6 Kc5 (1.281.732.142) 394

After 14... Kc5

[d]8/3R4/6K1/2k5/3nB2b/8/8/8 w - -

Shredder online 6-men tablebases say this is a mate in 80 moves with 15. Bb7, 15. Rh7 or 15. Rd5

After 11. Rxh7 six pieces are left

[d]8/7R/5K2/8/3n4/2k5/8/1B2b3 b - -

Here White gives mate in 77 moves after 11... Bg3 or 11... Kc4

[govert]

Why adjudicate this game? It should be played to it's conclusion. Anything else is pure speculation as to what would have happened. It doesn't matter what a 7 man tablebase says.
Jim

Yes I know. But I didn't. And now I'm curious...

[Mark]

I let R3 run for about 45 minutes with the krbkbn tablebases loaded and it didn't make a lot of progress:

[+0.32] d=26 77...Ke3 78.Bf1 Kd2 79.Re7 Kc2 80.Rf7 (0:24:42) 213805kN