endgame: passed pawns vs. pieces

[PauloSoare]

Jon, I looked at this initial position with Rybka 3 and Zappa Mexico II for 3 hours and I didn´t come to any conclusion. Can black win?

Paulo Soares

[jdart]

Can black win?

It could be this is just too hard a question to answer for sure.

But I think after Bh4 (Rybka's suggestion), Black can only draw. This is Arasan's output from the position after Bh4 (
4r3/8/p1k3K1/1p6/2p4B/2R5/5P2/8 b - -) at 2hrs/move:

result: Kc5 7200 seconds. score:+0.36 12128936304 nodes.
** error
Kc5 Ra3 b4 Rxa6 c3 Bf6 c2 Ra7 Kd5 Bb2 Re1 Rc7 b3 Rd7+ Kc6 Rd2 Rb1 Ba3 Rd1 Re2 c1
=Q Bxc1 Rxc1
result(2): Kd5 7200 seconds. score:+0.03 12787055520 nodes.
** error
Kd5 Ra3 Ra8 Be7 a5 f4 Ra6+ Kg5 Re6 Bf6 a4 f5 Re8 Kg6 Rg8+ Kf7 Rb8 Re3 b4 Re5+ Kc
6 Re3
result(3): Rg8+ 7200 seconds. score:+0.00 12995396822 nodes.
** error
Rg8+ Kf5 Re8 f4 a5 Kg6 Re4 Kf5 Re8

[Eelco de Groot]

Can black win?

It could be this is just too hard a question to answer for sure.

But I think after Bh4 (Rybka's suggestion), Black can only draw. This is Arasan's output from the position after Bh4 (
4r3/8/p1k3K1/1p6/2p4B/2R5/5P2/8 b - -) at 2hrs/move:

result: Kc5 7200 seconds. score:+0.36 12128936304 nodes.
** error
Kc5 Ra3 b4 Rxa6 c3 Bf6 c2 Ra7 Kd5 Bb2 Re1 Rc7 b3 Rd7+ Kc6 Rd2 Rb1 Ba3 Rd1 Re2 c1
=Q Bxc1 Rxc1
result(2): Kd5 7200 seconds. score:+0.03 12787055520 nodes.
** error
Kd5 Ra3 Ra8 Be7 a5 f4 Ra6+ Kg5 Re6 Bf6 a4 f5 Re8 Kg6 Rg8+ Kf7 Rb8 Re3 b4 Re5+ Kc
6 Re3
result(3): Rg8+ 7200 seconds. score:+0.00 12995396822 nodes.
** error
Rg8+ Kf5 Re8 f4 a5 Kg6 Re4 Kf5 Re8

Toga Mara Beta confirms Rybka's move and Arasan's analysis, in the sense that it also thinks it is a draw:


[d]4r3/8/p1k3K1/1p6/2p5/2R3B1/5P2/8 w - -

Engine: Toga Mara Beta/Toga II 1.4 Checkov Beta_4 test (Athlon 2009 MHz, 64 MB)
by Fabien Letouzey, Thomas Gaksch and Tam

9/39 0:01 +0.40 1.Kf7 Rd8 2.f4 Rd4 3.f5 b4 4.Rc1 Kd5
5.Kf6 b3 6.Rb1 Rd3 7.Bf4 (1.657.636) 900

10/39 0:02 +0.30 1.Kf7 Rd8 2.f4 Rd4 3.f5 b4 4.Rc1 Kd5
5.Be1 c3 6.f6 a5 7.Ra1 Ke4 8.Rxa5 c2
9.Ra1 Rd1 (1.862.057) 910

11/49 0:12 -0.08 1.Kf7 Re2 2.f4 Kd5 3.Ra3 b4 4.Ra5+ Kd4
5.Bh4 c3 6.Bf6+ Ke3 7.f5 Kf4 8.Ra4 Re4
9.Rxa6 Kxf5 10.Ra5+ Kf4 (11.876.880) 926

11/49 0:58 0.00 1.Bh4 Kc5 2.Kf7 b4 3.Rxc4+ Kxc4
4.Kxe8 a5 5.f4 a4 6.f5 b3 7.Bf6 a3
8.Bg7 b2 9.Bxb2 axb2 (53.059.592) 910

