Another endgame, no tablebases please

[Robert Flesher]

Here is another endgame where engines seem clueless to see its a draw.

[d] R7/P4r2/6p1/6kp/2K5/6PP/8/8 w - - 0 55

[AdminX]

[d]R7/P4r2/6p1/6kp/2K5/6PP/8/8 w - - 0 1

Analysis by Stockfish 1.7.1 JA 64bit:

1.Kd5 Kf6 2.Ke4 Kg5 3.Kd3 Rd7+ 4.Ke3 Re7+ 5.Kd4 Rd7+ 6.Ke5 Re7+ 7.Kd6 Rf7 8.Kc6 Kf5 9.Kb6 Rf6+ 10.Kb7 Rf7+ 11.Kc6 Rf6+ 12.Kd5 Rf7 13.Kc5 Kg5 14.Kb6 Rf6+ 15.Ka5 Rf7 16.Kb5 Rf5+ 17.Ka4 Rf7 18.Ka5 Rf5+ 19.Kb4 Rf7 20.Kc5 Kf5 21.h4 Kg4 22.Kb6 Rf6+ 23.Kb7 Rf7+ 24.Ka6 Rf6+ 25.Ka5 Rf5+ 26.Kb4 Rf7 27.Kc5 Kxg3 28.Kb6 Rf6+ 29.Kb7 Rf7+ 30.Ka6 Rf6+ 31.Kb7
+- (2.98 ++) Depth: 6 00:00:00 3kN
+- (2.70) Depth: 30 00:00:09 26793kN

1.Kb4 Kf6 2.Kc5 Rc7+ 3.Kb6 Rf7 4.Re8 Rxa7 5.Kxa7 Kf5 6.Kb6 Kg5 7.Kc6 Kf5 8.Rf8+ Ke4 9.Kb6 Ke5 10.Re8+ Kf5 11.Kc5 Kf6 12.Rf8+ Ke5 13.Rh8
+- (2.94 ++) Depth: 30 00:00:09 27741kN
1.Kd5 Rc7 2.Kd6 Rf7 3.Kc5 Kf5 4.Kb6 Rf6+ 5.Kc7 Rf7+ 6.Kc6 Rf6+ 7.Kc7
+- (2.78 ++) Depth: 31 00:00:10 30264kN
= (0.12 --) Depth: 38 00:02:19 567mN

[Kurt Utzinger]

Pro Deo 1.5 is in so far an exception as the program belongs to the ones not showing an evaluation of 2.00 + or even higher.
Kurt

