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Hot Topic (More than 10 Replies) Practical Knight Endgame 4 pawns vs. 3 (Read 18875 times)
chk
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Re: Practical Knight Endgame 4 pawns vs. 3
Reply #17 - 05/09/13 at 13:28:24
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I had forgot about this thread, until Micawber made a reminder in another thread.

So I finally had a chance to go through it (not in all detail) and must say it's a very nice piece of work - thanks Micawber!
  
"I play honestly and I play to win. If I lose, I take my medicine." - Bobby
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micawber
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Re: Practical Knight Endgame 4 pawns vs. 3
Reply #16 - 01/31/11 at 05:40:44
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Paragraph 4.2.2 Passive Defence; Blacks 7th move alternatives.


Diagram
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We will look at two alternatives:
{A] 7.... h5
{B] 7.... Nc4+

Variant A

[7] 7....      h5!?

Indicated by Polugajevsky commenting on a similar position, and a one move suggestion by Tisdal. 
This makes sense. For the moment there is no ideal position for White because the advance g4 will lead to exchanges.
If white carries out the advance e4-e5 we will end up in the pawn structure we studied in Aronian-Moiseenko and the related study positions.

Variation A1 8.e5
Variation A2 8Nb3

Variation A1

[8]e5            


Variation A1.x [8]e5,fxe5?!
Variation A1.y [8]e5,Nc4!

Variation A1.x
(7...h5 8.e5,fxe)

[9]fxe            



[9]            Nc4
[10]Kf4!

[10]Ke4,Nd2+ [11]Kf4,Kf7 [12]Ne2,Kg7
[13]Kg5,Ne4+ =

Diagram 52
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*

[10]            Kf7!

Forced. 
Blacks only other king move that makes sense is 
[10]...Kd7 [11]Nf3 (protecting e5)
[11]...Ke6 [12]Kg5! +- and White wins both Blacks g/h pawns.

After a knight move, e5 is no longer hanging so White can invade Blacks king side at once.
[10]....Nd2 [11]Kg5,Kf7 [12]e6!!+, Kg7
After other king moves Black loses all his remaining pawns without compensation.
[13]e7!, Ne4+! (13....Kf7 14.e8Q,Kxe8 15.Kxg6+-)
[14]Kf4,Nf6+ [15]Ke5,Kf7 [16]Kd6 +-

[11]Ke4!?
[11]            Nb6!

Keeping the White king away from d5

[u][11]...Ke7? [12]Ne2! Wins:[/u]
-a-12....Ke6 13.Nf4+,Kf7 14.Kd4+-
-b-12....Nb6 13.Nf4,Kf7 14.e6+ +-
-c-12....Nd2 13.Kd5,Nf1 14.e6!,Ne3 15.Ke4+-
-d-12....Kf7 13.Nf4,Nd2+ 14.Kd5+- eventually wins,
although the win is quite difficult in this case.

[11]....Nd2 [12]Kd5+-

[12]Ne2!                    Nc8!

Black is aiming for study positions 1 and 2.
His knight is going to e7 (from where it can defend the g6-pawn).

Both 12...Ke7 and 12...Nc4 would have lost to 13.Kf4.
\
[13]Kf3!?

[13]Kf4,Ne7 [14]Kg5,Ke6! (Or 14...Nc6=)[15]Nf4+,Kf7=
Study position 1 and 2

[13]            Ke6      

13....Ne7 draws as well
-a-[14]Nd4,Nd5 [15]Ke4,Nc3+=
-b-[14]Nf4,Nf5=
-c-[14]Kf4,Nc6= 15.Ke4,Kf7=
Transposing to the position after the 15th move of the main line
     
[14]Kf4

[14]Ke4,Ne7 15.Nd4+,Kf7 16.Kf4,Nd5+=

Diagram 53
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[14]            Ne7!


[14]...Ke7?? [15]Nd4+,Kf7 [16]Nc6! And the black knight no longer reaches e7. Suddenly blacks position is lost.

[15]Ke4,      Kf7=
[16]Kd4

[16]Kf4,Nc6!=

[16]            Kg7=
[17]Kf4      Nd5+!=


Variation A1.y

[8]            Nc4!
The simplest defence. We should realise that Black is not forced to take on e5:
if white plays e6 his e-pawn may become weak and difficult to support (for instance after f5)
If white exchanges on f6 a drawish 3 versus 2 pawn structure remains.

[9]Ke4!

[9]Kd3
(9.Ke4,Nd2+ 10.Kd5,Nf1! 11.Nc6+,Kf7  12.Kd6,Nxg3=)
[9]      fxe5!
And now [10]Kxc4,exd4 [11]Kxd4,Kf6=
leads to a drawn pawn endgame (see diag.54)

Diagram 54
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White can not outflank Black, because any manoeuvre involving Kd4-d5 by white will be answered by Kf5-g4 by Black.

Back to our main lines.
[9]            Nd2+
[10]Kd5      
[10]            Nf1!

Diagram 55
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[11]Ne2!

The attempt to promote the e-pawn does not succeed, because of Blacks counter attack against g3.

[11]Nc6+,Kf7 [12]e6!?,Ke8 [13]e7,
(13.Kd6,Nxg3=+)
[13]Kd7= [14]e8Q,Kxe8 [15]Ke6,g5!
[14]Kxf6,g4! [15]Kg6,Nxg3=

[11]            Ne3
[12]Kc5
     

[12]Ke4,Nf5=

[12]            Nf5=

Variation A2

[8]Nb3!

Much more dangerous than [8]e5.

[8]            Nc4+
[9]Kd4      


Diagram 56
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[9]            Nb2!