12/49 0:59 0.00 1.Bh4 Kc5 2.Kf7 b4 3.Rxc4+ Kxc4
4.Kxe8 a5 5.f4 a4 6.f5 b3 7.Bf6 a3
8.Bg7 b2 9.Bxb2 axb2 (54.133.596) 906

13/49 1:04 0.00 1.Bh4 Kc5 2.Kf7 b4 3.Rxc4+ Kxc4
4.Kxe8 a5 5.f4 a4 6.f5 b3 7.Bf6 a3
8.Bg7 b2 9.Bxb2 axb2 (57.577.083) 891

14/49 1:18 0.00 1.Bh4 Kc5 2.Kf7 b4 3.Rxc4+ Kxc4
4.Kxe8 a5 5.f4 a4 6.f5 b3 7.Bf6 a3
8.Bg7 b2 9.Bxb2 axb2 (67.812.411) 860

15/49 1:44 0.00 1.Bh4 Kc5 2.Kf7 b4 3.Rxc4+ Kxc4
4.Kxe8 a5 5.f4 a4 6.f5 b3 7.Bf6 a3
8.Bg7 b2 9.Bxb2 axb2 (86.660.494) 827

best move: Bg3-h4 time: 1:51.281 min n/s: 820.523 CPU 100.0% n/s(1CPU): 820.523 nodes: 91.270.000

Eelco

[PauloSoare]

I never have analised Bh4, but Rc1, althougth Bh4 seems to be a draw(not sure).

Paulo Soares

[Eelco de Groot]

I never have analised Bh4, but Rc1, althougth Bh4 seems to be a draw(not sure).

Paulo Soares

It would be interesting to see some of your analysis with 1. Rc1 Paulo!

At the moment Toga Mara Beta (it is not really Toga Mara but just a little part of the code that the programmer wanted some feed-back on) is also stuck it seems, on your move 1. Rc1. I made a new version of Toga Mara with all the eighteen variables that I am testing at the moment two points lowered, the first version I made had all variables at the bottom of their range so in theory this version should be less than optimal. But this is just testing basically whether the Mara code is making any sense the way I interpreted it, and I am just letting one analysis continue, also as an endurance test. I had not counted on a veeery long Fail Low though, that because of very little memory and using just the slow Athlon, took about twelve hours going from nineteen to twenty plies! But the result does have some value, the engine did not crash or take off into search-space, and move 1. Rc2 is still the best move at twenty plies, not 1. Bh4 and the position also is not so clearly drawn anymore:


[d]4r3/8/p1k3K1/1p6/2p5/2R3B1/5P2/8 w - -

Engine: Toga Mara Beta 1/ Toga II 1.4 Checkov Beta_4 (Athlon 2009 MHz, 64 MB) by Fabien Letouzey, Thomas Gaksch and Tam.
{Second Build with all variables minus two}

7/32 0:00 +0.36 1.f4 Kd5 2.Kf7 Re2 3.Ra3 b4 4.Ra5+ Kd4
5.Rxa6 c3 6.Rd6+ Kc4 7.Kf6 (217.543)

8/35 0:01 0.00 1.f4 Rg8+ 2.Kf7 Rg4 3.Re3 b4 4.Re6+ Kb7
5.Re7+ Kc6 6.Re6+ (1.013.960) 931

8/37 0:02 +0.30 1.Bh4 a5 2.f4 Kd5 3.Ra3 Rg8+ 4.Kf5 Rf8+
5.Kg4 Ke4 6.Bg5 a4 7.Rh3 (2.283.784) 860

9/37 0:03 +0.28 1.Bh4 a5 2.f4 Kd5 3.Ra3 Ke4 4.Rxa5 Kxf4
5.Rxb5 c3 6.Rc5 Kg4 7.Rc4+ Kh3 8.Kf5 (2.682.989) 826

10/38 0:05 -0.01 1.Bh4 Kc5 2.Kf7 Re2 3.Be7+ Kd5 4.f3 a5
5.Ra3 a4 6.Bf6 Rf2 7.Ke7 Rg2 (4.462.539) 848

10/38 0:05 0.00 1.f4 Rg8+ 2.Kf7 Rg4 3.Re3 b4 4.Re6+ Kb7
5.Re7+ Kc6 6.Re6+ (4.680.121) 848

