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micawber
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Re: Practical Knight Endgame 4 pawns vs. 3
Reply #2 - 12/27/10 at 15:33:21
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The endgame Taimanov-Stahlberg, continued

Diagram 7 Repeated
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* * * * * * * *
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*

[47] f5      Nb4
[48] f6!?      Kf8
White now first improves his king position, and imprisons his opponents king.
[49] Nb7      Na6
[50] Kd5      Nc7+
[51] Kd6

Diagram 10
* * * * * * * *
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*

[51]            Nb5

[51]....Ne6 fails on tactical grounds.
[52]Nc5,Nd4 (White threatened to exchange knights) [53] e6!,Nf5 ([53]...fxe6 [54]Nxe6+ and white exchanges knights after all) [54]Ke5,fxe6 [55]Nxe6,Kf7 [56]Ng5+,Kf8 [57]h3!
Analysis diagram C
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* * * * * * * *
* * * * * * * *
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*
And Black is in zugzwang.
[57]...Nxg3 fails to [58]Ke6 and with the help of Nh7+ the f-pawn will promote.

[52] Kd7
[52] Kc5 would have won as well
[52]      Nd4
[53] Nc5      Nf5
[54] Kd8      Nd4
[55] Nd7+      Kg8
[56] Ke8      Ne6
In the last few moves White managed to drive of the Black king and  improved his own kings position.

Diagram 11
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*

Now the most effect move would have been 
[57] Nb6! (taking measures to restrict the black knight.
Variation A
[57].....Ng5 [58] Nd5! Is already zugzwang. If the knight or king move the f7-pawn drops directly or after the intermediate Ne7+.
Variation B
[57]....Nc7 [58]Ke7!,Ne6 [59]Nd5!
And there is no defence against Ke8 followed by Ne7+.

[57] Ke7      g5

[51]....Nc7 [52]Nb6, Ne6 [53]Nd5! +-
Again with the threat Ke8 followed by Ne7+
[51]... Nd4 [52]Nc5 +-([52]h4,Ne6 [53]Nb6 wins as well)

[58] Ke8

Now the most efficient win again would have been 
[58]Nb6!,g4 [59]Nd5 +- with the by now familiar zugzwang position.

[58]            Nc7
[59] Kd8      Ne6
[60] Ke7
After this triangulation White has reached the same position as after Black's 57th move. But this time Black has to move.

Diagram 12
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*

Pawn moves don't help. White will just perform a new triangulation:
[60]...g4 [61]Ke8,Nc7+ [62]Kd8,Ne6 [63]Ke7 and again it is Blacks move while his pawn moves are now exhausted.

[60]            Nd4
[61] Nc5      Nc6+
[62] Kd6!      Na5
[63] e6!      Fxe6


Diagram 13
* * * * * * * *
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*

Now there is a direct win with
[64]Kxe6,Nc6 [65]Nd7! +-
And white controls all squares needed to promote the f-pawn.
[65]...Nd8+ [66]Kf5 wins
[65]...Nd4+ [66]Ke5 wins

[64] Ke7      Nc6+
[65] Ke8      Ne5
[66] Nxe6      Nf7
[67] Ke7

[67] Ng7,Nd6 [68]Ke7,Nc8 [69]Ke6 would also have won.

[67]            g4
[68] Ng7! +-

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

And White picks up the h-pawn with a clear win
It might seem that Taimanov did not always play optimal. But you should consider this was OTB, and he played it save giving Black no chance at all to complicate the game.
This is a principle from Russian endgame literature:
“Do not hurry”.

Retrospect.
In the main analytical lines, White transformed the position to N+3 vs. N+2 pawns with a passed e-pawn.
This has been the choice of GM's in similar positions.
Taimanov on the other hand choose to transpose to a 3 versus 2 position where, thanks to Zugzwang he created a passed f-pawn. We should point out that the latter method only worked out because of White's enormous space advantage and the far advanced position of the f-pawn.
In general N+3 versus N+2 on the same side without a passed pawn should be considered drawn..

