interesting endgame position

[jdart]

This occurred in an offline game:

[D] 8/5pk1/b5p1/3R2P1/1P2P3/3p4/2r5/5BK1 b - -

Black played .. d2 and went on to win.

After Bxa6 Rc1+ Kf2 d1=Q Rxd1 Rxd1 we have this endgame:

[D] 8/5pk1/B5p1/6P1/1P2P3/8/5K2/3r4 w - - 0 1

with R and 2 pawns vs B and 3 pawns. Theoretically (per Larry Kaufman's article) the Rook side should be slightly better. But in this case and in other similar cases I have seen the Rook wins. I hate to second guess IM Kaufman but I think maybe he is too conservative about valuing the exchange of R vs B, or at least other factors have to be considered.

Engines differ quite a bit in how they score this. Most seem to want to play d2 early on but give it only a small advantage for black. Shredder however very rapidly sees Black winning:

yes 12 280 +95 259431 d2 Bxa6 Rc1+ Kf2 d1=Q Rxd1 Rxd1 b5 Rb1 e5
Kf8 Ke3 Ke7
yes 13 410 +96 433918 d2 Bxa6 Rc1+ Kf2 d1=Q Rxd1 Rxd1 b5 Rb1 e5
Kf8 Ke3 Ke7 Kd4
yes 14 580 +98 677585 d2 Bxa6 Rc1+ Kf2 d1=Q Rxd1 Rxd1 b5 Rb1 e5
Kf8 Ke3 Ke7 Kd4 Ke6
yes 15 920 +121 1164691 d2 Bxa6 Rc1+ Kg2 d1=Q
yes 16 1590 +124 2013626 d2 Bxa6 Rc1+ Kf2 d1=Q Rxd1 Rxd1 b5 Rb1 e5
Rb3 Ke1 Kf8 Kd2 Ke7 Kc2 Rb4
yes 17 2520 +130 3184997 d2 Bxa6 Rc1+ Kf2 d1=Q Rxd1 Rxd1 b5 Rb1 e5
Rb3 Ke2 Rg3 b6 Rxg5 Kf2 Rf5+ Ke3 Rxe5+
yes 18 3640 +130 4534817 d2 Bxa6 Rc1+ Kf2 d1=Q Rxd1 Rxd1 b5 Rb1 e5
Rb3 Ke2 Rg3 e6 Rxg5 exf7 Re5+ Kf3 Kxf7
yes 19 7500 +112 7802974 d2 Bxa6 Rc1+ Kf2 d1=Q Rxd1 Rxd1 b5 Rb1 e5
Rb3 Ke2 Kf8 Kd2
yes 20 16890 +137 14872298 d2 Bxa6
yes 20 18880 +164 17606910 d2 Bxa6 Rc1+ Kf2 d1=Q Rxd1 Rxd1 b5 Rb1
Ke3 f6 e5 Re1+ Kf2 Rxe5 gxf6+ Kxf6 b6 Re8
yes 21 26230 +177 27852880 d2 Bxa6 Rc1+ Kf2 d1=Q Rxd1 Rxd1 b5 Rb1 e5
Rb3 Kg2 Kf8 Kf2 Ke7 Ke2 Ke6 b6 Rxb6 Bc4+
Ke7
yes 22 35670 +189 41744044 d2 Bxa6 Rc1+ Kf2 d1=Q Rxd1 Rxd1 Ke3 Rb1
Kf4 Rxb4 Ke5 Rb8

[Ovyron]

Theoretically (per Larry Kaufman's article) the Rook side should be slightly better. But in this case and in other similar cases I have seen the Rook wins. I hate to second guess IM Kaufman but I think maybe he is too conservative about valuing the exchange of R vs B, or at least other factors have to be considered.