11/50 0:19 -1.91 1.f4 b4 2.Rxc4+ Kb5 3.Rc7 Rg8+ 4.Kh5 Rxg3
5.Rb7+ Kc5 6.f5 Rf3 7.Kg4 Rf1 8.Rb8 a5
9.Ra8 Kb5 10.Rb8+ Kc4 11.Rc8+ Kd4
12.Rd8+ Ke4 (17.227.513) 898

11/50 0:19 +0.09 1.Bh4 Kc5 2.Kf7 Re2 3.Be7+ Kd5 4.f3 Rd2
5.Kf6 Kd4 6.Bb4 Rd3 7.Rxd3+ cxd3
8.Kf5 (17.524.108) 898

12/50 0:20 +0.02 1.Bh4 Kc5 2.Kf7 Re2 3.Be7+ Kd5 4.f3 Rd2
5.Kg6 Rd3 6.Bb4 Kd4 7.Rxd3+ cxd3
8.Kf5 Ke3 (18.487.561) 891

13/50 0:26 0.00 1.Bh4 Kc5 2.Kf7 Re2 3.Be7+ Kd4
4.Bf6+ Kd5 5.Rf3 b4 6.Rf5+ Kc6 7.Be7 b3
8.Rc5+ Kd7 9.Rd5+ Kc6 10.Rc5+ (22.954.282) 876

14/50 0:35 0.00 1.Bh4 Kc5 2.Kf7 Re2 3.Be7+ Kd4
4.Bf6+ Kd5 5.Rf3 b4 6.Rf5+ Kc6 7.Be7 b3
8.Rc5+ Kd7 9.Rd5+ Kc6 10.Rc5+ (29.639.745) 844

15/50 1:09 -0.17 1.Bh4 Kc5 2.Kf7 Re2 3.Be7+ Kd4
4.Bf6+ Kd5 5.Rf3 b4 6.Rf5+ Ke4
7.Re5+ Kd3 8.Rd5+ Kc2 9.Rd4 Kb3
10.Rd6 c3 11.Rxa6 c2 12.Ra1 Rxf2
13.Ke6 (56.497.780) 810

15/59 6:38 0.00 1.Rc2 a5 2.Bh4 a4 3.Kf7 Re4 4.Be7 Kd5
5.Kf6 Rf4+ 6.Kg5 Rf3 7.Kg4 Rd3 8.f4 c3
9.Re2 Rd4 10.Re5+ Kc4 11.Rc5+ Kb4
12.Re5+ Kc4 (336.492.494) 843

16/59 8:10 -0.18 1.Rc2 a5 2.Bh4 Kc5 3.Ra2 c3 4.Bf6 Kb4
5.Kf5 Rc8 6.Be7+ Kc4 7.Rxa5 c2 8.Ra1 b4
9.f4 Kb3 10.Rc1 Kb2 11.Re1 c1Q
12.Rxc1 Rxc1 13.Bxb4 Kb3 14.Be7 (403.669.591) 822

17/63 21:58 -0.13 1.Rc2 a5 2.Bf4 Ra8 3.Bc1 Kd5 4.f4 Rg8+
5.Kf7 Rg1 6.f5 b4 7.Be3 Rh1 8.f6 b3
9.Rb2 a4 10.Rd2+ Ke4 11.Bd4 Rh3
12.Bc5 c3 13.Rd4+ Ke5 14.Rxa4 (1.025.083.830) 777

18/63 37:18 -0.12 1.Rc2 Kd5 2.Rd2+ Kc5 3.Kf7 Rc8
4.Bd6+ Kb6 5.Be5 b4 6.f4 c3 7.Rc2 a5
8.f5 Kc6 9.Bxc3 Kb5 10.Bxb4 Rxc2
11.Bxa5 Kc6 12.f6 Kd7 13.Kf8 Rc8+
14.Kg7 (1.736.798.063) 775

19/63 52:01 -0.11 1.Rc2 Kd5 2.Rd2+ Kc5 3.Kf7 Rc8
4.Bd6+ Kb6 5.f4 c3 6.Rc2 a5 7.Be5 b4
8.f5 Kc6 9.Bxc3 Kb5 10.Bxb4 Rxc2
11.Bxa5 Rg2 12.f6 Re2 13.Bc7 Kc6
14.Bf4 (2.408.939.713) 771