  
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micawber
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Re: Practical Knight Endgame 4 pawns vs. 3
Reply #1 - 12/26/10 at 07:39:22
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2. White's winning chances

What is required for white?

(I)To create a passed pawn
This will usually be at least the e-pawn. However to do so without any preparation may result in a position where white can not make progress.
(II)To infiltrate with his king into Blacks position
To support the passed pawn, to restrict the movement of Blacks pieces or to attack Blacks remaining pawns.
(III) To create weaknesses in Blacks position.
In particular to create an isolated pawn in Blacks formation. Such a weak pawn will tie the weaker sides pieces to the defence of the pawn and restrict their freedom of movement.

Let us now look at an ideal example.

Diagram 3.
Portisch – Ljubojevic, Olympiad, 1988
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*

White has a second advantage beside his extra pawn. He controls more space, and his pawns have advanced further and are thus closer to promotion.
[42] Kc4
White improves his king's position and prepares an eventual penetration on the queenside
[42]            ,Kd7
Other moves would not have helped
[42] ....Kd6 [43] h5! (creating a pawn weakness), gxh5 [44] gxh5, Kd7 [45] Kd3! (White must think about the defence of his f-pawn [45] Nf5?,Ne6=)
[43] h5!
Creating a weakness in Blacks pawn formation. Of course white also ends up with a weak h-pawn, but this is less serious as it is difficult for Black to take advantage of.
[43]            gxh5
[43].....g5 [44] fxg5,fxg5 [45] Nf5 +-
[44] gxh5      Ke8

[45] Kd3!
As before white must guard the f-pawn
([45] Nf5,Ne6=)

diagram 4
* * * * * * * *
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* * * * * * * *
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*
Compared to diagram 3 the position has transformed.  Blacks pawn on h6 is potentially under threat after Nf5. So Black takes some defensive measures.
[45]            Kf8
[46] Nf5      Ne6!
[47] Ke3!      Ke8
[48] Kf3!
The h-pawn is going nowhere. But [48] Nxh6 is premature. After [48] ...Ng7 White loses his own h-pawn and the win is in doubt.
With the text move White assures he can answer ...Ng7 with Kg4.
[48]            Kd7
[48]....Kf8 [49]Nxh6,Ng7 [50] Kg4 +-
[49] Nxh6      Ng7

Diagram 5
* * * * * * * *
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* * * * * * * *
* * * * * * * *
* * * * * * * *
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*
White has achieved his goals. In only seven moves he has transformed an advantageous position to a
clear win.

Now [50] Kg4 would have been the thematic continuation. Remember that in a knight endgame a passed a- or h-pawn is a deadly weapon. On the edge the effectiveness of a knight is much reduced.

Ftacik indicated a second winning method
[50] Nf5!, Ne6 (only move since after [50]...Nxh5 [51] Kg4 traps the knight) [51] Kg4!,Nf8 [52] Nd4, Ke7 [53] Kf5 +-

Portisch on the other hand spots yet another winning method, based on the position of the Black king he transforms the position into a technical win of Kt+2p versus Kt.
[50] Ng8!?      Nxh5
[51] Kg4      Ng7
[52] Nxf6      Ke6 +-

Diagram 6
* * * * * * * *
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*

The rest is technique as they say.
Now Portisch played 53.Nh5 here and sent his king on a pilgrimage to the queenside and back again.
The game lasted another 22 moves!

However at this point the most direct winning method would have been.
[53] Kg5! (penetration through the king side),Kd6 [54] f5! +-
Blacks knight is lassoed in by the knight on f6 and the f5-pawn. Black is already in Zugzwang.

Example 2
Diagram 7, Taimanov – Stahlberg, Zurich, 1953
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*

This game is taken from the Zurich candidates tournament, made famous by Bronsteins marvellous book. Unfortunately Bronstein hardly commented on this phase of the game. 
The pawn structure is slightly different here. But again white has a clear space advantage beside his extra pawn.