[u][9].....Nd6= [/u]seems to hold as well
[u]10.Nd2 [/u](10.e5,Nf5+=) 
10......, Kf7 11.Kd7,Ke7 12.Nc4,Nb5=
Blacks knight is ready to follow the route Nb5-c3-e2 attacking g3. 

White's strongest move here is 13.Kc5 posing Black some difficulties, but objectively not winning either.
Black has less difficulties after:
13.e5,Nc3+ 14.Kd4,Ne2=

[10]Nc1!


King moves are also not very helpful to improve White's position:

[10]Kc3,Nd1+ [11]Kd2,Nf2 [12]Ke3,Nd1=
White has not made any progress.

[10]Kd5,Nd1 [11]Ne2,Nf2=
And now it is important to establish that creating a passed pawn does not lead anywhere.
[11]e5,Nh1 (or 11...Ng4) [12]Nf1,Nf2=

[10]            Na4!

[10]...Ke6?[11]Nd3!,Nd1 [12]f5!+,gxf [13]Nf4+-

[11]Nd3!      

[11]f5!?,gxf [12]exf5,Nb6 [13]Ne2,Nc8 [14]Nf4,Nd6 transposes to the main line.

[11]            Nb6
[12]f5!?      

A strategy we already now from Taimanov-Stahlberg. White splits the Black pawns hoping to win the now weak pawn on h5.


[12]            gxf
[13]exf      

Diagram 57
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[13]            Nc8!
Blacks h-pawn is now under a serious threat.
He cannot defend it, but he now has a counter-attack the f5-pawn.

[14]Nf4      Nd6!
[15]Nxh6      Nxf5+
[16]Ke4      Nd6+
[17]Kf4=
White obvious can play on for a while, but in my view his winning chances are small.


Diagram (repeated)
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Variant B
The knight behind enemy lines.
[7]            Nc4+!
[8]Kd3      Nb2+

[8]....Nd6?! [9]g4,Nf7=
With a transposition to Fine's line after [9]...Ke7?!
where Black can still draw as we saw earlier.

[9]Kc3

[9]Ke2,h5! [10]Nc6+,Kd7= is very similar to line [A2]

[9]            Nd1+
[10]Kd2      Nf2 unclear

-----------------------------------------------------
Now I had intended to publish my analysis on 7.e5! (in stead of 7.h4) . But re examining my analysis I kept discovering new ways for White to give Black a hard time (and improvements on earlier analysis). So I have to conclude I really need to do more work on this line.
The analysis is complicated by the fact, that knight endgames are relatively unexplored. Even the most elementary 2 versus 1 pawn endgames have not been examined, and require study and evaluation.

There is a logical reason why I think 7.e5 is more dangerous than 7.h4. White should not fix the pawn structure on the kingside so early. This eases Blacks defence. Instead White should adapt his pawn structure dependant on the relative knight and king positions. In many instances a pawn structure with say g4/h3 is much more dangerous than the g3/h4 formation where Black has a drawing path based on the study positions 1 and 2.

I will publish my discoveries some date in the near future, probably in a new thread, since I feel that the analysis of position after 7.e5 has become an endgame study in its own right.
--------------------------------------------------------

Wrapping up the results of this thread:
The general conclusion that the knight endgame with 4 against 3 pawns is generally won is exaggerated.
A closer examination of Fine's analysis - passive defence - shows that Black has much more defensive resources than have been explored in previous endgame literature.


Once again trying to remember concrete analysis is not very fruitful. Following Dvoretsky you should not remember lines, but methods.

White has good chances to win this endgame:
{1} if he can move all his pawns to the 4th rank
{2} if he can seduce Black to make a weaking move with his h-pawn (h6 in Portisch-Ljubovic; h5 in Taimanov-Stahlberg)
{3} the move e4-e5 creating a passed pawn needs preparation to the point that White at least assures that the enemy king is pushed back to the 7th rank or the g-line.
{4} If black has moved his h-pawn to h5, f5 is a useful strategy, splitting up blacks pawns in order to pick up the weak h-pawn later.

Black on the other hand should remember at least the following points:
{1} The h-pawn is best left on h7
{2} His ideal pawn structure is f6-g6-h7
{3} He should take care not to let his knight be confined to the back ranks, but activate it (behind enemy lines).
{4} An active knight, can be used for a counter attack white's g and h-pawns.



  
Knight_Endgames_4.pgn ( 12 KB | Downloads )
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micawber
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Re: Practical Knight Endgame 4 pawns vs. 3
Reply #15 - 01/22/11 at 09:27:57
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4.Passive Defence

diagram (repeated)
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[4]            Kd7!

From the previous paragraph we learned that neither 4...g5 nor 4...f5 is good enough to draw.

Note that Black should be wary about playing ...h5 when after f4/e5 we might get a position that is similar to Taimanov-Stahlberg.

[5]Nd4      f6!

An important move, that takes some important squares under control, and avoids the danger of being cramped to much by white's advancing pawns.

[6]f4            Ke7

A first important moment. Black passes over the opportunity to move his knight behind enemy lines.
(The strategy that might have saved him in Rossetto-Stein).

[6]....Nc4+ [7]Kd3,Nb2+ unclear
was a serious alternative.

[7]h4

Given an exclamation mark by several analysts  (Dvoretzky for instance). But we will come back to this position later on


[7]            Nf7!?

Black had two other moves here that might be good enough to draw: 7....Nc4+ and 7...h5
We will examine them later.


[8]g4

White is setting up his ideal position. 
We should note the little difference between this position and Portisch-Ljubojevic.
Blacks h-pawn is still on h7 (iso h6)
his knight is on f7 (iso of c7)

diagram 48
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[8]            Kd7

[8].....Nh6!? <not considered by Fine> Was another move that would have given Black excellent drawing chances.
Because the knight is on f7, this is a second possibility to activate the knight and target the slightly weakened g-pawn. (the other method is of course “knight behind enemy lines”).