It does! Latest versions of Rybka use Larry Kaufman's latest values, and Rybka gives an advantage of more than 2 pawns to the rook side fairly quickly:

CPU0: AuthenticAMD x86 Family 6 Model 10 Stepping 0 2133 MHz
Engine: Rybka 2.3.2a 32-bit (64 MB)
by Vasik Rajlich

First position:

10.00 0:00 -1.13 1...d2 2.Bxa6 Rc1+ 3.Kf2 d1Q 4.Rxd1 Rxd1 5.b5 Rb1 6.Ke3 Kf8 (10.182) 51
11.00 0:00 -1.21 1...d2 2.Bxa6 Rc1+ 3.Kf2 d1Q 4.Rxd1 Rxd1 5.b5 Rb1 6.Ke3 Kf8 7.Kd4 (16.008) 52
12.00 0:00 -1.18 1...d2 2.Bxa6 Rc1+ 3.Kf2 d1Q 4.Rxd1 Rxd1 5.b5 Rb1 6.Ke3 Kf8 7.Kd4 Ke7 (22.736) 52
13.00 0:00 -1.13 1...d2 2.Bxa6 Rc1+ 3.Kf2 d1Q 4.Rxd1 Rxd1 5.b5 Rb1 6.Ke3 Kf8 7.Kd4 Ke7 8.Kc4 (35.248) 52
14.00 0:01 -1.22 1...d2 2.Bxa6 Rc1+ 3.Kf2 d1Q 4.Rxd1 Rxd1 5.b5 Rb1 6.Ke3 Kf8 7.Kd4 Ke7 8.Kc4 (61.887) 55
15.00 0:01 -1.22 1...d2 2.Bxa6 Rc1+ 3.Kf2 d1Q 4.Rxd1 Rxd1 5.b5 Rb1 6.Ke3 Kf8 7.Kd4 Ke7 8.Ke5 (90.271) 54
16.01 0:02 -1.34 1...d2 2.Bxa6 Rc1+ 3.Kf2 d1Q 4.Rxd1 Rxd1 5.b5 Rb1 6.Ke3 Kf8 7.Kd4 Ke7 8.Kc5 (153.038) 54
17.01 0:04 -1.19 1...d2 2.Bxa6 Rc1+ 3.Kf2 d1Q 4.Rxd1 Rxd1 5.b5 Rb1 6.Ke3 Kf8 7.Kd4 Ke7 8.Kc5 (228.213) 51
18.01 0:06 -1.34 1...d2 2.Bxa6 Rc1+ 3.Kf2 d1Q 4.Rxd1 Rxd1 5.b5 Rb1 6.Ke3 Kf8 7.Kd4 Ke7 8.Kc5 (340.095) 50
19.01 0:12 -1.51 1...d2 2.Bxa6 Rc1+ 3.Kf2 d1Q 4.Rxd1 Rxd1 5.b5 Rb1 6.Ke3 f6 7.gxf6+ Kxf6 8.Kf3 (652.695) 51
20.01 0:19 -1.72 1...d2 2.Bxa6 Rc1+ 3.Kf2 d1Q 4.Rxd1 Rxd1 5.b5 Rb1 6.Ke3 f6 7.gxf6+ Kxf6 8.Kd2 (1.044.574) 54
21.01 0:31 -1.96 1...d2 2.Bxa6 Rc1+ 3.Kf2 d1Q 4.Rxd1 Rxd1 5.b5 Rb1 6.Ke3 f6 7.gxf6+ Kxf6 8.Kd2 (1.834.123) 58
22.01 0:41 -1.96 1...d2 2.Bxa6 Rc1+ 3.Kf2 d1Q 4.Rxd1 Rxd1 5.b5 Rb1 6.Ke3 f6 7.gxf6+ Kxf6 8.Kd2 (2.370.554) 58
best move: d3-d2 time: 0:48.660 min n/s: 55.840 nodes: 2.644.845

Second position:

10.00 0:00 -1.27 1.b5 Rb1 2.Ke3 Kf8 3.Kd4 Ke7 4.Kc4 (6.431) 38
11.00 0:00 -1.27 1.b5 Rb1 2.Ke3 Kf8 3.Kd4 Ke7 4.Kc4 Kd6 (9.862) 45
12.00 0:00 -1.23 1.b5 Rb1 2.Ke3 Kf8 3.Kd4 Ke7 4.Kc4 Kd6 5.Bb7 (17.180) 46
13.00 0:00 -1.36 1.b5 Rb1 2.Ke3 Kf8 3.Kd4 Ke7 4.Kc5 Kd7 5.b6 Rg1 (27.649) 50
14.00 0:00 -1.38 1.b5 Rb1 2.Ke3 Kf8 3.Kd4 Ke7 4.Kc5 Kd7 5.b6 Rg1 6.Bb5+ Kc8 (39.742) 54
15.00 0:01 -1.23 1.b5 Rb1 2.Ke3 Kf8 3.Kd4 Ke7 4.Kc5 Kd7 5.Kb6 Kd6 6.Bb7 Rg1 (65.443) 53
16.00 0:02 -1.12 1.b5 Rb1 2.Ke3 Kf8 3.Kd4 Ke7 4.Kc5 Kd7 5.Kb6 Kd6 6.Bb7 Rg1 7.Bd5 (95.641) 48
17.01 0:03 -1.32 1.b5 Rb1 2.Ke3 f6 3.gxf6+ Kxf6 4.Kd4 g5 5.e5+ Ke6 6.Bc8+ Ke7 7.Ba6 g4 (190.176) 53
18.01 0:04 -1.28 1.b5 Rb1 2.Ke3 f6 3.gxf6+ Kxf6 4.Kd4 g5 5.e5+ Ke6 6.Bc8+ Ke7 7.Ba6 g4 (243.304) 53
19.01 0:11 -1.76 1.b5 Rb1 2.e5 Kf8 3.Ke3 Ke7 4.Kd4 Kd7 5.Kc4 Rg1 6.b6 Rxg5 7.Bb5+ Kc8 (634.934) 55
20.01 0:16 -1.93 1.b5 Rb1 2.Ke3 f6 3.gxf6+ Kxf6 4.Kd4 g5 5.e5+ Ke7 6.Ke3 Rb4 7.Kd3 g4 (912.041) 58
21.01 0:23 -2.09 1.b5 Rb1 2.Ke3 f6 3.gxf6+ Kxf6 4.Kf4 Rb4 5.Ke3 Ke5 6.Kd3 g5 7.Kc3 Rxe4 (1.449.758) 62

[Harald Johnsen]

At the end of Rybka pv we have this position
[D] 8/8/B7/1P2k1p1/4r3/2K5/8/8 w - -
Tables say it's a win in 28 but on the winning path there are some non obvious positions with only one or two winning moves for black.

This position
[D] 8/8/B5p1/1P6/4k1K1/1r6/8/8 w - -
is Draw.

So the scores here are really too big.

HJ.

[Sven]

Second position:
[...]
21.01 0:23 -2.09 1.b5 Rb1 2.Ke3 f6 3.gxf6+ Kxf6 4.Kf4 Rb4 5.Ke3 Ke5 6.Kd3 g5 7.Kc3 Rxe4 (1.449.758) 62

I would be interested to see Rybka's analysis after 1.b5 Rb1 2.e5 which might be an important improvement for white here IMO.

Sven

[jdart]

Outside of very simple endgames, it is really impossible to replace tablebase knowledge with static evaluation code. So the real question is, what pragmatic rules will you use to guide the program into positions where the tablebases can take over? Trying to optimize the the Rook vs. Bishop trade sore is one way to do this, although you need other rules too, and in any case these rules will be imperfect and will make mistakes.

[PauloSoare]

Second position:
[...]
21.01 0:23 -2.09 1.b5 Rb1 2.Ke3 f6 3.gxf6+ Kxf6 4.Kf4 Rb4 5.Ke3 Ke5 6.Kd3 g5 7.Kc3 Rxe4 (1.449.758) 62

I would be interested to see Rybka's analysis after 1.b5 Rb1 2.e5 which might be an important improvement for white here IMO.

Sven

Sven, not sure, but I think:

1) 1. b5 Rb1?! 2. e5 Rb3! black wins.

2) 1. b5 Rb1?! 2. Ke3 draw.

3) 1. b5 f6! black wins.

Paulo Soares

[Ovyron]

2) 1. b5 Rb1?! 2. Ke3 draw.