[47] f5!!
The best moment to advance. 
In contrast to a pure pawn endgame, h3 followed by g4 would be less accurate. It would only lead to pawn exchanges, thus increasing Blacks drawing chances.
[47]            Nb4!

Taking on f5 will leave Black with a weak h-pawn. White will take advantage with Nf5-d4-e2-f4 putting pressure on this weakness. 
[47]....gxf5 [48] Nxf5!,Kg8 
[49] Nd4 ,Ne7 [50] Ne2!, Kg7 [51] Nf4,Kh6 [52] h4! +-
[The variation above was provided by Mednis]
The knight must move and white's king will infiltrate f5.
Analysis diagram A (after [52] h4)
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*

Back to our game.
After [47] ...Nb4 white as several winning methods.

[48] fxg6, fxg5 [49] Nb5 was proposed by Mednis.
And indeed this wins, but white will have to take some care to bring the beacon home.

[48] f6! Relying on Zugzwang and king infiltration through the queenside was Taimanov's choice in the game. We will come back to this later.

I think the most accurate method is
[48] Nc8+!
A usefull intermediate move.

Diagram 8 (Analysis)
* * * * * * * *
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* * * * * * * *
* * * * * * * *
* * * * * * * *
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*
Now Kd7 and Ke8 fail for tactical reasons:

[48]...Kd7 [49] e6+!,fxe6 ([49]...Kxc8 [50]exf7!+-) [50] fxg6!,Nd5
[51] Ke5, Kxc8 [52] Kxe6
and the g-pawn can not be stopped.

[48]....Ke8 [49]fxg6,fxg6 [50]e6!,
And the route for the White King to Blacks king side is wide open (Ke5-f6-xg6)
[50]....Kd8 [51]Nb6,Ke8 [52]Nd5! +- (winning a tempo) [52].....Nc6 [53] Nf4!,Ke7 [54]Nxg6,Kxe6 [55] Nxh4+ and White has a technical win.

The third variation to consider is 48...Kd8
[48]....Kd8 [49] fxg6,hxg6 ([49]..Kxc8? [50]gxf7+-) [50] Nb6!
(The white knight is on his route to the optimal square f4 Nb6-d4-f4)
[50] ..., Ke8
([50]..... Nc6 [51]Kd5; [50] Ke7??. [51]Nd5+))
[51] Nd5,Nc6 [52] Nf4 +-

Analysis diagram B
* * * * * * * *
* * * * * * * *
* * * * * * * *
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*
[52]...Kf7 [53]Kd5,Ne7 [54]Kd6,Ng8 [55] Nd5 +-
Black is in Zugzwang. After Nh6 the e-pawn will go all the way.

Back to the main line.
Diagram 8 (Analysis) - repeated
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*
[48]            Kf8
[49] fxg6!      hxg6
[50] e6!
White now has  a more favourable version of Mednis variation.
[50]            Nc6

This at least prevents Ke5 for the moment.
[50]...Ke8 [51]Ke5,Kf8 [52]Kf6 +-
[50]...Kg7 [51]Ke5,g5 [52]Kd6,Kf7 [53]e7+-

[51]Kd5      Na5
[52]Ke5      Kg7

[52]Nc4+,Kf6 loses at once.

Diagram 9
* * * * * * * *
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* * * * * * * *
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*

White has achieved much, if you compare the above diagram with diagram 8. He has created a passed pawn and his King has broken through to the 5th rank.

[53] Nb6
Restricts the freedom of the knight and prepares Kd6
[53] .....      Nb7
At least for the moment Kd6 is prevented.
Note that Black is almost in Zugzwang. After a king move White breaks in with Kf6. After another knight move Kd6 is dangerous.
[53]... g5 [54] Nd5! (After Blacks last move White no longer worries about Nc4 since now f5 has become available for his king) 

[54] Nc4!
Zugzwang
[54]            Kf8
[55] Nd6!
Threatening to exchange knights is now a powerful weapon in white's hands.
[55]            Nd8
[56] Kf6 +-
And Black will loose his remaining pawns.