[A] [9]g5,fxg [10]fxg5,Nf7 =
And I have not been able to find a method to push back Blacks king and advance white's king to d6.
{B}[9]Kf3,Nf7 (now 10.Ke3,Nh6 repeats the position) [10]Nb5,Nd8 [11]Ke3,Ne6! [12]f5,Nd8
(12....gxf seems to hold as well) [13]g5,Kf7=


[9]Kd3!
[9]g5?,fxg [10]hxg,Ke7 [11]e5,h6=!

[9]            Ke7?!

[9]....h6= (Not considered by Fine and others)
was another interesting option to make use of the f7-knight to force exchanges with g6-g5.
[A]10]h5,g5!? [11]Ke3,gxf4+ [12]Kxf4,Ne5=
And both sides have multiple weak pawns.
Black enjoys a strong square on e5 for his knight.
{B]}[10]Kc4,g5! [11]hxg,hxg [12]fxg,Nxg=

[10]Kc4

diagram 49
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[10]            Kd6??

This was the last point in Fine's analysis where Black has drawing chances. His best moves were [10]...g5 and [10]...Nh6

[10]....g5 [11]hxg5,fxg5 [12]fxg5,Nxg5=
seems the simplest solution:
[13]Kd5,Kf7 [14]e5,Ke7 [15]e6,Kf6!=

[10]...Nh6 offers good drawing chances as well:
[11]g5,Ng4 is the idea.
Again Black has found his way to position the knight behind enemy lines.
[A] [12]Kd3,fxg5 [13]hxg5,h6 [14]gxh,Nxh6=
{B} [12]Nc6+,Kd6 [13]Nb4,Ke6 [14]Kd3,h6=



[11]g5!
The winning move

[11]            fxg
[12]hxg5
[12]            h6

Fine also examined
[12]....Ke7 [13]e5! (I think 13.Kd5 wins as well)

[13]....h6! (Micawber)
(Fine gave only <= [13...Nd8 14.Kd6,Nf7 15.Nc6+,Ke8 16.e6+-)
[14]gxh6!,Nxh6 [15]Kd5+-
Transposing to Fine's alternative line 15th move

[13]e5+ wins

diagram 50
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*


White gladly accepts the free tempo given him by black on move 10.

[13]            Ke7
[14]gxh6      Nxh6
[15]Kd5!
White's extra tempo tells, if you compare this position with say the positions in the line [10]...Nh6 after Blacks 14th move.
He has used it to break through with his king.
[15]            Ng4
[16]Nc6+!
White now drives the Black king to the last rank

[16]            Ke8
[16]...Kd7 (is another line by Fine)[17]e6+,Ke8 [18]Kd6!
And White will continue by playing something like Nb4-d5; e7; Nf6/c7 winning.

[17]Ke6!+-

diagram 51
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It is no longer possible to stop the promotion of the e-pawn, or prevent the capture of his by now very weak pawn on g6.
[17]...Ne3 [18]Nb4 ([18]Ne7) Ng2 [19]Nd5+-


Retrospect:
Fine's winning line is not nearly as convincing as it has been considered by previous analysists. In fact Black passed over several promising drawing lines, and finally gave White a free extra tempo.
White's winning method is 
1.to cramp Black's position (g4-g5)
2.break through with his king
3.confine Blacks king to the back rank or to the g-line.
4.Advance his own e-pawn only after thourough preparation.
Black's defences arsenal consists of:
1.simplification/exchange of pawns. (Thx to the position of the knight on f7 this can be brought about by answering g5 with h6, or playing a well timed h6 to play g5 himself)
2.an active position of his knight – behind enemy lines – from where it can counter attack White's pawns.
3.block the advance of white's king keeping his own king on e7.


The pgn file will appear in my final post on this endgame where I will examine white and blacks alternatives on move 7.

It may look that I have been very critical on Fine's study.
But we should remember that it woud not have been possible to delve deep into this endgame without his pioneering work.
He discovered a number of important winning methods   
Finally, an author has only limited space and time he can devote to a single example. Fine's book was one of the first endgame encyclopaedias and  set a standard for subsequent authors to build on.

  
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micawber
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Re: Practical Knight Endgame 4 pawns vs. 3
Reply #14 - 01/17/11 at 07:41:37
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[4.1.2]
Active Defence 2 ...g5

Variation B
[4]            g5!?
This variation has largely ignored by analysts.
Fine's 13 move variation has been repeated without commentary over 70 years.
If we examine this line more closely, we find that Blacks play in Fine's line is rather cooperative.

Diagram  40
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[5] Nd4+      Kf6
[6] f4
[[6]            gxf
[7] gxf            Nc4+

[Var B1] 8.Kd3
[Var B2] 8.Kf2

Variation B1

[8]Kd3!            
Not considered by Fine or other analysts.
             Nb2+
(Otherwise White will play e5+ followed by Ke4)
[9]Kc2            Nc4
[10]e5+!      

Diagram 41
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*

[10]            Ke7

[10]....Nxe5?! [11]fxe5,Kxe5 [12]Kd3+-
White's last pawn ensures the win. (this is actually confirmed by the 6-men-tablebase)

[10].....Kg6 [11]Kd3,Nb6 [12]f5+,Kg7
[13]Nc2,Nd5 (White frees d4 for the king)
[14]Kd4,Nc7 [15]Kc5 +- and White breaks through.

