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Hot Topic (More than 10 Replies) Bacrot-Robson; a few explanantions (Read 13048 times)
zugzwang
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Re: Bacrot-Robson; a few explanantions
Reply #11 - 05/25/13 at 15:23:16
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micawber wrote on 05/12/12 at 05:55:17:
...
I have not posted a pgn file, since from the downloads there appeared not to much interest in downloading. There is a reasonable download file in the original thread anyway.


Dear micawber,

let me put it this way:

To express my admiration for your and Poghosyan's great job in precisely analysing some complex and important endgames is the reason why I registered here.
Thank you and Poghosyan for your highly instructive work and especially for the pgns. 
Some years ago I noticed the Hollis-Florian analysis here in addition to Dvoretsky/Mueller at chesscafe.
And now I see you are still very engaged in researching and explaining.

Svidler vs. Hammer and Carlsen vs. Wang Hao led me to this endgame corner and to your excellent postings.
  
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Re: Bacrot-Robson; a few explanantions
Reply #10 - 05/12/12 at 05:55:17
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5. Poghosyan’s defense

Diagram 47 (1…g6-g5!)
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Poghosyans defense requires the following statements to be true.
a) Black can hold the position after hxg5+
b) Black can hold the positions after he pushes his pawn to g4.


Black can hold the position after hxg5+
2.hxg,Kxg
3.Kc5,
These moves including 1...g5! were first seen in Grischuk-Radjabov, 2008. Grischuk continued 3.Kc4= .
After 3....Kg4 4.Kb3,Rxf2!= the game ended in a draw as well.
3....      Kg4!
4.Kb5!=

Diagram 48
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This is a position we have met before, in Dautovs defensive method (diagram 38 with the additional move 5...Ra2 6.Kb4-b5). Black holds the draw by taking on f2 just now.
Poghoysans  important discoveries concern the positions where Black moves his g-pawn to g4.

Black can hold the position after ....g5-g4
2.Kd5, g4!
Black also  draws after 2.Kc5,g4. The difference between Kc5 and Kd5is that 2.Kc5,gxh draws but 2.Kd5,gxh loses.
Besides 2.f3!? Deserves some attention since it prevents g5-g4:
2.f3,gxh4= 3.gxh4, Ra5! 4.Kc4,Ke5=  
3.Kd6!
The most cautious if he is aiming for b8. Keeping the king on the d-line, prevents lines with Black seeking counter play with Ke5/Kf5 followed by Kg4.
There are may transpositions from different king walks by White but they converge on the same critical positions.
3……., Rd2+
4.Kc7 , Rc2+
Diagram 49
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Now white has two basic choices: Kb8 or Kd8.
1)Kb8 signals his determination to extract his rook and try to queen his a-pawn. 
2)Kd8 reveals his intention to see if he can prey on the kingside pawns.

5.Kb7 is rather useless, since 5…Rb2+ forces the king back to the c-line (remember the trick 6.Ka8,Rb6!=)..
5.Kd7 generally will transpose to the main lines, after 5….Ra2!. But Black should not continue his checking spree since  5….Rd7+? 6.Ke8+ drops the f-pawn.

Plan 1: White plays on the queen side
5.Kb8!, Ra2!
5….Rxf2? 6.Rb7+-; 5...,Rb2+?? 6.Rb7+-
6.Ra8!, Rxf2!
A rule of the thumb is that it is generally safe to take on f2 if white cannot move his rook to another file, which is the case in the positions with Ra7/Kb7 and Ra8/Kb8
7.Ka7, Rf3
8.Rh8, Rxg3!=

Diagram 50
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The situation has drastically changed. 
Black has his own passed pawns, that guarantee him the draw.
9.Rxh5,  
Black has several ways to reach the draw. The simplest plans are
(1) To play Ke6 and set his f-pawn in motion, threatening to create two far advanced connected passed pawns. 
(2) To play Rg1 and set the g-pawn in motion, playing it all the way to g2, which forces White to keep his rook on the g-line.

If black follows the second plan White’s only plan to make progress is to push his a or h-pawn. 
But White cannot queen his a-pawn without the rooks help.
And if black trades the g-pawn for white’s h-pawn, the remaining endgame with  a-pawn versus f-pawn will in general be a draw, providing black has taken care to push his f-pawn  in time.

9.........Ke6!=
9........Rg1= 10.Kb6, g3!= draws as well.
10.Rg5,
10.Rh8, Rg1= 11.h5,g3=
10........f5!
11.h5
11.Kb7/b6 ,Rb3+ 12.Kc7 and now both 12..Ra3= and Kf6=
11….., Kf6!

Diagram 51
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And it has become clear that White’s winning chances have gone. 
12.Rg6+,Kf7 13.Kb7,Rb3+ 14.Ka8,g3!=

Plan 2: White plays on the kingside
First we show what kind of positions  white is aiming for:

Diagram 52
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1.a7!,    Kf6
2.Kg8,  Kg6
2…Ra1 3.Kg8,Ra6 4,Kh7,Ke7!? 5.Rb8!,Rxa7 6.Kg7!+-
Has basically the same idea.
3.Kh8!, Kf6
(forced because black threatened Rg8+ and 3.Kh8?? would allow 4.Rb8 threatening Rb6++)
4.Kh7,  Ra1
5.Kh6, Ra5
6.Rb8!
(6.Rg8,Rxa7 7.Kxh5 would win as well)

Diagram 53
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6……, Rxa7
7.Rb6+,Ke7
7……, Kf5 8.Rb4! with Rf4+ and Kxh5 to follow.
Eventually  the g-pawn will drop as well. Leaving white with a won 3 vs 1 endgame.
8.Kg7! , Rf2
9.Rf6!
And black first loses his f-pawn, while the rest of his pawns will follow shortly
The key to this endgame is to realize, that all this only happened because Black declined to take White's f-pawn off the board while he still could.

Now back to the main lines plan 2

Diagram 49 (repeated)
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*

5.Kd8, Ra2
5…..Rxf2? 6.Rb7 +- (followed by a7)
6.Ke8
6.Ra8!? Does not make any progress either 
6….Ra1= 7.Ke8!?,Ra2 8.a7 ,Kg7!= As we analyzed in the first five examples with the pawn a7, g7 is the safest place for the black king. 8.Ra7 (iso 8.a7) repeats the position after 6.Ke8. 
6…….,  Kg6!
6….Ra1/a3? 7.Rxf7+ +- 
After the text Black is prepared to capture on f2.
7.Kf8
7.Ra8, Rxf2!= 8 Rb8,Ra2 9.Rb6+,Kg7! 10 .Kd7,f5! 11.Ke6 f4!!=
7……, Rxf2=!
The right time for Black to pick off the pawn, waiting any longer would have lost.
7….Ra1/a3? 8.Ra8,Ra2 9.a7 +- and white wins.