In the second post of section 2, I will return to the actual course of Taimanov-Stahlberg. Taimanov's winning method although it is a bit lengthy (the game lasted till move78), is quite instructive as well.

Up till now not very much has been presented that is really new. 
And you might be misled to conclude that winning this endgame is quite simple. And so it is, under the most favourable circumstances. 
What I will try to prove in the final posts is, that Black has decent drawing chances with other pawn structures. And that the analysis of some of these structures leaves much to be desired.


PM. I will post a pgn on Portisch-Ljubojovic and Taimanov-Stahlberg in my next post, when I complete the analysis on Taimanov-Stahlberg.




  
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micawber
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Practical Knight Endgame 4 pawns vs. 3
12/23/10 at 23:01:10
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Knight endgames 4 pawns versus 3
Pawns on one side of the board.

1.Introduction

The theory of knight endgames involving two or more pawns on each side is somewhat limited. The best sources in my opinion are:
Batchford Chess Endings (Tisdall)
Practical Knight Endings (Mednis).

In other sources this kind of endgame is treated somewhat marginal:

Averbakh, Handbuch der Endspiele, 
Laufer und Springerendspiele: (20 pages/312)

Muller, Fundamental Chess Endings
(10 pages/400)

Dvoretzky, Endgame Manual, 2nd edition
(7 pages/377)

Howell, Essential Endings
(3 pages/155)

There is probably more than one reason for this somewhat shabby treatment.
The first is, that almost all manuals quote Botvinnik's maximum that Knight endgames are quite similar to pawn endgames.
The second, from my own experience, is that this type of endgame is quite difficult to analyse, since slightly different knight/pawn configurations may drastically change the evaluation.
The third, also from my personal experience, is that the winning methods in knight endgames may be quite long, and at times seem to depend on somewhat accidental tactical “tricks”.

At least I want to remark on Botvinnik's “rule”.
This is mainly dependent on an important fact in knight endgames:
A knight by itself cannot win or loose a tempo.
In this a knight is unique compared to all other pieces. (or stated otherwise a knight's square changes colour with each move).

The following position should bring this lesson home:

diagram 1
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* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

In the example above Black has the choice between Kf8 and Kf7. Only Kf8 draws. This is easy to see. On his next move the white knight moves to a white square controlling only the black squares.
But in order to win, the knight must eventually control the f7 square if the black king is on f8. This clearly is not possible. On the other hand Kf7 will loose.

However the presence of knights on the board, does add significantly to the complexity of the endgames.
One point is that quite a few simplified endgames with 3 vs 2 pawns or 2 vs. 1 pawn on the same side of the board can not be won because the weaker side has an additional drawing option:
To sac his knight against the stronger side's remaining pawns.
A second point is, that to convert an advantage often involves optimal cooperation between the stronger sides knight and king to limit the scope of the weaker side, and bringing about Zugzwang is generally more difficult than in a clear pawn endgame.

Back to the core of what I want to show in this thread. 
Fine, on the basis of his endgame study from 1941, assessed the endgame with 4 vs. 3 pawns on one side as a win. This judgement has been repeated by most endgame books. 
I want to take a closer look at this endgame and others like it, to show that the analysis is probably not al that accurate. 


It particularly concerns the following position, which I think has been evaluated incorrectly in the past. Further you will see that the analysis published on this and similar endgames contains quite a number of errors.

Diagram 2
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* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

Those who followed my threads before, know that I my approach to this endgame will be stepwise. 
a) First two clearcut examples on the winning method for the stronger side.
b) A few (in fact as few as possible) technical positions you need to know, when tackling this endgame.
c) The basic method of defence for Black, and the subtilities of this endgame.

As usual, it will probably take several posts and a week or two for a complete presentation.
And eh, I promise to post pgn files on the longer variations and the most interesting positions.

  
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