2 Bishops, 9 Pawns: only for big machines!

[ernest]

Pierre Nolot sent me this position by Mark Dvoretsky, calling it as one of his favorites!

Black to move, only Kf6! wins.

How many hours (days...) on your machine?
Houdini? or other?
Do endgame tablebases help?

[d]8/4p1kp/3p2p1/2pP2b1/B1P1P1P1/K7/8/8 b - - bm Kg7f6!; (Dvor) 124

[Evert]

Pierre Nolot sent me this position by Mark Dvoretsky, calling it as one of his favorites!

Black to move, only Kf6! wins.

How many hours (days...) on your machine?
Houdini? or other?
Do endgame tablebases help?

[d]8/4p1kp/3p2p1/2pP2b1/B1P1P1P1/K7/8/8 b - - bm Kg7f6!; (Dvor) 124

How many days until what?
Jazz selects 1. ... Kf6 at depth 6 after 0.01 seconds but it clearly doesn't understand the position very well since the score isn't that high (as expected, because the search depth is small). Thing is though that Kf6 is a fairly obvious candidate to look at, so it's likely to be picked for the wrong reasons. The continuation is probably more interesting...

[ernest]

The continuation is probably more interesting...

Where is the continuation?...

[kbhearn]

I think i remember this position from one of dvoretsky's books. it's a later position in an opposite bishop ending - the step to get to this position (and thus needing to recognise that it's won) involves sacrificing black's extra pawn. That might be a better test. I'll see if i can dig it up.

[kbhearn]

Full analysis of these positions is available in School of Chess Excellence I: Endgame Analysis by Mark Dvoretsky, chapter "what remained offstage"

The first position presented:
[d]8/2k1pp1p/3p2p1/2pP1PP1/2P1P1P1/pK6/8/1Bb5 b - -

It's asserted that the black king must come to g7 to make progress, hard to give it as a test position though as it's not really a fixed line thing. Still finding a plan to progress could be the biggest issue a computer faces.

Here's the first position given as a challenge to the reader:
[d]8/4ppkp/3p2p1/2pP1PP1/B1P1P1P1/p7/K7/2b5 b - -

There are however two winning moves supplied, neither is simple.
Bxg5! and f6!

Bxg5 leads to the position in ernest's post in one line.

[kbhearn]

though now that i've let stockfish look at it i see that it nails the two earlier positions and fails miserably in ernest's original diagram - the problem is that it believes h5? is winning when it leads through saccing the e-pawn to an opposite bishop fortress relying in some cases on wrong-rook-pawn (even after the line is played out to the e-pawn sac stockfish is stuck scoring the position at -3 shuffling the bishop around to avoid rep).

edit: switched engine configuration to a larger hash and at depth 41 after 150s it finally switches to Kf6 as its first choice, though not by a large margin. depth 42 might take longer than i care to wait :)

[peter]

How many hours (days...) on your machine?

Depends on which variant and eval of an engine's output you rely on, but you definitely don't need big machine here with Quazar, using one core only anyhow:

Code: Select all

8/4p1kp/3p2p1/2pP2b1/B1P1P1P1/K7/8/8 b - - 0 1

Analysis by Quazar 0.4 x64:

1...Kf6 2.Lc2 Le3 3.Kb3 h5 4.Ld1 h4 
  -+  (-1.90 ++)   Tiefe: 7   00:00:03  1kN
...
1...Kf6 2.Ld1 Ke5 3.Lf3 Kf4 4.Ld1 Kxe4 5.Ka4 Kd4 6.Kb3 Kd3 7.Lf3 Le3 8.Ld1 Ld4 9.Lf3 Ke3 10.Ld1 Lf6 11.Kc2 Lg5 12.Kb3 Kd2 13.Lf3 Lf6 14.Ka4 Ke3 15.Ld1 Kf4 16.Le2 Kg5 17.Kb5 h5 18.gxh5 gxh5 19.Lf1 h4 20.Lh3 Kf4 21.Kc6 Kg3 22.Lf5 h3 23.Le4 h2 
  -+  (-4.04 ++)   Tiefe: 36   00:00:13  9749kN
...
1...Kf6 2.Ld1 Ke5 3.Ka2 Kd4 4.Le2 Ke3 5.Ld1 Kxe4 6.Le2 Kd4 7.Ka3 Ke3 8.Ld1 Kd3 9.Kb3 Kd2 10.Lf3 Kd3 11.Ld1 
  -+  (-5.15 ++)   Tiefe: 51   00:03:29  218mN
...
1...Kf6 2.Ld1 Ke5 3.Lf3 Kf4 4.Ld1 Kxe4 5.Kb3 Kd3 6.Lf3 Ke3 7.Ld1 Kd2 8.Lf3 Ke3 
  -+  (-9.92)   Tiefe: 51   00:17:27  1099mN
...
1...Kf6 2.Kb2 Ke5 3.Kb1 Kxe4 4.Kc2 h5 5.gxh5 gxh5 6.Kd1 Kd3 7.Le8 Kxc4 8.Lxh5 Kxd5 9.Ke2 c4 10.Ke1 Kd4 11.Le8 e5 12.Lf7 d5 13.Lg8 e4 14.Kf2 
  -+  (-21.90 ++)   Tiefe: 53   01:40:21  6425mN
...
1...Kf6 2.Kb2 Ke5 3.Ka3 h5 4.Ld1 h4 5.Lc2 h3 6.Ka4 h2 7.Kb5 h1D 8.Kb6 Kd4 9.Ka7 Ke5 10.Kb8 Dxe4 11.Ka8 Dxc2 
  -+  (-30.53 ++)   Tiefe: 64   06:56:15  28222mN

Do endgame tablebases help?

Don't think so neither, at least Quazar doesn't need them here obviously.
You remember Erdogan Günes' posting about the study in CSS? Quazar is good for a nice surprise again,

[Uri Blass]

Pierre Nolot sent me this position by Mark Dvoretsky, calling it as one of his favorites!

Black to move, only Kf6! wins.

How many hours (days...) on your machine?
Houdini? or other?
Do endgame tablebases help?

[d]8/4p1kp/3p2p1/2pP2b1/B1P1P1P1/K7/8/8 b - - bm Kg7f6!; (Dvor) 124

How many days until what?
Jazz selects 1. ... Kf6 at depth 6 after 0.01 seconds but it clearly doesn't understand the position very well since the score isn't that high (as expected, because the search depth is small). Thing is though that Kf6 is a fairly obvious candidate to look at, so it's likely to be picked for the wrong reasons. The continuation is probably more interesting...

I think that the test is only for strong programs and probably a strong program that selects Kf6 after a significant time does it for the right reason.
stockfish2.2.2 selects Kf6 at depth 1 but changes its mind to h5 at depth 21 after less than 2 million nodes.

In case that the position is correct
I guess that h5 wins some material that is not enough to win the game
when Kf6 does not win material(assuming that you do not look very deep) so probably all top programs are going to select h5

[Uri Blass]

Pierre Nolot sent me this position by Mark Dvoretsky, calling it as one of his favorites!

Black to move, only Kf6! wins.

How many hours (days...) on your machine?
Houdini? or other?
Do endgame tablebases help?

[d]8/4p1kp/3p2p1/2pP2b1/B1P1P1P1/K7/8/8 b - - bm Kg7f6!; (Dvor) 124

I will be surprised if houdini is the fastest in some endgame test position.

Endgames are not the strong part of houdini.

I remember that stockfish was clearly stronger than houdini in winning against tablebases test and I think that even with slightly more pieces stockfish is stronger.

Unfortunately I do not know about endgame rating list when you start only from positions when white and black have not more than one single piece.

[Uri Blass]

Pierre Nolot sent me this position by Mark Dvoretsky, calling it as one of his favorites!

Black to move, only Kf6! wins.

How many hours (days...) on your machine?
Houdini? or other?
Do endgame tablebases help?

[d]8/4p1kp/3p2p1/2pP2b1/B1P1P1P1/K7/8/8 b - - bm Kg7f6!; (Dvor) 124

How many days until what?
Jazz selects 1. ... Kf6 at depth 6 after 0.01 seconds but it clearly doesn't understand the position very well since the score isn't that high (as expected, because the search depth is small). Thing is though that Kf6 is a fairly obvious candidate to look at, so it's likely to be picked for the wrong reasons. The continuation is probably more interesting...