Diagram 54
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*

From here white has two tries to clinch the win: 
Rb7(line 1)  and Ra8. (line 2).

Line 1
8.Rb7
With the plan a7 and a king walk to b8 and/or taking Blacks f-pawn.
8…..,  f5!=
8…f6 draws as well,  8….Ra2? ruins everything.9.Rb6+,f6 10Ke7! +- and the f-pawn drops.
With the text Black prepares counter play with f5-f4 giving him a free g-pawn.
9.Rb6+,
9.Kg8 (threatens mate) 9...,f4! 10.gxf4,Kf5!=
9…..,Kh7
10.a7, 
10.Rf6, Ra2 13.Rxf5,Kg6!= and Black wins the a-pawn.
10….,Ra2
11.Rb7+, Kg6
12.Kg8
Threatening Ra5 mate.
12…..,  f4!
The point of Blacks defense.

Diagram 55
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13.gxf, Kf5!!
Black had a final opportunity to go wrong here.
13…g3?? 14.Rf7!! threatening f5+ followed by Rf6/h7 mate.
14….Ra5  15.f5+,Rxf5 16.Rxf5,Kxf5 17.a8Q +-
14.Rf7+, Ke4!
15.f5, g3!=
And white must already take care to stop the g-pawn.

Line 2
8.Ra8, Ra2

Diagram 56
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9.a7
The only way to make progress. 
9..Ke7,Kf5! 12.Kxf7,Ke4= and black breaks through..
9….., Ra3
10.Kg8,
If White decides to send his king toward the a-pawn again, with 10.Ke8/Ke7  then Black plays 10…Kg7!=  The white king has no shelter on the queenside, and cannot threaten the h-pawn because Black has always Ra5+.
See our earlier discussion on positions with a7, i.e. diagram 5.
10….,Ra6!
The most simple method.
11.Kh8,Kf6
12.Kh7,Ke7!
The White king is cut off just in time from the h5/g4 pawns 

Diagram 57
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Here white cannot make any progress. On any king move Black gives a rook check. He keeps checking if the white king is on g7/g8/h8. Only if the king goes to h7 he plays Ra6.

13.Kg7,Rg7+ 14.Kh7 (16.Kh8,Rh6+),Ra6 repeats the position.

Also important is that any attempts to capture blacks g/h-pawn with the rook now fail. Blacks takes on a7 and because of the absence of the f2 pawn can directly attack g3, with sufficient counter play.

Time to sum up what has been learned

Black's defense:
1) Cut the white king of on the lower half of the board.
2) If it is not possible to cut off the king, put your rook on the same rank as the White f-pawn. So you are ready to take it off when the opportunity arise.
3) Keep in mind that you need counter play on the kingside anyway. If the white rook is on a8, then given the chance
3a)  Take of the f-pawn, while the white king is still far removed from the a-pawn
3b)The king maneuver Kf6-Kf5!-Kg4 is highly desirable to take off white's kingside pawns off and create the right circumstances to sac the rook against the a-pawn.
4) If the white rook is on a7, special care is needed. 
The counter play with Kf5 will probably not work, and (depending on the position of the White king), taking of the f-pawn immediately is often not possible either. It my be necessary to drive the White king as far away as possible from the kingside pawns so a R vs. pawn(s) endgame is drawn.
5) With the rook on a7 the pawn break ...g5 is needed to generate counter play.
5a) Dautovs defense requires studying. It answers the question how to deal with white's answer hxg+.
5b) Pogheysian's method is required if White's king is already far advanced beyond the 3rd rank. It involves pushing the pawn to g4.
Black must defend against two major white plans.
5B1) If white plays his king to the queenside. Black often needs to defend an endgame with f+g pawns versus a+h-pawns. The best moment to take of the f-pawn is often when the king blocks the rook from moving sideways (Ra7/Kb7 or Ra8/Kb8)
5B2) If white plays on the king side, Black must often activate his forces with f5-f4 creating a passed g-pawn. Should white at any point play a7, black must deny the white king access to h6. The optimal position in that case is to put his own king on g7.

White's attacking chances:
1) Post the rook on the 7th rank. This makes it much harder for Black to generate counter play.
2) White's primary goal is to extract his rook from its position in front of the pawn. Rc7 followed by a7 is what White is looking for.
3) The method of rank checks to move the rook on the 7th rank to a position behind the a-pawn is a powerful weapon.
4) Once the king has reached the a6-pawn 
4a) Position the rook on b4/c4 so it can shield the king from checks, keep an eye on a4 and cut the black king off from your pawn(s).
4b) White should remember how to  provide shelter for his king and extract his rook:
----The correct sequence is Ra7-a8,Kc7/8-b7,Kb7-a7, Ra8-b8.
----A position with Ra7-Ka8 with blacks rook on the a-line is itself  useless since your rook cannot move. However it can be redeemed by starting with Ka8-b8 and following the extraction procedure above.
----A position with Ra7-Ka8 with the black rook on b6 is even worse. It is no longer possible to extract either rook or king without giving up the a-pawn.
5) Pushing the pawn to a7 will often destroy any winning chances. However there is one important exception The Unzicker-Lundin position with the Black king on f5 and his pawn on f6. Then the white formation pawna7-Ra8 and pawns f3-g3-h4 wins.

I have not posted a pgn file, since from the downloads there appeared not to much interest in downloading. There is a reasonable download file in the original thread anyway.
« Last Edit: 05/12/12 at 19:35:21 by micawber »  
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micawber
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Re: Bacrot-Robson; a few explanantions
Reply #9 - 05/05/12 at 07:33:43
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Blacks Defensive Resources (part 2)

Having solved all of this, the analysts were not satisfied. The next question being: Can Black hold the Kantorovich position if it is his turn to move in diagram 25?

Diagram 25 (repeated; Black to move)
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*

It turns out that Black has several defensive resources, But Black should prepare counter play immediately.
Playing 1...Ke6 or 1...Ke5 is insufficient to save the position.
One key variation is:
1...Ke6 2.Kd4,f6 3.Ra8!,Kf5? 4.f3,Ra3 (4...g5!? 5.hxg,Kxg 6.a7!,Kf5 7.g4+-) 5.a7!+- (transposes to Unzicker-Lundin)
While 1...Ke6 2.Kd4,Rxf2 3.Rc7,Ra2 4.a7,Kf5 5.Kc4 tranposes to Steckners win (diagram26)
Rather complex analysis showed that 1...g5!?=  just draws.
(for details see the pgn)

1........, Ra4! (Dautov)
A logical move, following the principle to make it as hard as possible for the White king to move up the board.
2.Kd3,
2.Ra8, Kf5! Drawing as in the Fine/Kopaev study
2.........g5!
Black loses is he defends passively (2...Ra2? 3.Kc4!+-)
3.hxg5
This is necessary . Black threatened to take on h4 twice.3.Kc3,gxh! 4.gxh,Rxh4! And the already free h-pawn guarantees the draw. Note that 4.Kb3 is answered by h3!!.
3........, Kxg5
4.Kc3 , Kg4!
5.Kb3,  Ra1
6.Kb4

Note the rook on a4 did much to delay white's king in his approach to the a-pawn. As a consequence Black could safely leave his f-pawn undefended, since he would get the a6-pawn in return with a drawn endgame.