[11]Kd3      Nb6
[12]f5      Kd7
[13]Ke4      Nc4
[14]h3

This tiny move, removes the h-pawn from any attack by Nf3. White can well afford this, since Black has no active counter play.
Next on the agenda is the final push of the e-pawn.
It seems that if Black is pushed back sufficiently, despite the reduced material, there always seems a win. The far advanced e-pawn, in combination with Blacks'weak h-pawn seems to provide a sufficiently large advantage.
[14]Nc2 preparing Kd4 and pre-empting Nc4-e3 is good as well.

[14]            Ke8
[15]Nc6

Diagram 42
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*

Again room is made for the white king on d4.
In general White intends to support his e-pawn with his king approaching from the queenside.

[15]            Kd7

[15]...Kf8 [16]e6!,fxe [17]fxe,Kg7 [18]Ne5,Nd6
[19]Kd5 +- is another win.

[16]Nb4

White by now also threatens Nb4-d5-f6-xh6

[16]            Ke8
[17]Nd5

Confining Blacks king to the back rank.
Notice that all the while, the black knight has had no access to the white h-pawn, so no counter play.

[18]            Kf8
[19]e6!      Fxe6
[20]fxe      Kg7


Diagram 43 White wins
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*

Blacks pieces can no longer coordinate to prevent the invasion of white's king. This is most easy to see if you suppose that it is Black to move.
And indeed this is the winning method after
20...Nd2+ 21.Kd3,Nb1 22.Ke4,Nd2 23.Kd4!
When 24.Kc5 is next, aiming for d6/d7

Variation B2
This was Fine's original variation

Diagram 44
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[8] Kf2?! (Fine)
I have my doubts if this really wins.
It's aim seems to win a tempo against Black's knight, since the king eventually will return to the queen side.

In the variation Fine now gives, White gets full cooperation from Black. He moves his king to a position on the kingside from where it is hardly effective. While the proposed tour of the Black knight rather helps than hinders White.      

Var B.2.1

[8]            Kg7? (Fine)
After this move, I consider the position to be won for white. Even though the win is harder than Fine suggested.

[9] e5!
White prevents .....f6!
[9]            Kg6
[10]Ke2      Nb2+

[10]......Nb6!? (Not considered by Fine)
A sample line:
[11] f5!,Kg5 [12]Kf3,Nd5 [13]Ke4!
(13.Kg3?,Ne3 Only draws)
[13]...Nc3 14.Kd3!,Nd5 15.f6! ,Kg6 16.Nc6,Kf5 17.Kd4 +-
More analysis on this line is provided in the pgn-file

[11]Kf3      
[11]            Nc4+ (Fine)

[11].... f5!? [12]h4!(not considered by Fine)
With the intention to exchange the h-pawn for black's f-pawn.([12] Nc6 wins as well)

A sample line.
[12]....,h5 [13]Ke3,Nd1 [14]Kd3,Nf2+ [15]Kc4
And the king breaks through on the queenside.

[12]Ke4      
[12]            Nd2+
[12]....Kg7 (not considered by Fine) [13]f5! 
A sample line
[13]f5!,Kf8 [14]h3!,Ke8 [15]Nc6,Nd2 [16]Kd5,Nf3
[17]Nd4,Nh4 [18]Ke4 +-

[13]Kd5
After a short detour finally the King is on his way to the queenside.

[13]            Nf1?

[13]...Kg7 was more stubborn
A sample line.
[13]....Kg7 [14]f5!,Kf8 [15]h3!,Ke7
[16]Nc6,Ke8 [17]e6!!,fxe6 [18]fxe6+-
An important position
Diagram 45
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Black intends Nc6-d4-f5; Kd6; Ng7+ followed by e7+

[14] f5      Kg5?
White has established his targeted pawn formation, and is now ready for the final break through e5-e6. 

Diagram 46
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[14]....Kg7 (not considered by Fine)
15.e6!,fxe6 16.fxe6 +-
[16]....Nxh2? [17]Nf5+!,Kf6 [18]Kd6 +-
And the e-pawn promotes.

[15] e6!      fxe6
[16] Kxe6      Nxh2
[17] f6 +-
Black can no longer prevent the promotion of the f-pawn.

For additional details on the analysis of the side lines I refer to the pgn-file.
I skipped several analytical side lines, with a reason. The line we just saw, is slightly irrelevant in the light of our final line. This will provide some proof that Black has good drawing chances after 8.Kf2?!

Var B.2.2
Diagram 44 repeated
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[8]            Ke7! (Micawber)

This is probably good enough to draw.
But at least it is a far better defence than Fine's 
[8].....Kg7:

It hinders white to set up the e5/f5 pawn formation, and robs him of an essential tempo.

[9]Nf5+

[9]e5, f6! 
(the point; Black hinders White ideal setup e5/f5)
[10]e6,

[10]Nf3?,fxe [11]fxe,Ke6= and the f-pawn drops.
[10]exf6,Kxf6= This endgame is very drawish, 
You should also note that if white moves his h-pawn, the endgame without knights is a draw (only with the pawn on h2 the pure pawn endgame can be won).

[10]..... f5!!=
Now white's e-pawn is isolated, and essentially weak, since it is not easy to support.
Once again Black need not fear the transition to an endgame with f- and h-pawn versus h-pawn.

[9]Ke2, f6=
The point, Black once and for all prevents White's ideal pawn formation. With the pawn on f6 and the King available to repel any White king invasion White's win becomes very problematic.

[9]            Kf6


I believe Black also draws after [9]....Ke6 [10]Ke2,f6!
Once again Black has prevented White in setting up his ideal pawn formation.
[11]Kd3,Nb6 [12]Kd4,Nd7

diagram 47
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I did find nothing for White here. In the present formation it is hardly possible to push the e-pawn successfully. 
White's second option playing f5+ to cramp Black is far less dangerous than the similar manoeuvre with e5/f5 against f7.
A march with the white king to the queenside has little effect, as long as the Black king controls d8/d7/d6 from e7 or e6.