I think that the test is only for strong programs and probably a strong program that selects Kf6 after a significant time does it for the right reason.
stockfish2.2.2 selects Kf6 at depth 1 but changes its mind to h5 at depth 21 after less than 2 million nodes.

In case that the position is correct
I guess that h5 wins some material that is not enough to win the game
when Kf6 does not win material(assuming that you do not look very deep) so probably all top programs are going to select h5

I guess that my guess is wrong because my own movei that has not special knowledge about endgames selects Kf6 even after a significant time and the score is increasing every iteration.

In other words the position is really a bad test position because the score for Kf6 is increasing every iteration from iteration 20 to 24 so it seems that it is easy to see that Kf6 wins something and
it is not obvious that programs without special knowledge are going to choose h5 if they search deep enough(this is what I initially thought)
espacially when houdini3 with 2 options showed significant difference between the evaluation of Kf6 and the evaluation of h5 and prefered h5.


FEN: 8/4p1kp/3p2p1/2pP2b1/B1P1P1P1/K7/8/8 b - - 0 1

Movei00_8_438:
1 00:00 28 0 +0.70 h7-h5
2 00:00 64 0 +0.56 h7-h5 Ba4-d7
2 00:00 138 0 +0.56 h7-h5 Ba4-d7
3 00:00 191 0 +0.82 h7-h5 g4xh5 g6xh5
3 00:00 309 0 +0.82 h7-h5 g4xh5 g6xh5
4 00:00 489 0 +0.58 h7-h5 g4xh5 Bg5-c1+ Ka3-b3 g6xh5
4 00:00 1,045 0 +0.59 Kg7-f6
4 00:00 1,306 0 +0.63 Kg7-f6 Ka3-b2 Kf6-e5 Ba4-c2
4 00:00 1,420 0 +0.63 Kg7-f6 Ka3-b2 Kf6-e5 Ba4-c2
5 00:00 1,874 0 +0.87 Kg7-f6 Ka3-b2 Kf6-e5 Ba4-c2 e7-e6
5 00:00 2,475 0 +0.87 Kg7-f6 Ka3-b2 Kf6-e5 Ba4-c2 e7-e6
6 00:00 4,837 0 +0.96 Kg7-f6 Ka3-b2 Kf6-e5 Kb2-c3 Ke5xe4 Ba4-c2+ Ke4-f3
6 00:00 6,648 0 +0.96 Kg7-f6 Ka3-b2 Kf6-e5 Kb2-c3 Ke5xe4 Ba4-c2+ Ke4-f3
7 00:00 8,447 0 +1.04 Kg7-f6 Ka3-b2 Kf6-e5 Kb2-c3 Ke5xe4 Ba4-d7 Bg5-f6+ Kc3-d2