Rybka thinks black still wins:

[d]8/5pk1/B5p1/1P4P1/4P3/4K3/8/1r6 b - - 0 1

CPU0: AuthenticAMD x86 Family 6 Model 10 Stepping 0 2133 MHz
Engine: Rybka 2.3.2a 32-bit (64 MB)
by Vasik Rajlich

[Snip]
10.00 0:00 -1.31 2...Kf8 3.Kd4 Ke7 4.Ke5 Rb3 5.Kd5 Kd7 (8.825) 49
11.00 0:00 -1.31 2...Kf8 3.Kd4 Ke7 4.Ke5 Rb3 5.Kd5 Kd7 6.e5 (10.905) 48
12.00 0:00 -1.31 2...Kf8 3.Kd4 Ke7 4.Ke5 Rb3 5.Kd5 Kd7 6.e5 Kc7 (14.916) 50
13.00 0:00 -1.17 2...Kf8 3.Kd4 Ke7 4.Kd5 Rb4 5.Kc5 Rxe4 6.b6 Kd7 7.Bb5+ Kc8 (29.132) 48
14.00 0:01 -1.09 2...Kf8 3.Kd4 Ke7 4.Kd5 Rb4 5.Kc5 Rxe4 6.b6 Kd7 7.Bb5+ Kc8 8.Bc4 (64.512) 46
14.00 0:03 -1.59 2...f6 3.gxf6+ Kxf6 4.Kd2 Ke5 5.Kc2 Rb4 6.Kc3 Rxe4 7.b6 Kd6 8.Bd3 Re6 (168.309) 53
15.01 0:04 -1.72 2...f6 3.gxf6+ Kxf6 4.Kd2 Ke5 5.Kc2 Rb4 6.Kc3 Rxe4 7.b6 Kd6 8.Bb7 Rf4 9.Kd3 (226.817) 55
16.01 0:05 -1.78 2...f6 3.gxf6+ Kxf6 4.Kf3 Rb3+ 5.Kg4 Rb2 6.Kf3 Ke5 7.Kg4 Rb3 8.Kg5 Rg3+ 9.Kh6 (304.754) 58
17.01 0:05 -1.68 2...f6 3.gxf6+ Kxf6 4.Kf3 Rb3+ 5.Kg4 Rb2 6.Kf3 Ke5 7.Kg4 Rb3 8.Kg5 Rg3+ 9.Kh6 (340.607) 58
18.01 0:11 -1.64 2...f6 3.gxf6+ Kxf6 4.Kd4 g5 5.e5+ Ke7 6.Kd3 Ke6 7.Kd4 Rb2 8.Kc5 Rc2+ 9.Kd4 (686.459) 59
19.01 0:15 -1.75 2...f6 3.gxf6+ Kxf6 4.Kd4 g5 5.e5+ Ke7 6.Kd3 Ke6 7.Kd4 Rd1+ 8.Ke4 Re1+ 9.Kd4 (906.150) 60
20.01 0:30 -2.30 2...f6 3.Kf4 Rb4 4.b6 fxg5+ 5.Kxg5 Rxb6 6.Bc4 Rb4 7.Bd5 Rb1 8.Kf4 Rf1+ 9.Ke5 (1.849.564) 63
21.01 0:34 -2.41 2...f6 3.Kf4 Rb4 4.b6 fxg5+ 5.Kxg5 Rxb6 6.Bc4 Rb4 7.Bd5 Ra4 8.Bb7 Ra1 9.e5 (2.184.586) 65
22.01 0:39 -2.41 2...f6 3.Kf4 Rb4 4.b6 fxg5+ 5.Kxg5 Rxb6 6.Bc4 Rb4 7.Bd5 Ra4 8.Bb7 Ra1 9.e5 (2.513.337) 65
23.01 0:50 -2.41 2...f6 3.Kf4 Rb4 4.gxf6+ Kxf6 5.Kf3 g5 6.Kg3 Rb3+ 7.Kg4 Rb4 8.Kf3 Rb3+ 9.Kg4 (3.281.962) 66

[Ignacio]

2) 1. b5 Rb1?! 2. Ke3 draw.