[10]Ke2      Nb2

10....Ke6 is possible as well, playing f6 in the next few moves.

[11]Nd4      Ke7!

Essential, after the knight moved away, e5 was once more a threat, and Black has to make sure he can answer with ....f6.

[12]Nc2      

[12]e5,f6 [13]e6,f5!=
as in the note to move 9

[12]            f6=

And again White's prospects for a win have been reduced.
An advance of the e-pawn will reduce the material
I studied several positions with the e- plus h-pawn versus h-pawn. And though there are several positions that are actually won for the stronger side, I found no convincing way to reach them.
As allready stated Black can provoke the exchange on f6 as well (after e5). The endgame of f- plus h-pawn versus h-pawn is even more drawish.
So although it is not possible to give a definite proof that the position is drawn, I believe Black's drawing chances are quite good.

Therefore [8]Kd3! (iso [8]Kf2) is a more convincing solution.


One final note. The pawn structure seems e4/f4 against f6 also appeared in Portisch-Ljubojevics (top of this thread. The significant difference however is the position of the h-pawn. Ljubojevic had allready played the weakening h6. Therefore the h-pawn became a target and eventually fell. 
On h7 the black h-pawn is on his optimal square, since it is difficult to attack, in particular if Black has played f6 preventing Ng5

Retrospect active defences
What can we learn from the variations that where shown:
1] Exchanging the knight for another two pawns and transposing to an endgame with 4 pawns versus pawn and knight is an important weapon.
[2]The active defences where black plays ...f5 leaves him with a troublesome weak f-pawn.
[3]The active defence g5 allows Black to exchange g-pawns.
[3a] White's plan is to set up an e5/f5 pawn formation, and push Black's king back to the 8th rank. His own king is ideally placed on d6/d7.
[3b] Black given the chance should try to get f6 in, to thwart White's intentions. His king should be on e7/e6 rather than on g7/g6. His h-pawn is best left on h7, where it is difficult to attack. On h6/h5 it is likely to be a significant weakness.



All that is left for me is to consider the alternative of a prolonged passive defence. Here the previously presented material will be useful and its significance will become clear.
« Last Edit: 01/17/11 at 08:47:46 by micawber »  
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Re: Practical Knight Endgame 4 pawns vs. 3
Reply #13 - 01/15/11 at 10:07:46
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[4] Fine's Endgame study. Part 1

After all the preliminaries we are finally ready for the "main course".  


The study is by now seventy year old. And in the passed two decades already some corrections have been made. 
Still a number of inaccuracies remain. So it might be wise, to pencil some remarks in the margins of your endgame book, after examining my presentation Smiley.

Diagram 30
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[1]            Kf6
[2] g3      Ke5
[3] Nc6+      Ke6
[4] Ke3


White's goal is the position Portisch-Ljubojovic with pawns on e4,f4,g4 and h4 as we have seen. So Black can not remain passive for ever.
On the other hand, immediate activity backfires as Fine and others have proved.

[4.1] Early activity by black

We will deal with these active defences first,
As the solution is only partially complete.

[Var A] 4.....f5
[Var B] 4.....g5

[4.1.1] Active Defence 1

Variation A

[4]            .....f5
[5] Nd4+!


[5] e5??
(given by Fine as winning as well. Dvoretzky was the first after 60! years to question this verdict. In fact Benko in his revised edition left [5]Nd4+ out and only presented [5]e5 A blunder in itself)
[5].....Nc4+ (Dvoretzky.Fine only considered 5...Nf7 6.f4 +-) [6]Kd4 ([6]Kf4,Kd5= ) [6]...Nd2= (Dvoretzky)

diagram 31
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After 5.Nd4+ Black has two defences:
[Var A1 5....Ke7]
[Var A2 5....Kf6]


Variation A.1

[5]            Ke7
This variation is not in Dvoretzky's endgame manual.
[6]e5            Nc4
[7]Kf4            h6
[8]h4            Nb2
[9]Nxf5!!

diagram 32
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A fantastic solution by Fine. White transforms into a won endgame where he has 3 pawns for a knight.

[9]            gxf5
[10]Kxf5      Kf7
[11] g4!!      (Tisdal)

Fine's original solution is flawed:
[11]f4?, Nc4!= (Tisdal). And you should note that White has robbed himself of the g4-advance that is now answered by Ne3+ and the unfortunate g-pawn drops.
Actually Fine only considered [11]f4?,Nd3? 
When [12]g4!,(Micawber. After Fine's [12]h5? Black can answer Nc5! And the win is once more in doubt)[12]...Nc5 [13]g5 +- wins. 

Tisdal's analysis stopped after g4!!, giving no variations
I suppose he saw the winning method. But unfortunately he left the solution to the readers. Since this win is not trivial an explanation is helpful I think.

Diagram 33
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[11]            Nc4      (Micawber)
[12]h5!            

Now White's winning plan involves playing f4 followed by g5. The remaining position will always yield two connected passed pawns + one isolated passed pawn.

Other moves dont win.

[12]g5,hxg [13]hxg,Ne3+[14]Ke4,Nf1=

[12]e6!? Is tricky but does not win either.
[12].....Kg7! (12...Ke7 13.h5,Ne3 14.Kg6 +-)
[13]h5!,Ne3+ [14]Ke4,Nc4 [15]Kd4,Nd6 [16]Kd5,Ne8 [17]Kc6,Nf6! [18]Kc7,Nd5+!= is probably a draw.