7 00:00 10,594 0 +1.04 Kg7-f6 Ka3-b2 Kf6-e5 Kb2-c3 Ke5xe4 Ba4-d7 Bg5-f6+ Kc3-d2
8 00:00 15,586 0 +1.12 Kg7-f6 Ka3-b2 Kf6-e5 Ba4-d7 Bg5-f6 Kb2-c2 Ke5xe4 Bd7-e6
8 00:00 21,176 0 +1.12 Kg7-f6 Ka3-b2 Kf6-e5 Ba4-d7 Bg5-f6 Kb2-c2 Ke5xe4 Bd7-e6
9 00:00 28,722 0 +1.11 Kg7-f6 Ka3-b2 Kf6-e5 Kb2-c3 Ke5xe4 Ba4-d7
9 00:00 38,568 0 +1.11 Kg7-f6 Ka3-b2 Kf6-e5 Kb2-c3 Ke5xe4 Ba4-d7
10 00:00 54,572 0 +1.17 Kg7-f6 Ka3-b2 Kf6-e5 Ba4-d7 Ke5-d4 Kb2-b3 Kd4xe4 Kb3-c2
10 00:00 70,191 0 +1.17 Kg7-f6 Ka3-b2 Kf6-e5 Ba4-d7 Ke5-d4 Kb2-b3 Kd4xe4 Kb3-c2
11 00:00 92,085 0 +1.17 Kg7-f6 Ka3-b2 Kf6-e5 Ba4-d7 Ke5-d4 Kb2-b3 Kd4xe4
11 00:00 117,729 0 +1.17 Kg7-f6 Ka3-b2 Kf6-e5 Ba4-d7 Ke5-d4 Kb2-b3 Kd4xe4
12 00:00 195,208 0 +1.21 Kg7-f6 Ka3-b2 Kf6-e5 Ba4-d7 Ke5xe4 Bd7-a4 h7-h5 Ba4-c2+ Ke4-d4 g4xh5 g6xh5
12 00:00 240,261 0 +1.21 Kg7-f6 Ka3-b2 Kf6-e5 Ba4-d7 Ke5xe4 Bd7-a4 h7-h5 Ba4-c2+ Ke4-d4 g4xh5 g6xh5
13 00:00 380,803 0 +1.21 Kg7-f6 Ka3-b2 Kf6-e5 Kb2-c3 Ke5xe4 Ba4-e8 Bg5-f6+ Kc3-d2 Bf6-e5 Kd2-e2 Be5-f4 Be8-d7
13 00:00 463,032 0 +1.21 Kg7-f6 Ka3-b2 Kf6-e5 Kb2-c3 Ke5xe4 Ba4-e8 Bg5-f6+ Kc3-d2 Bf6-e5 Kd2-e2 Be5-f4 Be8-d7
14 00:00 673,501 0 +1.24 Kg7-f6 Ka3-b2 Kf6-e5 Kb2-c3 Ke5xe4 Ba4-e8 Bg5-f6+ Kc3-d2 Bf6-d4 Kd2-e2 Ke4-f4 Be8-d7
14 00:00 793,618 0 +1.24 Kg7-f6 Ka3-b2 Kf6-e5 Kb2-c3 Ke5xe4 Ba4-e8 Bg5-f6+ Kc3-d2 Bf6-d4 Kd2-e2 Ke4-f4 Be8-d7
15 00:01 1,483,258 0 +1.25 Kg7-f6 Ka3-b2 Kf6-e5 Kb2-c3 Ke5xe4 Ba4-e8 Bg5-f6+ Kc3-d2 Bf6-e5 Be8-a4 Ke4-d4 Ba4-b5
15 00:01 1,680,596 0 +1.25 Kg7-f6 Ka3-b2 Kf6-e5 Kb2-c3 Ke5xe4 Ba4-e8 Bg5-f6+ Kc3-d2 Bf6-e5 Be8-a4 Ke4-d4 Ba4-b5
16 00:03 3,824,904 0 +1.26 Kg7-f6 Ba4-d1 Kf6-e5 Ka3-a4 Ke5xe4 Ka4-b5 Ke4-d3 Bd1-f3 Bg5-f6 Bf3-d1
16 00:03 4,200,638 0 +1.26 Kg7-f6 Ba4-d1 Kf6-e5 Ka3-a4 Ke5xe4 Ka4-b5 Ke4-d3 Bd1-f3 Bg5-f6 Bf3-d1
17 00:04 4,845,820 0 +1.28 Kg7-f6 Ba4-d1 Kf6-e5 Ka3-a4 Ke5xe4 Ka4-b5 Ke4-d3 Bd1-f3 Bg5-f6 Bf3-d1 Bf6-d4 Bd1-f3 Kd3-e3 Bf3-d1 Bd4-c3
17 00:05 5,511,423 0 +1.28 Kg7-f6 Ba4-d1 Kf6-e5 Ka3-a4 Ke5xe4 Ka4-b5 Ke4-d3 Bd1-f3 Bg5-f6 Bf3-d1 Bf6-d4 Bd1-f3 Kd3-e3 Bf3-d1 Bd4-c3