Rybka thinks black still wins:

[d]8/5pk1/B5p1/1P4P1/4P3/4K3/8/1r6 b - - 0 1

CPU0: AuthenticAMD x86 Family 6 Model 10 Stepping 0 2133 MHz
Engine: Rybka 2.3.2a 32-bit (64 MB)
by Vasik Rajlich

[Snip]
10.00 0:00 -1.31 2...Kf8 3.Kd4 Ke7 4.Ke5 Rb3 5.Kd5 Kd7 (8.825) 49
11.00 0:00 -1.31 2...Kf8 3.Kd4 Ke7 4.Ke5 Rb3 5.Kd5 Kd7 6.e5 (10.905) 48
12.00 0:00 -1.31 2...Kf8 3.Kd4 Ke7 4.Ke5 Rb3 5.Kd5 Kd7 6.e5 Kc7 (14.916) 50
13.00 0:00 -1.17 2...Kf8 3.Kd4 Ke7 4.Kd5 Rb4 5.Kc5 Rxe4 6.b6 Kd7 7.Bb5+ Kc8 (29.132) 48
14.00 0:01 -1.09 2...Kf8 3.Kd4 Ke7 4.Kd5 Rb4 5.Kc5 Rxe4 6.b6 Kd7 7.Bb5+ Kc8 8.Bc4 (64.512) 46
14.00 0:03 -1.59 2...f6 3.gxf6+ Kxf6 4.Kd2 Ke5 5.Kc2 Rb4 6.Kc3 Rxe4 7.b6 Kd6 8.Bd3 Re6 (168.309) 53
15.01 0:04 -1.72 2...f6 3.gxf6+ Kxf6 4.Kd2 Ke5 5.Kc2 Rb4 6.Kc3 Rxe4 7.b6 Kd6 8.Bb7 Rf4 9.Kd3 (226.817) 55
16.01 0:05 -1.78 2...f6 3.gxf6+ Kxf6 4.Kf3 Rb3+ 5.Kg4 Rb2 6.Kf3 Ke5 7.Kg4 Rb3 8.Kg5 Rg3+ 9.Kh6 (304.754) 58
17.01 0:05 -1.68 2...f6 3.gxf6+ Kxf6 4.Kf3 Rb3+ 5.Kg4 Rb2 6.Kf3 Ke5 7.Kg4 Rb3 8.Kg5 Rg3+ 9.Kh6 (340.607) 58
18.01 0:11 -1.64 2...f6 3.gxf6+ Kxf6 4.Kd4 g5 5.e5+ Ke7 6.Kd3 Ke6 7.Kd4 Rb2 8.Kc5 Rc2+ 9.Kd4 (686.459) 59
19.01 0:15 -1.75 2...f6 3.gxf6+ Kxf6 4.Kd4 g5 5.e5+ Ke7 6.Kd3 Ke6 7.Kd4 Rd1+ 8.Ke4 Re1+ 9.Kd4 (906.150) 60
20.01 0:30 -2.30 2...f6 3.Kf4 Rb4 4.b6 fxg5+ 5.Kxg5 Rxb6 6.Bc4 Rb4 7.Bd5 Rb1 8.Kf4 Rf1+ 9.Ke5 (1.849.564) 63
21.01 0:34 -2.41 2...f6 3.Kf4 Rb4 4.b6 fxg5+ 5.Kxg5 Rxb6 6.Bc4 Rb4 7.Bd5 Ra4 8.Bb7 Ra1 9.e5 (2.184.586) 65
22.01 0:39 -2.41 2...f6 3.Kf4 Rb4 4.b6 fxg5+ 5.Kxg5 Rxb6 6.Bc4 Rb4 7.Bd5 Ra4 8.Bb7 Ra1 9.e5 (2.513.337) 65
23.01 0:50 -2.41 2...f6 3.Kf4 Rb4 4.gxf6+ Kxf6 5.Kf3 g5 6.Kg3 Rb3+ 7.Kg4 Rb4 8.Kf3 Rb3+ 9.Kg4 (3.281.962) 66

After 2...f6 3.gf6+ Kxf6 4.Kd4 the position is draw.