[12]            Ne3+

After other knight moves, f4 is possible at once.
So there remain two king moves two consider.

[12] .......Kg7 (12...Ke7 13.e6 +-)
[13] Ke6!
White immediately takes advantage of the possibility to invade with his king.
[13]......Ne3!
Other moves are answered by f4.
In order to win, White wants this position, but with Black to move.
[14]Kd7,Nd5 [15]Kd6!,Ne3 [16]Ke6!
Analysis Diagram 34
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Mission accomplished:
[16]....Kf8 [17]Kf6!,Nc4 [18]e6+-
[16]....Nc4[17]f4,Ne3 [18]g5+-

[12] .......Ke7 (we allready examined [12]...Kg7 above)
[13]e6!Only move
[13]g5,hxg 14.h6,Kf7 15.e6+,Kg8 16.Kf6,Kh8! (..Kh7? 17.e7,Nd6 18.Kxg5 +-) 
17.Kxg5?,Kh7!=

[13]......, Nd6+

[14] Kg6!!. Kxe6 [15]Kxh6 +- 
win confirmed by the tablebases.

[13]Ke4
[13]            Nf1

Other knight moves would not have been better.
[13]...Nd1 [14]f4!,Kg7 [15]g5!
White executes his winning plan.
[15].....Nc3+ [16]Kf5,Ne2 [17]g6+

[14]f4
with the by now familiar plan 15.g5!, if the knight moves from f1.
[14]            Kg7!
[15]f5!

Diagram 35
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White had to change course
[15]g5? (iso 15.f5) ,Ng3+! and the h-pawn drops.

[15]            Nd2+

[15]...Kf7 [16]Kf4!,Kg7 [17]g5! (finally),hxg [18]Kxg+-
Now white gets connected e/f pawns.

[16]Ke3,      Nc4
[17]Kd4      Nd2
[18]Kd5!

And Black can no longer stop the white's pawns. After [18]...Kf7 There is a direct win with the pawn break [19]g5,hxg [20]h6!+-

variation A2
Diagram 31 (repeated)


[5]            Kf6
This variation has received more scrunity than 5...Ke7. It is for instance analysed in Dvoretzky's manual.

[6] exf5
The usual strategy, splitting Blacks pawns.
[6]            gxf5
[7] Kf4      Kg6

7...h6 8.h3+- (Fine). Black will soon run out of tempo-pawn moves.

[8] Ke5
Breaking through to the 5th rank is an achievement in itself.


[8]            Nf7!

[8]....Nc4 [9]Ke6,Nfe3 [10]f4,h5
(10...Nf1 11.Nf3! Will put Black into zugzwang. There is no longer a good answer against Nh4+)
[11]h4!,Nf1 [12]Nxf5 +- (Fine)

[9]Ke6!      Nd8+
[10]Ke7      Nb7

Diagram 36
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And from this position analysts have uncovered several winning methods for White.

[Var A2.1] 11.Ne6 (Chekhover)
[Var A2.2] 11.f4 (Fine)

Interestingly all previous analysts seem to have overlooked 11.Nb3! Trapping the knight on b7 right away.

Variation A2.1
[11]Ne6 (Chekhover)
[11]              Na5
[12]Nf4      Kg5??
More stubborn (and not considered by Chekhover/Averbakh) is 
[12]...Kg7 [13]Ke6,Nc4 [15]kxf5,Ne3+ [16]Ke4
Although with 3p vs 1p the win is not in doubt.
[13]h4            Kh6
[14]Kf6! +-
White will mate within a few moves with g4-g5

Variation A2.2
Diagram 36 repeated
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[11] f4! 
The original solution by Fine. White threatens 
Nd4-f3-h4+ winning the f5 pawn.
[11]            Nc5!
And we have another split in variations

[Var A2.2.x] 12.g4!! (Mueller)
[Var A2.2.y] 12.Nf3? (Fine)

Variation A2.2.x
[12]g4!!
This winning pawn break was uncovered by Mueller.      
[12]            Fxg4
12....Nd3 13.gxf+,Kh5 14.f6 +-
[13] f5+!      Kg5
13...Kg7 14.f6+,Kg6 15.f7,Nd7 16.Ne6! +-

[14]f6!+-
Mueller who stops here. However black can set one last trap just here.

Diagram 37
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[14]            Nd3 (Micawber)
[15] Nc6!
White could throw the win away by playing
[15]f7?,Ne5!!
----16.f8N, Nf3 17.Ne2,Nxh2= 
----16.Ke8,Nxf7 17.Kxf7,Kh4=
In both cases white's last pawn disappears.
[16]            Nf4
[17] f7      Ng6+
[18] Ke8
And white ensures promotion, driving the black knight away with Nc6-e7.

Variation A.2.2.y

[12] Nf3
This was Fine's original solution, continuing with the Nh4-plan. But he overlooked a defence pointed out by Panchenko/Dvoretzky.

Diagram 38
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[12]            Kh5!
Fine's main line ran.
12....Ne4 13.Nh4+,Kg7 14.Ke6 +-
[13] Ne5?

This was Fine's intention. He considered it winning.
At this point we should note that white has a better move:
[13] Kd6! (overlooked by Dvoretzky/Panchenko)
-----[13].....Nb3 [14]h3! +-Keeping the black king out of g4 before resuming the attack on f5
-----[13].....Ne4+ [14]Ke6 +-
[13]            h6
[14] Kf6
Fine's analysis stops here.
In my opinion White may well throw away the win here.
[14] Nd7! (not mentioned by Dvoretzky), Ne4 [15]Ke6,Kg6 [16] Nf8!+
(16.Ne5+,Kh5 17.Kxf5,Nxg3+ is unclear since it would allow the Panchenko/Dvoretzky stalemate resource from the main line)
[16]....Kh5! [17]Ke5!
(17.Kxf5?,Nxg3! =)
[17]....Kg4 [18]Nd7!,Nf2 [19]Nf6+ +-
And white finally can take the f-pawn.