18 00:06 6,779,365 0 +1.28 Kg7-f6 Ba4-d1 Kf6-e5 Ka3-a4 Ke5xe4 Ka4-b5 Ke4-d3 Bd1-f3 Bg5-f6 Bf3-d1 Bf6-d4 Bd1-f3 Bd4-e3
18 00:07 7,960,624 0 +1.28 Kg7-f6 Ba4-d1 Kf6-e5 Ka3-a4 Ke5xe4 Ka4-b5 Ke4-d3 Bd1-f3 Bg5-f6 Bf3-d1 Bf6-d4 Bd1-f3 Bd4-e3
19 00:09 10,164,673 0 +1.28 Kg7-f6 Ba4-d1 Kf6-e5 Ka3-a4 Ke5xe4 Ka4-b5 Ke4-d3 Bd1-f3 Bg5-f6 Bf3-d1 Bf6-d4 Bd1-f3 Bd4-e3
19 00:11 12,985,771 0 +1.28 Kg7-f6 Ba4-d1 Kf6-e5 Ka3-a4 Ke5xe4 Ka4-b5 Ke4-d3 Bd1-f3 Bg5-f6 Bf3-d1 Bf6-d4 Bd1-f3 Bd4-e3
20 00:23 25,531,613 0 +1.44 Kg7-f6 Ba4-d1 Bg5-e3 Ka3-b3 Kf6-g5 Kb3-c2 h7-h5 g4xh5 g6xh5 Kc2-d3 Be3-d4 Bd1-a4 h5-h4 Ba4-d7 Kg5-f4 e4-e5 Bd4xe5
20 00:26 28,880,506 0 +1.44 Kg7-f6 Ba4-d1 Bg5-e3 Ka3-b3 Kf6-g5 Kb3-c2 h7-h5 g4xh5 g6xh5 Kc2-d3 Be3-d4 Bd1-a4 h5-h4 Ba4-d7 Kg5-f4 e4-e5 Bd4xe5
21 01:18 85,358,905 0 +1.65 Kg7-f6 Ka3-b3 Kf6-e5 Kb3-c3 Ke5xe4 Ba4-d1 Bg5-f4 Bd1-c2+ Ke4-e3 Bc2-d1 Bf4-e5+ Kc3-c2 Ke3-d4 Kc2-b3 Kd4-d3 Bd1-f3 Be5-d4 Bf3-d1 Kd3-e3
21 01:23 91,386,903 0 +1.65 Kg7-f6 Ka3-b3 Kf6-e5 Kb3-c3 Ke5xe4 Ba4-d1 Bg5-f4 Bd1-c2+ Ke4-e3 Bc2-d1 Bf4-e5+ Kc3-c2 Ke3-d4 Kc2-b3 Kd4-d3 Bd1-f3 Be5-d4 Bf3-d1 Kd3-e3
22 03:29 206,901,907 0 +1.84 Kg7-f6 Ka3-b3 Kf6-e5 Kb3-c3 h7-h5 g4xh5 g6xh5 Kc3-d3 h5-h4 Ba4-d7 Ke5-f4 e4-e5 d6xe5 Kd3-e2 e5-e4 Ke2-d1
22 03:37 215,238,289 0 +1.84 Kg7-f6 Ka3-b3 Kf6-e5 Kb3-c3 h7-h5 g4xh5 g6xh5 Kc3-d3 h5-h4 Ba4-d7 Ke5-f4 e4-e5 d6xe5 Kd3-e2 e5-e4 Ke2-d1
23 06:39 380,951,126 0 +2.07 Kg7-f6 Ka3-b3 Kf6-e5 Kb3-c3 h7-h5 g4xh5 g6xh5 Kc3-d3 h5-h4 Ba4-d7 Ke5-f4 e4-e5 Kf4-g3 e5xd6 e7xd6 Bd7-f5 h4-h3 Kd3-e2 h3-h2 Bf5-e4 Kg3-f4 Be4-g2 Bg5-f6 Bg2-f3
23 06:51 393,119,677 0 +2.07 Kg7-f6 Ka3-b3 Kf6-e5 Kb3-c3 h7-h5 g4xh5 g6xh5 Kc3-d3 h5-h4 Ba4-d7 Ke5-f4 e4-e5 Kf4-g3 e5xd6 e7xd6 Bd7-f5 h4-h3 Kd3-e2 h3-h2 Bf5-e4 Kg3-f4 Be4-g2 Bg5-f6 Bg2-f3
24 11:42 638,381,937 0 +2.14 Kg7-f6 Ka3-b3 Kf6-e5 Kb3-c3 h7-h5 g4xh5 g6xh5 Kc3-d3 h5-h4 Ba4-d7 Ke5-f4 Kd3-e2 Kf4-g3 Ke2-f1 Bg5-e3 Kf1-e2 Be3-d4 Bd7-e8 h4-h3 Be8-h5 Kg3-g2 Bh5-f3+ Kg2-g1 e4-e5 h3-h2