Diagram 38  (Black to move)
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6......,      Ra2!
Black intends to capture on f2 with his rook anyway. Mueller showed that 7...f5 8.Rg7+,Kf3! also draws. 
(Details are in the pgn-file)
7.Kb5,         Rxf2!
8.Ra8!

8.Rc7 /Rb7 also draws . Black does not capture at once on g3, but gives an intermediate check on b2. 
8.Rc7, Kg3?? 9.Rc3+!  Followed by Ra3 making Blacks life very very difficult, but just drawn. (See the pgn for a further explanation.) 
Black should play 8.Rc7, Rb2+!=

Diagram 39 (Black to move)
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8.......Rb2+!
8.....Kxg3?? 9.Rg8+!,Kh3 10.a7,Ra2 11. a8Q,Rxa8
12.Rxa8,h4 14.Rg8! +-Wins by the methods outlined in the technical intermezzo.
The intermediate check 8...Rb2+ has a dual purpose. Blacks goal is to force the white king to make a choice.  If the king moves up the board, he will need extra tempi to return towards blacks kingside pawns making a rook sac feasible. If the king moves to the 4th /5th rank it cant support the pawn to move to a7.
9.Kc4!, 
White decides to keep his king close to the black pawns, to keep winning chances against...Kxg3 followed by a rook sac:
9.Kc6, Kxg3!=  10.Rg8+, Kf3 11.a7,Ra2 12.a8Q,Rxa8 13.Rxa8,h4=
9........, Ra2
9....Kxg3?? 10.Rg8+,Kf3 11.a7,Ra2 12.a8Q,Rxa8+- now wins, thanks to whites better king position on c4 rather than c6.
10.Rg8+, Kf3!
11.Kb5 
White has not managed to improve the position of his king) and the rook is tied to the protection of the g-pawn.
Diagram 40
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Now with a next series of checks Black is going to force the White king in front of the rook pawn before he sets out to use his f-pawn to force a drawing position.
11......Rb2+!
12.Kc6,
12..Kc4,Ra2 13.Kb5 repeats the position after 11.Kb1 so white makes no progress
12.......,Rc2+
Now Black drives the king even further up the board.
13.Kb7,Rb2+   
14.Ka8, f5!        
Black start his pawns moving once the white king blocks a7.

Diagram 41
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*

Note that the White king is now confined to the a-line, and cannot make room for the a-pawn without the help from the white rook. But the rook has a double task. It is already occupied defending g3. If it gives up this defense Kxg3 allows an immediate draw Black simply gives up his rook for the a-pawn after g3 is gone.
15.Rg5!?
The only decent winning try.
After 15.a7,Rb3 16.Rb8,Ra317.Kb7,Rxa7+ 18.Kxa7,Kxg3=.
So white is aiming to win both f- and h-pawn for his g-pawn,
hoping for an endgame R+a-pawn vs. R that is winning thx to the distant position of the Black king.
15...........,  f4!!
Blacks aim is to eliminate all kingside pawns and draw an elementary endgame R+a-pawn vs.R
16.gxf
Forced because white can’t allow black to play fxg3.
16..........    h4!
Black can’t allow white to take the h-pawn without concessions.
Besides there is a finesse. If Black can force the f-pawn to f5 and only then take it with his king, he can just manage to get in to the safe drawing zone of a technical endgame R+h/a-pawn vs. R.
16......Kxf4?? 17. Rxh5 +- wins, because Blacks king is cut off on the 5th  rank.
17. f5,
17.Rh5,Kg4!= 18.Rh8,h3!= (17...Kxf4 18.Rxh4+ ,Ke5 19.Rh6!+- and Black loses because his king is cut off on the 5th rank similar to move 16 and 18....Kxf4 19.Rxh4+ loses for the same reason).
17...........    Kf4!
17....., Rb5!? May be an even simpler way to draw (intending to take the now pinned f-pawn with the rook)
18.Rh5      Kg4!
Black wins back the f-pawn under favorable circumstances.
19.Rh8      Kxf5
20.Rxh4      Ke6!=

Diagram 42
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* * * * * * * *
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*

And Black is inside the drawing zone for this elementary technical endgame. As can be seen after 21.a7,Kd7! 22.Rh8,Kc7! (see technical intermezzo)
A devious try is 
21.Rh7 (cutting of the black king on the 6rh rank)
21.......,  Kd6!
22.a7,    Rb1
23.Rb7, Rh1!=
(Note that 24.Kb8??, Ra8++ while a rook move along the b-line allows Kc7!; a rook move along the 7th rank is answered by Rb1)

What is true for Steckner/Kantorovich is also true for Lerner-Dorfman. Black to move draws.

Diagram 43 (teaching example 11)
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White to move would play 1.Kc5! And win by Vulfsons method. Black to play draws. 
Note that the same position with the Black king on f5 iso f6 was proved an easy draw by Fine (see diagram 10).
1......., Rxf3!
(Actually 1....Kf5 2.Kc5,Rxf3= draws as well)
2.Kc5, Rxg3
3.Rd8,
Similar to Vulfson's method
3..Kb4,Rb1 4.Kb5, Kf5=! 5.Rc8,Kg4 6.Ra4+,Kxg3 7.Ra4,Re3=
8.a7, Re8= 
And we have reached  technical intermezzo diagr. 20.
3...........Ra3!
4.Kb6
Similar to Vulfsons method
4........,   g5!=
Black also can give an intermediate check, to force the king in front of the pawn before applying this break.
4....., Rb3+ 5.Ka7,g5=
Diagram 44
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*
With his last move (g6-g5) Black created a free h-pawn, which guarantees the draw.
5.hxg5+,
5.Rh4,gxh! 6.Rxh5,Ke6! 7.Rxh4,f5!= (each side has a passser)
5.Rd6+,Ke5!= Followed by gxh
5............, Kxg5
6.Rd5+  , Kg4=
After 7.Ra5,Re3! 8.a7,Re8!= black sacs his rooks and draws.
The previous two  examples show the  downside of the white-king march: white's king may be too far removed from the king side to win the endgame of rook vs pawns.

We will add  an additional example that shows another method for Black to create a passed pawn.