Code: Select all

FEN: R7/P4r2/6p1/6kp/2K5/6PP/8/8 w - - 0 55 

ProDeo 1.5:
   1	00:00	           4	4.000	+0.76	Kd5
   2	00:00	         209	209.000	+0.76	Kd5 Kf5
   3	00:00	         566	566.000	+0.68	Kd5 Kf5 Kc5
   3	00:00	       1.060	1.060.000	+0.76	Kc5 Tb7 Kd5
   4	00:00	       2.177	2.177.000	+0.76	Kc5 Tb7 Kd5 Td7+ Ke5
   4	00:00	       3.974	3.974.000	+0.82	Kb5 Kf5 Kb6 g5
   5	00:00	       7.794	7.794.000	+1.32	Kb5 Kf5 Kb6 h4 gxh4
   6	00:00	      15.104	15.104.000	+0.80	Kb5 Kf5 Kb6 Tf6+ Kb7 Tf7+ Kb8
   6	00:00	      26.163	26.163.000	+0.82	h4+ Kf5 Kc5 Kg4 Tg8 Txa7 Txg6+ Kf5
   7	00:00	      37.910	37.910.000	+0.87	h4+ Kf5 Kc5 Kg4 Tg8 Txa7 Txg6+ Kf3 Kd5 Td7+ Ke5
   7	00:00	      47.323	47.323.000	+0.91	Kb5 Tf5+ Ka6 Tf6+ Kb5 Tf7 Kb6 Tf6+ Kb5
   8	00:00	      85.269	85.269.000	+0.80	Kb5 Tf5+ Ka6 Tf6+ Ka5 Tf7 Kb6 Tf6+ Kc5 Tf5+ Kd6 Tf7 Kc6 Tf6+ Kc7 Tf7+ Kb8 Td7 g4 hxg4
   8	00:00	     124.811	124.811.000	+0.85	h4+ Kg4 Tg8 Txa7 Txg6+ Kf3 Tg8 Td7
   9	00:00	     225.638	225.638.000	+0.77	h4+ Kg4 Tg8 Txa7 Txg6+ Kf3 Kd3 Ta4 Kd2 Ke4 Te6+ Kd5
   9	00:00	     301.854	301.854.000	+0.84	Kc5 Tf5+ Kd4 Kf6 Th8
   9	00:00	     404.285	404.285.000	+0.85	Kd5 Tb7 h4+ Kg4 Tg8 Txa7 Txg6+ Kf3 Tg5 Ta5+ Ke6 Ta6+ Kd5
  10	00:00	     750.148	750.148.000	+0.84	Kd5 Tb7 Ke5 Te7+ Kd4 Tc7 h4+ Kg4 Tg8 Txa7 Txg6+ Kf3 Tg5 Ta4+ Ke5 Ta7 Kd6 Ta6+ Kd5 Ta3 Ke5 Ta8 Kd6 Ta6+
  11	00:00	   1.482.878	1.482.878.000	+0.82	Kd5 Tb7 Ke4 Te7+ Kd4 Td7+ Kc5 Te7 Kb6 Te6+ Kb5 Te5+ Kc4 Te4+ Kd5 Te7 Kd4 Td7+ Kc5 Te7 Kb6 Te6+ Kb5 Te5+
  12	00:01	   3.033.485	3.033.485	+0.85	Kd5 Kf5 Kd6 Kf6 Kc6 Kg5 Kb6 Tf6+ Kb7 Tf7+ Ka6 Tf6+ Ka5 Tf7 Kb5 Tf5+ Ka6 Tf6+ Ka5 Tf7 Kb5 Tf5+ Ka6
  13	00:02	   6.897.648	3.448.824	+0.83	Kd5 Kf5 h4 Kg4 Tg8 Txa7 Txg6+ Kh3 Ke4 Th7 Kf3 Tf7+ Ke3 Ta7 Kf4 Ta4+ Kf5 Ta5+ Kf6 Ta8 Kg5 Kxg3 Kxh5+ Kh3
  14	00:04	  12.115.117	3.028.779	+0.87	Kd5 Kf5 Kd6 Kg5 Kc6 Te7 Kb6 Te6+ Kb5 Te5+ Ka6 Te6+ Kb7 Te7+ Kc6 Tf7 Kb6 Tf6+ Kb7 Tf7+
  15	00:09	  26.304.859	2.922.762	+0.81	Kd5 Kf5 Kd6 Kg5 h4+ Kf5 Kd5 Td7+ Kc5 Tf7 Kb6 Tf6+ Kb5 Tf7 Kc5 Kg4 Kc6 Tf6+ Kd5 Tf5+ Ke4 Ta5 Tg8 Ta4+
  15	00:11	  31.120.401	2.829.127	+0.82	Kc5 Tf5+ Kd6 Tf7 Ke6 Tc7 h4+ Kg4 Tg8 Txa7 Txg6+ Kf3 Tg5 Ta6+ Kf5 Td6 Ke5 Ta6 Kd5 Ke3 Tf5 Ta2 Te5+ Kd3
  16	00:18	  50.460.756	2.803.375	+0.82	Kc5 Tf5+ Kd6 Tf7 h4+ Kg4 Ke6 Tb7 Tg8 Txa7 Txg6+ Kf3 Tg5 Ta1 Kd5 Ta5+ Kd4 Ta6 Ke5 Ta5+ Kf6 Ta6+ Kf5 Tb6
  16	00:24	  66.464.096	2.889.743	+0.82	Kd5
  16	00:24	  50.460.756	2.803.375	+0.82	Kc5 Tf5+ Kd6 Tf7 h4+ Kg4 Ke6 Tb7 Tg8 Txa7 Txg6+ Kf3 Tg5 Ta1 Kd5 Ta5+ Kd4 Ta6 Ke5 Ta5+ Kf6 Ta6+ Kf5 Tb6
  17	00:40	 112.956.196	2.823.904	+0.82	Kc5 Tf5+ Kb4 Tf7 Kc4 Te7 Kd5 Tc7 Ke6 Tb7 h4+ Kg4 Tg8 Txa7 Txg6+ Kf3 Tg5 Ke4 Txh5 Ta6+ Kd7 Kf3 Tb5 Kxg3
  18	01:30	 259.641.397	2.884.904	+0.82	Kc5 Tb7 Kd5 Td7+ Ke6 Tc7 h4+ Kg4 Tg8 Tc6+
  19	02:38	 464.891.518	2.942.351	+0.86	Kc5 Tb7 Kd6 Tf7 Ke6 Tc7 Kd6 Tf7 Ke6 Tc7 Kd6
  20	05:42	1.023.362.880	2.992.289	+0.83	Kc5 Tb7 Kc6 Tf7 Kd6 Tb7 h4+