20/85 786:42 -0.49 1.Rc2 a5 2.Bf4 Kc5 3.Kf7 Re4 4.Bg3 Kd5
5.Bc7 a4 6.Ba5 Rf4+ 7.Kg6 Rf3 8.Rb2 Kc6
9.Re2 a3 10.Kg5 Kc5 11.Kg4 Rd3 12.f4 c3
13.f5 b4 14.f6 (44.400.640.708) 940

The regular UCI-options in use are:

[OPTIONS]
Bitbases Path=D:\egbb5\egbb\
NullMove Reduction=5
Verification Reduction=5
Delta Margin=70

Delta Margin actually is a variable in Toga Checkov, no longer a constant..

This reminds me, with all the variables that I am supposed to be evaluating at the moment in Toga I feel a little like Spock on the USS Enterprise, who has to find a course back from earth in the twentieth century, through space-time, back to the twenythird century

Dialogue between Leonard Nimoy as Spock and DeForest Kelley as Leonard H. "Bones" McCoy in Star Trek IV - The Voyage Home:

(As Spock looks baffled, Bones ENTERS SHOT.)

BONES
You, ah...
(diplomatically)
You present the appearance of a man
with a problem.

SPOCK
Your perception is correct, Doctor...
In order to return us to the exact
moment at which we left the 23rd
Century, I have used our journey back
through time as a referent,
calculating the coefficient of
elapsed time in relation to the
acceleration curve.

BONES
Naturally.
(then)
So what is your problem?

SPOCK
Acceleration is no longer a constant.

BONES
Well, then you're just gonna have to take your
best shot.

SPOCK
... Best shot...?

BONES
Yes, Spock! Your best guess.

SPOCK
"Guessing" is not in my nature Doctor...

BONES
(has waited 10
years for this)
Well nobody's perfect...

Piece Activity=103
Toga Exchange Bonus=40 (but this is no longer in use by the program)


Regards, Eelco

[Eelco de Groot]

I never have analised Bh4, but Rc1, althougth Bh4 seems to be a draw(not sure).

Paulo Soares

20/85 786:42 -0.49 1.Rc2 a5 2.Bf4 Kc5 3.Kf7 Re4 4.Bg3 Kd5
5.Bc7 a4 6.Ba5 Rf4+ 7.Kg6 Rf3 8.Rb2 Kc6
9.Re2 a3 10.Kg5 Kc5 11.Kg4 Rd3 12.f4 c3
13.f5 b4 14.f6 (44.400.640.708) 940

Finally, after 1375 minutes, Toga has a new PV with 1. Rc1:


20/85 1375:42 -0.21 1.Rc1 Kc5 2.Bc7 b4 3.f4 b3 4.Rb1 Rg8+
5.Kf5 Rc8 6.Be5 a5 7.Ke4 a4 8.f5 a3
9.f6 a2 10.Rc1 Kb4 11.f7 Rf8 12.Kd5 Rxf7
13.Rxc4+ Ka3 14.Bd6+ (73.787.268.296) 893

best move: Rc3-c1 time: 1409:59.719 min n/s: 891.286 CPU 100.0% n/s(1CPU): 891.286 nodes: 75.402.480.000

Eelco

[PauloSoare]

Eelco, some variants. I am not sure if black can win.


[Event "?"]
[Site "?"]
[Date "2008.08.20"]
[Round "?"]
[White "?"]
[Black "?"]
[Result "*"]
[SetUp "1"]
[FEN "4r3/8/p1k3K1/1p6/2p5/2R3B1/5P2/8 w - -"]