Diagram 45 (teaching example 12)
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

Here we have a similar position. White has already put his rook behind his pawn. His g3 pawn is defended and it is his move.
1.a8Q
1.Kc6, f4! 2.gxf4,Kxh4= is similar to the main line.
1........,  Rxa8
2.Kxa8=
(2.Rxa8,Kxg3= and black draws (technical intermezzo 20-21)
2........., f4!
Black really needs a free passed pawn if he is to survive.
3.gxf4,
White can not allow fxg3. And 3.Ra4,Kxg3= is again similar to the technical intermezzo 20-21)
3.........,  Kxh4!!=
The right choice, creating a passed pawn at once. Taking the f-pawn loses. The point being that after Kxf4 Black will still need some moves to create a passer, and when he finally takes on h4 his king will be imprisoned on the h-line:
3...Kxf4 4.Ra6!,Kg4 5.Rxg6,Kxh4 6.Kb7+- with a technical win as in the start of the technical intermezzo.

Diagram 46 (Technical example 12)

* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*
4. Ra6,
4.Ra4,Kg4 5.Kb7,h4!= 6.Kc6,h3 7.Kd5, h2 8.f5+, Kg3=
4.........., Kg4!
5.Rxg6+,Kxf4=

With a technical draw. The difference with 3....Kxf4 becomes clear. In both cases Black ended up with a passed h-pawn. But now his king is much better placed and not imprisoned on the h-line.

Time to sum up Blacks defensive chances.

Strategy:
1. To cut off the white king on the lower half of the board.
2. To generate counter play on the king side and create a passed pawn.
3. Black may sac his rook against the a-pawn provided that he can hold the remaining rook vs. pawn endgame.

Tactical operations against formations with the rook on a8
1. Counter Play often starts with activating the king. The king maneuver Kf6-f5-(g4-xg3) is typical for this king of endgame.
2. Timing the capture of white's f-pawn is critical. With the f-pawn still on the board it is difficult to start any counter play.
3. The capture of the g3-pawn is in most cases better left to the black king.
4. If white's h-pawn is the final remaining pawn on the board seek to exchange it to create your own free h-pawn:
4.a)  The technical intermezzo (interference with f7-f5-f4) against a lone white h-pawn.
4b) The pawn advance g6-g5 to exchange the final pawn, against a lone white h-pawn.
4c) The temporary pawn sac f5-f4 against a white pawn formation (g3-h4).

Tactical operations against formations with the rook on a7
Here Blacks task is much harder, since the activation of the king with Kf6-f7 is hindered, and capturing the f-pawn is answered with Ra7-c7 followed by a7.
Dautovs method against the Steckner/Kantorovich set-up requires and deserves studying.

I will probably need one more post to complete this thread.
That will involve Poghesians drawing method.

  
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Re: Bacrot-Robson; a few explanantions
Reply #8 - 04/28/12 at 07:46:02
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TN wrote on 04/25/12 at 06:56:02:
That's some fantastic analysis and explanations there micawber.

Smiley as well!
  
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Re: Bacrot-Robson; a few explanantions
Reply #7 - 04/28/12 at 05:31:43
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Thx TN,

Though the important parts of the analysis that was presented, really were discovered some time ago by various analysts.
And no: I wont write a book: it's simply too much work. Smiley
First of all you cant get away with judgements like "chances for both sides", "white is better" or "unclear"
so everything has to be checked. 
At the same time, it is not very helpful to present every line you looked into, because this would obscure any teaching value. So solving a position to my own satisfaction is maybe 10% of the work.

What I hope to bring across is, that you dont need to be a superb endgame technician to play the type of endgame we look at reasonably well (the technical section is not that long) and that understanding these endgames need not be limited to players of master strength. 



  
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Re: Bacrot-Robson; a few explanantions
Reply #6 - 04/25/12 at 06:56:02
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That's some fantastic analysis and explanations there micawber. Have you thought of writing a book on endgames?
  
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Re: Bacrot-Robson; a few explanantions
Reply #5 - 04/25/12 at 06:50:31
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Steckner/Kantorovich White's chances (part 1)

What are exactly white's chances
In the ideal world white would like
1. First bring out his rook to c7/d7 and his a/pawn to a7.
2.a. Then bring his king to b8 and then push his pawn.
2.b. To bring out his rook from the 7th rank behind his pawn.

The next diagram shows an essential building block:
How does white get his king from the 7th behind his pawn.
The answer is, with rank checks, benefiting from the fact that the Black king has no shelter against these checks once it moves down the board.

Diagram 23 (Gurevich-Glek, Vlissingen, 2002)

* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

1.Rc4+!, Kxg3
2.Ra4! +-, Rxa7
3.Rxa7 , Kxh4

Diagram 24 (White to move)

* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

And White had no difficulty  to convert his material advantage into a win starting with the accurate  9.Kc3!,Kg3 10.Kd2!

Following the receipt given in the technical section, that getting the White king in front of the pawns has priority.
Note that the greedy 9.Rxf7,Kg3= would still have thrown away the win after all because Black will play ...h4! on the next move.
Reaching a position that is drawn even without the presence of the f- and g-pawn (a reminder to my  advice  to concentrate calculation on the most advanced pawn).

We are now ready to appreciate the Kantorovich/Steckner study.

Diagram 25
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

Compared to the position by Fine, White has two advantages.
It is his move, and his rook is on the 7th rank, keeping an eye on the f-pawn and hindering counter play with Kf5.

It was not until 2003 that this position was considered to be extremely dangerous for Black. Indeed Kantorovich had published this position as drawn in 1989. In 2003 Steckner showed variations on which the position was judged a win for white. But now thx to Poghesyan we can pronounce it a draw after all.

1.Kd4! (Steckner)
1.Ra8?, Kf5!= as shown in the study by Fine (diagram 10 and 11).
1.......,  Rxf2?
It was not realized that this was the losing move, until Poghosyan's discovered that 1...g5!! still draws.
1....Kf5? Is no longer sufficient. Thx to his rook on the 7th white replies 2.Rxf7+ We will illustrate that below.
2.Rc7!!
This is the first important step. White extracts his rook from its unfavourable position. Now it can cover the pawn from the side.
2.........,, Ra2
To prepare the advance of the black king, and stop the a-pawn.
3.a7!!
An important point. White wants to push the pawn as far as possible. Kantorovich proved correctly that 3.Rc6 only draws.
It is absolutely necessary to advance the pawn to the 7th rank.
3.........,  Kf5!
Black cant wait. 3....Ra3 4.Kc4!+- is even more favourable for white.
Diagram 26
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

4.Kc4!!,
Steckner’s discovery.
Kantorovich only considered 4.Rxf7+,Kg4 5.Kc5,Kxg3=
when there is no longer a win. Black next captures the h-pawn and sacs his rook against the a-pawn if necessary.
We have seen this method in diagram 10 (Krogius-Ilitzky)
4........, Kg4
Both 4....f6 and 4....Ra1 are answered by 5.Kb5!
Setting up the threat1. Rc5+ Kf6 2Rc6-a6 or  1...Kg4 2.Rc4-a4.
After 4....Rc2+ 5.Kb3/4, Rxa2 6.a8Q+- Black lacks the time to build a fortress (the details are in the pgn-file).