[Ovyron]

After 2...f6 3.gf6+ Kxf6 4.Kd4 the position is draw.

Rybka doesn't see it:

[d]8/8/B4kp1/1P6/3KP3/8/8/1r6 b - - 0 1

Engine: Rybka 2.3.2a 32-bit (64 MB)

[Snip]
10.00 0:00 -1.65 4...g5 5.Ke3 Rb3+ 6.Kd4 g4 7.e5+ Ke7 8.Kc4 Rb2 (13.279) 50
11.00 0:00 -1.92 4...g5 5.e5+ Ke7 6.Kd3 g4 7.Ke3 Rb3+ 8.Kf2 Kd8 9.Kg2 (30.566) 55
12.00 0:00 -1.61 4...g5 5.e5+ Ke7 6.Kd3 Ke6 7.Kd4 Rb2 8.Bc8+ Ke7 9.Ba6 g4 (40.410) 54
13.00 0:01 -1.92 4...g5 5.e5+ Kf5 6.b6 Rxb6 7.Bc8+ Kg6 8.Kc5 Rb2 9.Be6 Rd2 10.Kc6 (87.068) 58
14.01 0:01 -1.92 4...g5 5.e5+ Kf5 6.b6 Rxb6 7.Bc8+ Kg6 8.Kc5 Rb2 9.Be6 Rd2 10.Kc6 Rd1 (100.551) 59
15.01 0:02 -1.98 4...g5 5.e5+ Kf5 6.b6 Rxb6 7.Bc8+ Kg6 8.Kc5 Rb8 9.Bg4 Kf7 10.Kd6 Rb6+ 11.Kd7 (138.545) 62
16.01 0:08 -2.38 4...g5 5.e5+ Ke7 6.Kd3 g4 7.Ke3 g3 8.Kf3 Rb3+ 9.Kg2 Ke6 10.b6 Kxe5 11.Bc4 (492.906) 58
17.01 0:10 -2.38 4...g5 5.e5+ Ke7 6.Ke4 Rb4+ 7.Kf3 Ke6 8.Bc8+ Kxe5 9.Bd7 Kd6 10.Bc6 Kc5 11.Kg3 (588.655) 59
18.01 0:11 -2.38 4...g5 5.e5+ Ke7 6.Ke4 Rb4+ 7.Kf3 Ke6 8.Bc8+ Kxe5 9.Bd7 Kd6 10.Bc6 Kc5 11.Kg3 (667.554) 60
19.01 0:13 -2.38 4...g5 5.e5+ Ke7 6.Ke4 Rb4+ 7.Kf3 Ke6 8.Bc8+ Kxe5 9.Bd7 Kd6 10.Bc6 Kc5 11.Kg3 (793.608) 61
20.01 0:16 -2.38 4...g5 5.e5+ Ke7 6.Ke4 Rb4+ 7.Kf3 Ke6 8.Bc8+ Kxe5 9.Bd7 Kd6 10.Bc6 Kc5 11.Kg3 (985.121) 61
21.01 0:21 -2.38 4...g5 5.e5+ Ke7 6.Ke4 Rb4+ 7.Kf3 Ke6 8.Bc8+ Kxe5 9.Bd7 Kd6 10.Bc6 Kc5 11.Kg3 (1.293.711) 60
22.01 0:32 -2.38 4...g5 5.e5+ Ke7 6.Ke4 Rb4+ 7.Kf3 Ke6 8.Bc8+ Kxe5 9.Bd7 Kd6 10.Bc6 Kc5 11.Kg3 (1.768.464) 56
23.01 0:49 -2.38 4...g5 5.e5+ Ke7 6.Ke4 Rb4+ 7.Kf3 Ke6 8.Bc8+ Kxe5 9.Bd7 Kd6 10.Bc6 Kc5 11.Kg3 (2.634.210) 54



I guess it's a good test position as other engines also think black is winning by more than a pawn.

[Ignacio]

Try 4...g5 5.e5+ Ke7 6.Kc5