[metax]

Well, my engine also doesn't show a very high score for white...


R7/P4r2/6p1/6kp/2K5/6PP/8/8 w - -

Engine: ChessMind 0.72 (0 MB)
by metax

9/20 0:01 +0.09 1.Rd8 Rc7+ 2.Kb4 Rb7+ 3.Kc5 Rxa7
4.Rd5+ Kf6 5.Rd3 Rc7+ 6.Kd6 Rc4 207

10/27 0:03 +0.06 1.Rd8 Rc7+ 2.Kb4 Rb7+ 3.Kc5 Rxa7
4.Rd5+ Kf6 5.Rd6+ Kg5 6.h4+ Kf5
7.Kc4 Ra4+ (885.657) 280

10/27 0:04 +0.20 1.h4+ Kf6 2.Kb4 Kf5 3.Kc5 Kf6 4.Re8 Rxa7
5.Re4 Kf5 (1.153.637) 284

11/27 0:05 +0.20 1.h4+ Kf6 2.Kb4 Kf5 3.Kc5 Kf6 4.Re8 Rxa7
5.Re4 Kf5 6.Rd4 Ke5 (1.461.123) 284

12/27 0:07 +0.06 1.h4+ Kf6 2.Kd3 Kf5 3.Ke3 Kf6 4.Rd8 Rxa7
5.Rd6+ Kf5 6.Rd5+ Ke6 7.Rd4 (2.187.042) 287

13/28 0:18 +0.25 1.h4+ Kf6 2.Kd5 Kf5 3.Kd6 Kf6 4.Rd8 Rxa7
5.Rf8+ Kg7 6.Rf3 Ra6+ 7.Kc5 Ra4
8.Kd5 (5.389.256) 289

14/28 0:21 +0.14 1.h4+ Kf6 2.Kd5 Kf5 3.Kd6 Kf6 4.Rd8 Rxa7
5.Rf8+ Kg7 6.Rf3 Ra6+ 7.Kc5 Re6
8.Kd5 (6.241.709) 290

15/30 0:26 +0.17 1.h4+ Kf6 2.Kd5 Kf5 3.Kd6 Kf6 4.Rd8 Rxa7
5.Rf8+ Kg7 6.Rf3 Ra6+ 7.Kc5 Ra8
8.Kd5 Ra5+ 9.Kc6 (7.751.981) 293