5.Kb3!,
The final stage. White is ready to put his rook behind his pawn, with the help of a rank check. Note that this method was also employed frequently in the Hollis-Florian analysis.
Note that Kb3 wins an essential tempo:
5.Kb4?, f5! Would have thrown the win away:
6.Rc4+, f4!!=

Diagram 27
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

5....,Ra5 (5...Ra6 makes no difference) 6.Rc4+
transposes to Gurevich-Glek above.
5....Ra1 is even worse since after Rc4+-Ra4 the white
rook is between blacks rook and the a-pawn. So Black not even gets to sac the rook for the a-pawn.

One final observation, to illustrate how vital tempi are in these positions. Suppose in the above position that blacks rook is already on a6.
The Black saves himself with 
5.....Kxg3 6.Rc3+,Kxh4 7.Rc4+,Kg3! 8.Ra4,Rxa7 9.Rxa7
And this endgame R vs. 3p is drawn!.

We still have to illustrate that actually 
1.Kd4, Kf5  does not work

Diagram 28
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

1.Rxf7+
This move is of course not possible with the rook on a8.
1..........,   Ke6
1...Kg4 2.a7!+-
And the white king walks to the a-pawn, while Black has no counter play whatsoever.
2.Rg7!
Winning an important tempo 
2........,      Kf6
3.Ra7,      Rxf2
3.....Kf5 4.Ra8! (4.f3 +-), Kg4 (4...Rxf2+ 5.Rf8+ +-)5.Kc5,Rxf2 6.Rg8!+- And White takes on g6 with check, simultaneously defending the a-pawn. Notice how Blacks defence is crippled by the absence of his f7-pawn.
4.Rb7
First part of whites plan: looking for Rook and a-pawn on the 7th
4........,    Ra2
4......Kf5?? 5.Rf7+ +-
5.a7   ,    Kf5
6.Kc5,    Kg4
White has completed the first part of his plan. While black is running late with his counter play.
Diagram 29
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*
7.Rb4!!+ 
A move to remember. White provides a shelter for his king while simultaneously defending his h-pawn. 
7..........,  Kxg3
8. Kb6 +-
There is nothing Black can do about Kb7-a8Q. Had the f-pawn still been on board ....f5 would have provided drawing chances.
(See the final examples of the technical intermezzo)

Even if the rook is on a8 White is not without chances.
Provided that his king is close enough to the a-pawn.

Diagram 30 (Lerner-Dorfmann/analysis)

* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

This position was actually thought to be drawn as late as 2003.
But looking at it from an objective point of view we can see that it is actually as favourable for  White as the Kantorovich/Steckman position. His king is closer to the a-pawn than in Steckners position. And the pawn on f3 – if it remains on the board- preempts counter play with Kf5-g4.
(In the game Blacks king was on g7 and he played Rxf3 (see pgn))
1.Kc6
Vulfson showed that 1.Kc5 wins as well.
1........,   Rxf3
1.....Kf5 is lost as well as shown by Steckner 2.Kb5!,Rxf3 3.Rf8 +-
2.Rb8??,  Ra3!
3.Rb6 ,  Kf5
4.Kb7    , Kg4
5.a7     ,   Rxa7+
6.Kxa7,   Kxg3= (Anakaev)
The variation above was the intended drawing solution.
After 7.Rb4,f5!=  we have the drawn position form the technical intermezzo.

Vulfson showed the correct solution to the position in 2003.
2.Rd8!   (instead of 2.Rb8??)

Diagram 31

* * * * * * * *
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* * * * * * * *
* * * * * * * *
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*

2......, Ra3
Obviously there is no time for Rxg3 since after a7 the a-pawn promotes under favourable circumstances.
Checking the king does not help:
2...Rc3+, 3.Kb5,Rb3+ 4.Ka4,Rb1 5.Rd3! +-
3.Kb5!
Shows the point. Now Black is no longer in a position to initiate counter play with Kf5. White intends to complete the manoeuvre Rd4 followed by Ra4 winning simply.

3......., Ke5!
The only move to prevent Rd4. Checking the king does not help here either: 3....Rc3+? 4.Ka4,Rb1 5.Rd3+-
4.Rd7!,
Ensures that White can move his a-pawn to the 7th rank. 
5.........., f6
6.a7!
Phase 1 completed. Rook and a-pawn are on the 7th!.

Diagram 32

* * * * * * * *
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* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

And Blacks position has become hopeless. He has no longer any counter play. White will move his rook to c7 and threaten a rank checks followed by either Rc6/Ra6 or Rc4/Ra4.
For instance 6...g5 7.Rc7!,gxh 8.gxh,f5 9.Rc5+,Ke4 10.Ra4+-
or 6..Kf5 7.Kb4!,Ra6 8.Rd5+,Kg4 9.Ra5!+-

The above method does not always work. Sometimes White's king must seek a temporary shelter on a7, and the white rook must help the king to escape eventually.

Diagram 33 (Teaching example)

* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

1.Ka7!
1.Kc?,Ra2 2.Kb7,Kf5!= would give Black the extra tempo needed to draw. Note that Black has an extra tempo over diagram 31.
1........,  Rb3
Eying the g3-pawn. An alternative was 1....Kf5 2.Rb8,Rg2!?
3.Rb4! +- cutting off the Black king.or 3.Rb3 +- (defending the g3-pawn).
2.Rb8
With gain of tempo.
[b]2.........,  Rxg3[/b]
There is nothing better. 2....Ra3 3.Rb5!+- compared to the main line. Black doesn't even get a pawn for his troubles.
3.Rb5!!
The key move. White cuts off the black king from the important g4-square. At the same time he provides shelter from rook checks along the line and rank. 

This position coincides with one given by Mueller (his analysis on move 73 Bacrot-Robson).

Diagram 34 (Mueller)

* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

3........, Re3
With the aim to give rank checks.  Hopeless is  3....Ra3 4.Kb6,g5 (on waiting moves  like 4...Ra4 5.a7! To be followed by Ra5) 5.hxg+,Kg6 6.a7 +-
4.Kb6, Re6+
5.Ka5!,
5.Ka7, Re3 repeats the position after move 3.
5..........Re7
Obstructs the march of the a-pawn.

Diagram 35

* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

In the above diagram. 6.Rb7, Re5+ 7.Rb5,Re7
would make no progress so White needs something else.
6.Rc5!!
Prepares Kb6, since Re6+ can now be answered with Rc6 winning immediately.
6.........,    Ke6
6....Re1 7.a7,Ra1+ 8.Kb6 +- with Ra5 to follow.
7.Kb6,,   f6
8.a7+-
The endgame after 8...Rxa7 9.Kxa7+- is an easy win, since Black has no counter play whatsoever.