[14]            Ne4!
[15] Kxf5      Nxg3+!!=/+

Diagram 39
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This fantastic stalemate resource was uncovered by Panchenko/Dvoretzky.
Although White keeps some of his advantage I have not been able to find a win from this position.

The pgn-file belonging to this post, will appear with my second post on the active defence ...g5 (iso f5)
« Last Edit: 01/16/11 at 05:38:05 by micawber »  
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Re: Practical Knight Endgame 4 pawns vs. 3
Reply #12 - 01/11/11 at 06:13:28
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Thx Stigma and Proustiskeen for the additional info.

3.3] A slightly less favourable pawn structure
(makes all the difference)

Grischuk – Moiseenko, Ch Russia, 2006
Diagram 22
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Compared with the previous example Rossetto-Stein, the kingside pawn-chain is moved one rank back. A circumstance that clearly benefits the defender.
White's king has yet to break into the defender's half of the board.
Besides this the White knight is not on an optimal square, since it will take some moves to reach f4.



[85]            Nd3+!

The importance of the study positions now becomes clear:
[85]...Nc6 is also sufficient to draw:
[86] e5+,Ke6 [87] Ke4!
[87]...Ne7! [88] Nd4+,Kf7 
And we have reached study position 1.

[86] Ke3,      Nb4?!

Missed oportunity Number 1
[86]....Nc1=!
The knight goes behind the enemy lines.
It's goal is the e2-square from where it can attack the g3-pawn.
We will come back to this position later on.

[87] Kd4      Ke6?!

Missed opportunity Number 2
Here again Black should have activated his knight
[87]...Nc2! [88]Kd3,Nb4+ [89]Kc3=
And now 89...Na6, 89...Nc6 and 89...Na2+= all would have drawn.

[88] Ng5+      Kd6??

This is the final mistake. Black allows White to advance his e-pawn with a tempo gain.

Missed opportunity 3

[88]...Kd7!= would probably still have saved the game. 
The idea is eventually to reach the setup from the study positions. It seems that Black has just enough time to repost his knight on e7.
When White's king turns to the kingside, Black plays Ke6-f7.

Diagram 23
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[89]e5+      Ke7

[89]...Kd7 no longer helps 
[90]Nh3,Nc6+ [91]Ke4,Ne7 [92]Nf4 (taking away e6) [92]....Ke8 [93]e6! +-(taking away f7). The road for the white king is now open. His king will move on to e5-d6. [93]...Nf5 [94]Nxh5+-

[90] Nh3!      Ke6
[90].....Kd7 [91]Nf4! +- and the pawn on g6 is doomed.

[90]...,Nc6+
Now White breaks through on the queenside.
[91]Kd5,Nb4+ [92]Ke4!,Nc6 [93]Nf4,Kf7
[94]Kd5! And the promotion of the e-pawn is only a matter of time.

[91] Nf4+      Kf5
Finally Black takes some active measures. But his counter play such as it is comes to late.
Passive defence would not have helped either:
[91]...Kf7 [92]e6+,Kg7 (92...Kf6 93.Nd5+ exchanges the knights) [93]Kc5,Na6 [94]Kd6+-


[92] e6!      Nc6+
[93] Kc5      Ne7
[94] Kd6      Ng8

Diagram 24
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*

White has reached his goals. The Black knight is reduced to passivity and White's king has broken through on the queenside.
Black will have to give his knight for White's e-pawn

[95]e7!,Nxe7 [96]Kxe7,g5 [97]Ng2,Kg4 [98]Kf6,gxh [99]gxh, Kg3 [100]Ng2 +- and white converted his advantage.

We now will take a look at the first of the opportunities missed by Black.

Missed opportunity 1.


[86]            Nc1=!
Moiseenko played [86]..Nb4 here 
Diagram 25
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Variation A
[87]e5+      Kf5
[88]Kd4,      Ne2+!
[89]Kd5      Nc3!
[89]...... Nxg3?? [90].Nd4! +- and the e-pawn promotes.
[90]Kd6      Ne4+
[91]Kd7      Kg4!

With his last move Black makes his defence strategy clear. He wants to eliminate White's kingside pawns, and is prepared to give his knight for the e-pawn.

Diagram 26
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*
[92]Ng5
[92]Nd4,Kxg3! [93]e6,Nc5+ [94]Ke7,Nxe6
[95]Kxe6,Kxh4=
[92]            Nxg3!
[93]e6      Nf5!
Black is planning to eliminate all white's pawns.
[94]Nf7      Kxh4=
[95]Nd6      Nh6!
[96]e7            Ng8!!

The point: 
Black's knight is on the desired circuit Ng8-f6-d5 
White must promote now, because of the threat Nxe7.. 
If White takes a queen, it directly falls after Nf6+. 
But [97]e8N, does not offer any winning chances.