16/34 0:38 +0.22 1.h4+ Kf6 2.Kd5 Kf5 3.Kd6 Kf6 4.Rd8 Rxa7
5.Rf8+ Kg7 6.Rf3 Ra6+ 7.Kc5 Re6
8.Kd5 Re2 9.Rc3 Rd2+ 10.Ke4 (11.139.956) 291

17/36 1:24 +0.20 1.h4+ Kf6 2.Kd5 Kf5 3.Kd6 Kf6 4.Rd8 Rxa7
5.Rf8+ Kg7 6.Rf3 Ra6+ 7.Kc5 Ra8
8.Kd5 Rd8+ 9.Ke4 Re8+ 10.Kd4 Rd8+
11.Ke5 Re8+ 12.Kd6 (24.818.362) 294

best move: h3-h4 time: 1:27.173 min n/s: 295.000 nodes: 25.200.567


+0.20 is really not much regarding the score of other engines in this position...

[Kurt Utzinger]

Well, my engine also doesn't show a very high score for white...
[...]
+0.20 is really not much regarding the score of other engines in this position...

Fully agreed.
Kurt

[michiguel]

Here is another endgame where engines seem clueless to see its a draw.

[d] R7/P4r2/6p1/6kp/2K5/6PP/8/8 w - - 0 55

This is not a simple draw. Black needs to play carefully and the full demonstration must be very deep ending in a drawish KRPKP (rook pawn but with an awful black king).

White could bring the King to g2 and the only way black can draw is key discover check Ke5+ when the crosses f2, and play Re7. So, with the Re7 the King can move freely in the e column.

for instance, this position is a win for white

[D]R7/P4r2/6p1/6kp/8/6PP/6K1/8 w - - 8 63

h4+ Kf6 (Kg4 Rg8! Rxa7 Rxg6+ Kf5 Rg5 +-) Kh2! Kf5 Kh3 Kf6 g4 hxg4 Kxg4 zugzwang.

My point is, engines should not dismiss this as a draw w/o a lot of search.

Miguel

[Robert Flesher]

Here is another endgame where engines seem clueless to see its a draw.

[d] R7/P4r2/6p1/6kp/2K5/6PP/8/8 w - - 0 55

This is not a simple draw. Black needs to play carefully and the full demonstration must be very deep ending in a drawish KRPKP (rook pawn but with an awful black king).

White could bring the King to g2 and the only way black can draw is key discover check Ke5+ when the crosses f2, and play Re7. So, with the Re7 the King can move freely in the e column.

for instance, this position is a win for white


No! black has full control of the position and can control the white king with ease. Simple draw!

[D]R7/P4r2/6p1/6kp/8/6PP/6K1/8 w - - 8 63

h4+ Kf6 (Kg4 Rg8! Rxa7 Rxg6+ Kf5 Rg5 +-) Kh2! Kf5 Kh3 Kf6 g4 hxg4 Kxg4 zugzwang.

My point is, engines should not dismiss this as a draw w/o a lot of search.

Miguel

[Sven]

for instance, this position is a win for white

No! black has full control of the position and can control the white king with ease. Simple draw!

[D]R7/P4r2/6p1/6kp/8/6PP/6K1/8 w - - 8 63

h4+ Kf6 (Kg4 Rg8! Rxa7 Rxg6+ Kf5 Rg5 +-) Kh2! Kf5 Kh3 Kf6 g4 hxg4 Kxg4 zugzwang.

The position given by Miguel is indeed a win for white, check the analysis above. After h4+ Kg4, the line ends with Rg5+ which is a tablebase win. After h4+ Kf6, the line ends with hxg4+ Kxg4 and black is in zugzwang and loses. Other moves than hxg4+ create zugzwang as well. After h4+ Kf5 white would immediately play Kh3.

So I do not get your point. Did you perhaps address the original position you posted while Miguel meant his other example?

Sven

[Robert Flesher]

for instance, this position is a win for white

No! black has full control of the position and can control the white king with ease. Simple draw!