The next example bears some similarity to  diagram (32). It has been taken from the Kantorovich/Steckner Study (side variation 4...f6), but has also occurred in an actual game.

Diagram 36 (Coenen-Kern/2001)

* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

Despite the fact that the a-pawn is now supported by the white king, White's task is not simple.
1......., Rb2+!
Gives white the opportunity to go wrong.
1....Kg4+- 2.Rc6!! (threat: Ra6), Rxa7+ 3.Kxa7,Kxg3 4.Rxf6+-
2.Kc8!
White evades the imprisonment of his king, because there is insufficient time for the extraction maneuver.
2.Ka8?=,Kg4! 3.Rb7,Ra2 4.a8Q,Rxa8 5.Kxa8,Kxg3 6.Rb4,f5!=
We have reached diagram 20 from the technical intermezzo.
2..........  Ra2
3.Rg7!!
Steckners discovery and the only winning move, but missed in Coenen-Kern,2001. Now  3.Kb8?=,Kg4! 4.a8Q,Rxa8 5.Qxa8,Kxg3= Now 6.Rc4, f5!= Again drawing by example 20 technical intermezzo.
3.........,  Kxg3
4.Rxg6+, Kh3
5.Rg7!+-

Diagram 37

* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*
The fight is over. White is ready to promote
5...f5 6.Kb8,Rb2+ 7.Rb7,Ra2 8.a8Q,Rxa8 9.Rxa8,.Kxg3 10.Rg8+,Kxh4 11.Kb7+-
see technical intermezzo (diag 20-22)

  
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Re: Bacrot-Robson; a few explanantions
Reply #4 - 04/07/12 at 06:26:41
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Thx to Fling to post a bit of feedback and encouragement  Wink


A technical intermezzo

This post is probably the easiest part, since it mostly discusses basic knowledge. If you're confident that you know your basics you can skip to the final section (pratical application).

a lonely h-pawn
As I showed you, Black often has to rely on the promotion of his h-pawn to achieve a draw. In most cases the race starts when Black sacs his rook against the a-pawn either on a7 or a8.
If the White king is on the a-file,  a pawn on h4 is generally sufficiently close to promotion, while a pawn on h5 has to be calculated accurately.

The defender is under some temptation to go for a stalemate position with pawn on h2, Kh1. But it makes sense to keep the king on the g- and f-file, as long as possible. If only to prevent the approach of the white king.
Besides the same circumstances that facilitate the stalemate create conditions for white to introduce Zugzwang motives.

Diagram 13
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* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

Black must decide where to go with his King.
Now. 1....Kf1! 2.Rh8,Kg2= ensures the draw.

1...Kh1/h2  seems attractive because of the stalemate motive. But the move obstructs the h-pawn and confines the black king.
1...Kh1? 2.Kf3, h2 (2....Kh2 3.Rg3) 3.Ra8,Kg1 4.Ra1++

Diagram 14
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

1.Kg3!  (This position occurred in Davie-Toothill, Hastings,1965)
1........., Kg1
2.Ra8!
2.Kh3+! is even simpler 3.Kh1,Ra8! Wins the h-pawn.
2........, h1N+
At least prevents the mate on a1, but the new knight is trapped.
3.Kf3, Kh2
(2....Nf2 3.Ra1+ and 4.Kxf2)
3.Rg8!
And the knight is lost, since 3...Kh3 4.Rh8++

Diagram 15 Bacrot – Robson (2011)
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

With the previous two examples in mind we can now understand what happened in the final phase of Bacrot-Robson

1....h2???
1...Kg2! 2.Rg6+,Kf1= was correct (see diagram 13)
2.Rg6+,Kh3
3.Kf2!!
The only winning move!. Black is forced to a minor promotion.
But from diagram 14 we already know the knight gets trapped.
3........., h1N+
3......., h1Q 4.Rh6++
4.Kf3! (here Robson resigned)
Taking away the last square from the knight.
4.........,  Kh2
5.Rg8
With the same final position as from diagram 14.

R vs. 2/3 pawns

These positions are often much harder to assess from a human point of view. I don't know many positions of this type by heart, and I suspect that goes for most players (even some GM's).
A computer of course has no such problem since he can read this type of endgame from his table bases.

First of all it is good to remember that 2 connected passed pawns on the 6rh rank are worth a rook if the  King cannot assist the rook.

That goes a long way to formulate some rules of the thumb for the  attacker:
1) Not to let the pawns move to close to the promotion field.
2) It is highly desirable to post your king in front of the opponents pawns.

By the same reasoning it is important for the defender:
1)to have king in front of the passed pawns to assist their promotion 
and – equally important –
2)to cut off access to important squares for the attacker's king, with his own king (shouldering)


Diagram 16
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

Just as an illustration. This position is drawn, white to move.
He is not in time to put his king in front of the pawns.
Had the king been on e2,e3 or e4 (i.e., in the square before the most advanced pawn) he wins.
As it is Black must still be careful. After 1.Kd5,  it turns out 1...h4 is the only move to draw !. If 1.Kd5,Kf4? 2.Ra4!+,Kg3 3.Ke4! White manages to bring his king to the battlefield.

In defending such positions it is useful not to get too much distracted by the multitude of pawns, and trying to advance them all. It makes often better sense  to concentrate on the question if the defender can  promote his most advanced pawn.

R+a/h-pawn vs. R


Diagram 17
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* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*
Blacks ideal defence position.. White is unable to evict the Black king from c7/c8.Remembering this position is easier than remembering the next one.

Diagram 18
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*
With the previous position in mind it is very easy to solve positions of this kind. This position is drawn.
White requires 3 moves to get his rook to b8:
Rd1-h1-h8-b8
In the mean time Black can reach c7 and draw:
1.Rh1,Kd7 2.Rh8, Kc7 3.Rb8,Rc2= (diagram 17)

Had the black king been on e6, the position would be lost.
Now White manages the required maneuver in only two moves while hindering the approach of the Black king:
1.Rd8,Rb3 2.Rb8 +-

Diagram 19 (Vencura position)


* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*
Black only needs to remember three things about this position.
1.To keep checking the white king until it no longer covers the
pawn on a6.
2. If the king is lose  to return his rook to the 6th rank
3. If White plays a6-a7 to answer with Ra6!

1.......Rf5+!
(1...Re6 2.Rc8+- and the White king is shielded from rank checks )
2.Kb4,Rf6
3.a7,  Ra6!=
(3....Rf7??,Rg8+)

This position actually would have been drawn, if we had added a white pawn on the h-line.

If  the rook in the diagram position had been on a1 instead of f6 however White wins, because the black king is too far away and Black can not transfer his rook from a1 to the 6th rank. 
1....Rf1 2.Rc8!+-
1....Ra2 2.Kb6,Kf7 3.a7!,Kg7 4.Rb8+-

a practical application

Diagram 20
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

This position might easily result from Black's battle against an a-pawn.
White has executed his program: His king has reached the  a-pawn and is ready to support its promotion. So is his rook that is already behind the pawn (iso in front). 
Black has not quite completed his defensive plan. He still needs to eliminate the pawn on h4 before he can safely sac his rook for the a7 pawn.