1. Rc1 Kc5 2. Kf7 Re2 3. f4 b4 4. Re1 Rg2 5. Bh4 c3 6. f5
b3 7. Bf6 Kc4 (7... Rg3 8. Re8 b2 (8... a5 9. Rb8 Kc4
10. Rc8+ Kb4 11. Be5 Re3 12. Ke6 c2 13. f6 b2 14. f7 c1=Q
15. f8=Q+ Kb3 16. Rb8+ { and now?}) 9. Rb8 Rg1 10. Bxc3
b1=Q 11. Rxb1 Rxb1 12. Ke6 {tablebases draw}) 8. Re3 c2
(8... Rc2 9. Re4+ Kb5 10. Re5+ Ka4 11. Re4+ Ka3 12. Re6 a5
13. Ra6 Kb4 14. Rb6+ Ka3 15. Ra6 Ka4 16. Rc6 b2 17. Rb6 Rc1
18. Bxc3 b1=Q 19. Rxb1 Rxb1 20. Bxa5 {=}) 9. Bb2 Rg1
10. Rc3+ Kb4 11. f6 Rb1 12. Ke6 Rxb2 13. f7 Rb1 (13... Kxc3
14. f8=Q c1=Q 15. Qc5+ Kd2) 14. f8=Q+ Kxc3 15. Qf6+
{perpetual} *

[Eelco de Groot]

Eelco, some variants. I am not sure if black can win.


[Event "?"]
[Site "?"]
[Date "2008.08.20"]
[Round "?"]
[White "?"]
[Black "?"]
[Result "*"]
[SetUp "1"]
[FEN "4r3/8/p1k3K1/1p6/2p5/2R3B1/5P2/8 w - -"]

1. Rc1 Kc5 2. Kf7 Re2 3. f4 b4 4. Re1 Rg2 5. Bh4 c3 6. f5
b3 7. Bf6 Kc4 (7... Rg3 8. Re8 b2 (8... a5 9. Rb8 Kc4
10. Rc8+ Kb4 11. Be5 Re3 12. Ke6 c2 13. f6 b2 14. f7 c1=Q
15. f8=Q+ Kb3 16. Rb8+ { and now?}) 9. Rb8 Rg1 10. Bxc3
b1=Q 11. Rxb1 Rxb1 12. Ke6 {tablebases draw}) 8. Re3 c2
(8... Rc2 9. Re4+ Kb5 10. Re5+ Ka4 11. Re4+ Ka3 12. Re6 a5
13. Ra6 Kb4 14. Rb6+ Ka3 15. Ra6 Ka4 16. Rc6 b2 17. Rb6 Rc1
18. Bxc3 b1=Q 19. Rxb1 Rxb1 20. Bxa5 {=}) 9. Bb2 Rg1
10. Rc3+ Kb4 11. f6 Rb1 12. Ke6 Rxb2 13. f7 Rb1 (13... Kxc3
14. f8=Q c1=Q 15. Qc5+ Kd2) 14. f8=Q+ Kxc3 15. Qf6+
{perpetual} *

Thanks much Paulo! Very impressive! Would it not be a surprise if it turns out that to draw, White actually does have to give up the blocking square c3? And if you wanted to change the evaluation routine so a program knew when not to block a passed pawn, how many lines would be needed? I'm afraid it would be incredibly complex! But as it is now Toga needs 1375 minutes to find 1. Rc1 That is also not acceptable!
But your analysis at least gives a baseline for what programs should see, somewhere in the twentythird century aboard the Enterprise perhaps?

Regards, Eelco

[pijl]

Thanks much Paulo! Very impressive! Would it not be a surprise if it turns out that to draw, White actually does have to give up the blocking square c3? And if you wanted to change the evaluation routine so a program knew when not to block a passed pawn, how many lines would be needed? I'm afraid it would be incredibly complex! But as it is now Toga needs 1375 minutes to find 1. Rc1 That is also not acceptable!
But your analysis at least gives a baseline for what programs should see, somewhere in the twentythird century aboard the Enterprise perhaps?

If you look just below you can see the analysis of CTD. In 9.5 minutes it selects Rc1 in a transposition of Paulo's line: Kf7 Re2 Rc1 Kd5 f4. And this is on an ancient P4-2.8. I don't have the time right now to do a longer analysis on this position with CTD. Maybe in the evening.
Richard.

[jdart]

But as it is now Toga needs 1375 minutes to find 1. Rc1 That is also not acceptable!

If Bh4 is good enough for a draw (as it seems ) then I wouldn't worry about not finding Rc1.

The fact it switched to Rc1 after a long time does not prove that the previous move wasn't nearly as good.

--Jon