[D]R7/P4r2/6p1/6kp/8/6PP/6K1/8 w - - 8 63

h4+ Kf6 (Kg4 Rg8! Rxa7 Rxg6+ Kf5 Rg5 +-) Kh2! Kf5 Kh3 Kf6 g4 hxg4 Kxg4 zugzwang.

The position given by Miguel is indeed a win for white, check the analysis above. After h4+ Kg4, the line ends with Rg5+ which is a tablebase win. After h4+ Kf6, the line ends with hxg4+ Kxg4 and black is in zugzwang and loses. Other moves than hxg4+ create zugzwang as well. After h4+ Kf5 white would immediately play Kh3.

So I do not get your point. Did you perhaps address the original position you posted while Miguel meant his other example?

Sven

Correct! I was referring to my original position, as his will never occur if the player/engine has any clue. I original position is a simple draw any 1600 player should know. I agree with the assessment of his position, but it is clear with knowledge that it need never happen. This was my point. A simple search should avoid any of those zugzwang positions.

[Sven]

I was referring to my original position, as his will never occur if the player/engine has any clue. I original position is a simple draw any 1600 player should know. I agree with the assessment of his position, but it is clear with knowledge that it need never happen. This was my point. A simple search should avoid any of those zugzwang positions.

So now I would like to learn a bit from your playing strength, maybe the authors of the strongest engines can learn a bit about rook endings, too

What is the simple plan which all those ELO 1600 players are aware of in order to draw easily when playing black in your original position?
[D]R7/P4r2/6p1/6kp/2K5/6PP/8/8 w - - 0 55[/D]

How does black prevent white from reaching the position Miguel showed above, in order not to need knowledge about that zugzwang situation?

What is the advice for black, in conformance to your strategy, after these first moves: 1.Kd4 Kf5 2.Ke3 Kg5 3.Ke4 - should black play Rg7, Rh7, Re7+, or Kf6 (they all allow white to cross the f-file with its king)? Or better play Rb7, and if yes, why?

So if black really plays 3...Rb7, now the white "surprise": 4.h4+ Kg4 5.Rg8. Will they play 5...Rxa6 and know how to draw after 6.Rxg6+ Kh3 7.Kf5, since they know that they should keep their black rook on rank 6 in order to avoid Kg6-Kxh5, and that they must not exchange rooks for instance on g3 or g5 in a wrong moment? Or are they even more clever, avoid that and play 5...Re7+ 6.Kd4 Rxa7 7.Rxg6+ Kf3, or 7...Kh3 8.Ke4 Rf7 with a simple draw?

Will all ELO 1600 players avoid this sequence of play: 1.Kd4 Kf5 2.Ke3 g5 3.Kf3 Ke5+ 4.Kg2 Kf5 5.Kh2, or will they know how to draw this position? 5...Kf6?? 6.g4 +-; 5...g4 6.Rh8 Rxa7 7.Rxh5+ Kg6 8.hxg4 - a simple draw? O.k., a tablebase draw, but is it simple to play for a weak player? And what about an engine: from the given starting position there are 15 plies until a 6-men ending is reached after 8.hxg4, will it be found by TB probe at that depth? Oops - you said "no TB please", so will the engine know it is a draw despite the +2 pawns minus double pawn penalty? Has it built-in knowledge about such rook endings?

It seems I have been underestimating the deep knowledge of all ELO 1600 players about the subtleties of rook endings until today ...

To be serious again, I think that it is quite a difficult task for even the strongest chess engines to find the draw, since there is no support yet from 7- or even 8-men TBs (and will probably not be for a very long time). A "simple search" as you claim seems to fail revealing the truth within the current limitations of search depth, and I think it is due to the fact that positions like this have many subtrees for which evaluating them to draw requires very special and complex knowledge, for instance "give up the pawn, give horizontal checks from long distance and then either win back the pawn, convert to a known draw, or chase the king around the open board".

Sven