1.......f7-f5!!
A move with a dual purpose. Black now threatens f5-f4 interfering with the rooks defense of the white h-pawn. Besides the f-pawn can become a dangerous free pawn in his own right.
2.a8Q
White also might try2.Rc4 intending Rc8. But black can always sac his rook: 2....f4 3.Rc8,Re7+ 4.Rc7,Re8 etc.
(2.Ra6!? Is more subtle and is examined in the pgn-file.)
2......., Rxa8
3.Kxa8
3.Rxa8,Kxh4= is an even easier draw.
3......,., f4!
And the h-pawn is going to fall.
4.Ra6!
White does not want to leave black with 3 connected pawns,and asks a pawn in return for his h-pawn.
5.........,   Kxh4
6.Rxg6

Diagram 21
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

Now Black must choose which pawn to push:
6.....,  f3!

The right choice. Eventually this forces White to give up the confinement of the Black king on the h-line.
7.Kb7,f2
8.Rf6,Kg3
The black king escaped his prison. Now white has to be careful
9. Kc6,Kg2
10.Rg2+=, Kf1
If the black king gives up the protection of the pawn, the rook returns to the f-line (10...Kh2 11.Rf6)
11.Rh6!=
The king must leave his shelter or his h-pawn falls.

It would be a mistake for Black to concentrate on pushing the h-pawn.

Diagram 21 (repeated)
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

5......., Kh3?!
6.Kb7, h4?!
6....f3!=
7.Kc6, Kh2?!
7.....f3!=
8.Kd5!,h3??
The last opportunity to draw with 8...f3!=
9.Ke4!+-
And the white king stops the a-pawn on his own.
After 9....Kh1 10.Kf3!, h2 11.Ra6 +- we basically have the position of diagram 13-15 The extra f-pawn does not matter.

Diagram 22
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

This position is very similar to diagram 21.
Except for white's king that is now close enough for a win.

1.........f3
2.Kc4!
2.Rf6?=,lets the king escape prematurely Kg3! 3.Kc4,h4! 4.Kd3,Kf2!= Black has successfully shouldered white's king. It cant approach the h-pawn in time. (4.Ke4,Kg2! 5.Rxf,h3=)
3........., f2
4.Rf6, Kg3
5.Kd3, Kg2
6.Ke2+-
The combined force of R+K have stopped the f-pawn.
The rest is simple.
6.........., h4
7.Rg8+!, Kh2
8.Kxf2 +-

With a position similar to the ones shown in diagram 13-15

We can formulate a rule for this position. The position is won for white is his king is one step away
from entering the square of the f-pawn.

The reasoning is simple. From the diagram position Black needs still 2 king moves to reach g2-square from where he can support the promotion of the f-pawn.
For White to stop the f-pawn he also has two moves to spare:
One is used to move his rook behind the pawn, and one is used to step into the square of the f-pawn with his king.

« Last Edit: 04/07/12 at 08:00:46 by micawber »  
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Re: Bacrot-Robson; a few explanantions
Reply #3 - 04/02/12 at 10:15:56
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Thanks, very helpful that you are breaking down an endgame (that other analysts have failed to correctly analyze) into small instructive pieces. Everything will help readers to understand rook endgames better, not just this one.
  
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Re: Bacrot-Robson; a few explanantions
Reply #2 - 04/02/12 at 04:06:43
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Pawn on a6
Black's defensive resources part 1

But what if the a-pawn is still on a6?.
This significantly improves White's chances for success.
At least White's king now has a  shelter on a7 from Rook checks along the file. It was not realized until 2003 how careful Black must  play to gain a draw.

First I would like you to show Blacks optimal defense strategy.
It has two elements:
1. Make it as hard as possible for White to get his king to the a-pawn. Especially make it hard to move up the board.
2. Black's survival depends on his ability to create his own passed pawn. To achieve this it is normally necessary that he
2.a. Can remove the f-pawn. To this end, Black should post his rook on the same rank as the f-pawn, unless this allows the escape of the king to the upper half of the board.
2.b  Can execute the king maneuver Kg7-f6-f5-g4 in time to threaten White's remaining pawns..

Diagram 9 (Ilivitsky – Krogius, 1954)
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

Black to play starts of with
1.......,  Ra3! Preventing Kf3
2.Kf1,  Ra2! Preventing Ke2
3.Ke1, Kf6

And now white is at a junction. To make progress
he must give up the defense of his f-pawn.
He can either do this directly with 4.Kd1, aiming to play his king first to b1 and then up the board.
The other method is to play 4.f3, Ra3! When matters are only postponed, and White will still have to give up his f-pawn.
Note that as long as the pawn is still on a6, Black can safely pick up the f-pawn with his rook.

However this is not all. White has also a subtle move to slightly improve his position. 4.Ra7!?  Trying to hinder  black playing ...Kf5. (Dvoretzky notes in several similar positions that the optimum position of White's rook is on the 7th rank)
The position after 4.Ra7 is more similar to Kantorovich/Steckner. 
However Black has a good waiting move of his own 4....Ke6.
When he still has sufficient time for his counterplay because White's king is still confined to the back rank.

We will concentrate on the situation where White plays Kd1 and gives up his f-pawn in order to push his a-pawn with king support.

Diagram 10
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

The above diagram shows a typical position, where white give up his f-pawn and moved his king to the queenside.
White now finally can move his king up the board. Now it is time for Blacks counter play.
1........, Kf5! (on the road to g4/g3)
2.Kb3, Kg4
3.Kb4, Ra1
And Blacks next moves will be Kxg3 followed by Kxh4 when his own free h-pawn assures him of a draw.

But what if Black had not taken immediate steps to obstruct the White king?
If we had seen the following moves:
1....Ra2?! 2.Kf3,Kf6 3.Ke3 arriving at the following diagram.

Diagram 11 Fine, 1941.
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*
This position is referred to by Dvoretsky and other Russian authors before him, as a study by Kopaev, 1958. But actually the position had already been examined by Fine in his Basic Chess Endings 1941.

In this position the correct solution is:
1.........Kf5! (immediate counter attack)
2.f3....          (postponing the loss of the f-pawn)
2.Kd4,Rxf2! 4.Rf8,Ra2 4.Rxf7+,Kg4= is similar to the main line.
2......, Ra3+!
(2...f6? 3.a7! And white wins as in Unzicker-Lundin),
3.Kd4!,
3.Ke2?!, Kf6!= And Black has time for a waiting move. Since the White king is once again cut off on the lower half of the board.
3.........., Rxf3
4.Rf8  , Ra3! (necessary to prevent a7-a8Q)

Diagram 12, Fine 1941

* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

5.Rxf7+ , Kg4! (Blacks counter attack is in time)
6.Rf6     , Kxg3
7.Rxg6  , Kxh4=

And Blacks free h-pawn guarantees him the draw.
The entire line was given by Fine, but later attributed to Kopaev.

(First by Averbakh and later by Dvoretsky. The attribution by Averbakh reeks a bit of the old Soviet practice to attribute every discovery to Soviet chessplayers and minimize the contributions of others. Actually Averbakh was very wel acquainted with Fine’s manual and it’s hard to imagine he missed this particular section.
This more are less confirms my view that the refutation of Hollis’ analyses must be attributed to van Wijgerden and that Averbakh quoted this without referencing the source.)

Once again a small warning. The above does not apply to positions where the white rook is initially on a7. The point is that Kf6-f5 is then answered with Rxf7+ followed by a7, and new technical problems are created.

This leaves us with a last question. Did Black have any alternatives beside 1....Kf5?
Well passivity would have put Black in the danger zone.

After  1....Kg7/e6 2.Ra7!,Kf6 3.Kd4 we arrive at a position now known as the Kantorovich/Steckner study.
Where Steckner provided a winning method, against 3....Rxf2.
But thanks to Poghesyan, we now know that Black still has a draw by 3....g5, although he must play extremely accurate.

We'll come back to that later, after a technical intermezzo.

There is a pgn attached to this post. That only contains the lines essential to this tutorial. There is more to say about these positions and I plan to post full analysis later on.

« Last Edit: 04/02/12 at 06:36:42 by micawber »  
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Re: Bacrot-Robson; a few explanantions
Reply #1 - 03/26/12 at 05:13:08
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We just thought that the next post was forthcoming. Smiley  Now I know what I'll be looking at this week!  Thank you!
  
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Bacrot-Robson; a few explanantions
03/26/12 at 04:44:35
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In this thread I will present a tutorial on rook endgames with a passed a-pawn on the 6th or 7th rank and the rook of the stronger side in front. In the presentation I will rather rely on verbal explanation than on trees of variations. These will be tucked away in accompanying pgn files.


Pawn on a7
In an endgame with R+a-pawn vs. R the drawing margin is very wide. If the pawn is on a7 and the R in front of it on a8, the white king has no shelter against rook checks (along the file or rank).
Provided that the black king is on the safe squares g7/h7 there is no win.
Even if we add a g- or h-pawn the result still will be a draw.
The result changes however as soon as we add an f-pawn.

Diagram 1

* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

In the above position white wins directly with 1.f6+
1...Kxf6,2.Rf8+ followed by a8Q
1...Kf7 2.Rh8,Rxa7 3.Rh7+ followed by Rxa7
The problems for the stronger side to convert an extra rook pawn on a7 while his own rook is in front of the pawn extends to multiple pawns.
The following example illustrates the drawing margin, when both sides have additional pawns on the kingside. Even here two extra pawns may be insufficient for white.

Diagram 2 (Emms/1999)

* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

White’s only hope to win this position is to create a free f-pawn.
But how is he going to accomplish this?
f3 followed by g4 does not seem to help very much
since Black exchanges on g4
and if White takes back with fxg4 his f-pawn and his winning chances are gone forever.

There is however an ingenious plan. White can answer fxg with f4 instead and follow up with h5 to create his free f-pawn.
Unfortunately analysis shows that Blacks free duo of passed pawns can generate just enough counter play to make the draw. (See the pgn-file for details).

Diagram 3

* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

Here we see the outlined plan in action.
Now Black has two methods to hold the draw.
Black can actually take on g4 as the pgn file shows
But it is simpler is to give rank checks until the White king is either on the d-file or on the 4th rank and only than take on g4.
This ensures that Blacks counter play with g3-g2 is  sufficient.

1....Ra2+
a) 2.Kf3,Ra3+ 3.Ke4,hxg4=
b) 2.Kf1,Ra1+ 3.Ke2, Ra2+ 4.Kd1,Ra1+ 5.Kc2,hxg4=


A final try for white is to play f4 followed by f5 in the hope of  picking up both blacks kingside pawns while keeping his own.

Diagram 4

* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

Here Black needs to be a little attentive.
1.Kf4, Kh7!
(1.....Ra3! Draws as well, since
2.Kg3,Rxg3+ and 2.Kxf5,Ra1 3.Kg5,Ra5+=)
2.Kg5
Using the f-pawn as a shield to pick of the h-pawn.
2........, f4+=

Diagram 5


* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*
After the discussion above it will come as no surprise that the position above is also perfectly safe for Black. The h5-pawn is not really loose. There is no way the White King to approach it, since Kf5 or Kg5 will always be answered by Ra5+.

Diagram 6

* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*
The same goes for the above position. There is again no way for the White king to invade the kingside. For instance put the white king on e4/f4 and Ra5 repels all boarders.
However White can make use of the loose h-pawn with his rook. But even this gives him no realistic winning chances. 
1.Rh8,Rxa7 2.Rxh5,Ra2 3.Rf5,Ke6 4.Rf4,f5=
Or 3.Rg5,Rxf2 4.Rxg4= with a drawn R+2p vs R+p.

The position below is of significant practical importance.
Diagram 7 Unzicker – Lundin, 1954


* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

White wins by 1.a7+-, when Black is suddenly helpless.
1). Of course the f-pawn is now immune since 1...Rxf3? 2.Rb8 ensures a8Q on the next move.
2) Black's king cannot move to the e-file: 1..Ke5 2.Re8+ followed by a8Q.
3)  Black cannot move his g-pawn, since after hxg he can not take back. Both fxg and Kxg are followed by a check on the back rank.

All Black can do is move his rook up and down the a-file.
So White is free to move his king, and indeed the winning plan is a very long king walk to h6!.

(Note: In the pgn-file, you will find a correction on a side variation provided by Dvoretsky).

Diagram 8 Unzicker-Lundin, 1954)

* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

White's next plan is to give up the a-pawn, and win blacks kingside pawns.

1.Rb8!,Rxa7 2.Rb4+,Ke6 3.Kxg6 +-
and blacks h- pawn will eventually drop as well.

Summary
The previous analysis and examples allow us to answer the question if there are any situations where the pawn on a7 rook on a8 provide winning chances. There are:
1) when White has an additional passed pawn that is not on the g/h-line.
2) when black has a loose pawns that are not defended by the king on g7. White's king can often pick them up, since the Black rook cannot leave the a-file to protect them.
3) when the Black king is not on g7 or h7 new chances develop since a check along the back rank immediately frees White's rook and guarantees pawn promotion. 


We will come across some additional examples when we examine Poghosyan’s defensive method.

PM I accidently deleted this post, and with it the thread two days ago but nobody seems to have noticed......
Shocked
  
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