Diagram 25 repeated
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

Variation B

[87] Kd2      Na2!
[88] Kd3      Nc1+
[89] Kd4      
[89] Kc2,Ne2 [90]Kd3,Nxg3 =
[89] Kd4      Ne2+
Now white's g-pawn will drop
[90] Kd5      
[90] Kc5,Nxg3 [91]Kd5,Ne2!=
[90]            Nxg3=


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

[91] e5+      Ke7
[92] Nd4      Nf5=

Diagram 25 repeated
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

Variation C

[87] Kd4!      Ke6
[88] Ng5+

[88] Kc4,Kd6! (88...Ne2?? 89.Nd4+ +-)
Now ...Ne2 is a real threat. 
[89] Nd2 (to defend against Ne2 with Nf1)
[89]......., Ke5!= (And Black regains a pawn)

[88] Ke3,Kf6!
(Note that after 89.Kf4,Ne2+ the g-pawn again drops off)
[89] Nd4, Ke5 [90] Nc6, Kf6 [91]Kf4,Nd3+!
[92] Kf3, g5!! [93] Ke3

Analysis diagram (28)
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

We have seen positions like this before. There the exchange of the g-pawns benefited the attacker.
Here the situation is different. 
The White knight is away from the main field of battle, while its Black colleague is excellently placed to attack both the e- or the h-pawn (it can easily reach g2 for instance).
So in this particular situation white's h-pawn is weaker than blacks!

[93] ...gxh4!! 94 gxh4
(94.Kxd3??, h3! And black wins)
[94]....Ne1 (eying the g2-square)
[95] Kf2, Nd3+ [96]Kg3,Ke6=
White can not make any progress.


Back to variation C main line

[88] Ng5+      Ke7
[89] Ke5      

[89]Ke3,Kf6 [89]Nf3,Ke6=

[89]            Ne2!
[90] Ne6      Nxg3
[91] Nd4      Nh1!

[91]...Kf7 92.Kf4,Nf1! 93.e5,Nd2=

[92] Nf3
[92] Nc6,Kf7 [93]Kd6,Ng3=
[92]            Nf2=

Diagram 29
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

Black is eyeing the e-pawn now.
And if the White knight moves ...g5 is on the menu!
[93] Kf4,Nd3+ [94]Kg5,Kf7=
[93] Kd5,Nh3!= With the point Nf4+ followed by ng2 and pressure on the h-pawn


I did not give to many side variations on this endgame, in fact only a small proportion of what I analysed. 
Here we encounter the problem, I pointed out in the introduction. A complete exhaustive analysis is hardly possible.

Conclusion:
The type of position from this section is won if White:
-can push back the defenders king to the 7th/2nd rank
-can confine the defender's knight to a passive position away from the stronger sides own pawn chain.

Black's defensive chances depend on:
-An active position of his knight. Mostly behind enemy lines, binding the stronger sides forces to defence of his own pawns.
-White's g-pawn is a natural weakness that invites counter attack. For the defender e2 is a very good square for his knight.
-The setup in the study positions with Kf7/Ne7 should be sufficient for a more passive defence.
Black should remember that he can sac his knight for the e-pawn, provided he can eliminate White's h- and g-pawn.

Retrospect
The pawn structure was similar, to that in the analysis on Taimanov-Stahlberg: 
passed e-pawn, g+h vs g+h, black pawns on h5-g6.
In that example White won without much difficulty.
Now what made the difference?.

The essential difference was that in that example White's h-pawn was on h2 instead of h4. 

The h2-pawn in the h2-g3 chain was far less vulnerable than the g-pawn in the g3-h4 chain.
That single fact robbed Black of any counter play in previous examples.
  
Knight_endgames_2.pgn ( 17 KB | Downloads )
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Re: Practical Knight Endgame 4 pawns vs. 3
Reply #11 - 01/10/11 at 02:55:36
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Panchenko has also been available for several years as a multi-lingual computer program "Theory and Practice of Chess Endings":

http://chessok.com/shop/index.php?main_page=product_info&cPath=7_26_28&products_...

But I too only have the German (book) version. I wonder if much updating/checking of analysis has been done between the different versions; it being Convekta I wouldn't bet on it.
  
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Re: Practical Knight Endgame 4 pawns vs. 3
Reply #10 - 01/09/11 at 23:43:17
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I think the Panchenko has been published in English.

http://www.chess4less.com/mm5/merchant.mvc?Screen=PROD&Store_Code=chess4less&Pro...
  
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Re: Practical Knight Endgame 4 pawns vs. 3
Reply #9 - 01/09/11 at 23:28:50
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Thx Stigma for the additional sources you provided:

I actually browsed the set of the three Beliavski's books
but found nothing of direct interest to these particular endgames.

Panchenko does have two pages / 7 examples that bear directly on the endgame type under consideration. Unfortunately in the relevant section he has little in the way of comments. 
Actually Panchenko's book is quite good and could do with a reprint or a first time English edition (i still have the German edition, which had rather poor printing quality/lay out).
  
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Re: Practical Knight Endgame 4 pawns vs. 3
Reply #8 - 01/09/11 at 18:19:57
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I looked at other endgame books not listed yet for coverage of knight endings with 2 or more pawns each and found:

Systematic coverage:

Panchenko: Endspieltheorie und Praktik 
Ca. 16 pages + exercises

Beliavsky/Mikhalchishin: Winning Endgame Strategy
Ca. 14 pages + exercises
(neither of these chapters are strictly divided by material)

Emms: Starting Out: Minor Piece Endgames
8 pages

Alburt/Krogius: Just the Facts
9 pages (but large font and too many diagrams)

More random coverage:

Mednis: From the Middlegame into the Endgame: 7 pages on "The Value of the Passed Rook's Pawn in Knight Endings"

Silman: Reassess Your Chess (3rd ed.): 2 pages on the value of a space advantage

Soltis: GM Secrets: Endings: 9 pages

Karolyi/Aplin: Endgame Virtuoso Anatoly Karpov: Ca. 7 pages (in 6 different games)

Giddins: 101 Chess Endgame Tips: 6 pages

Lutz: Endgame Secrets: 2 pages (Position 7 + one position that reduces to a knight ending)

The Panchenko and Beliavsky/Mikhalchishin chapters could be useful to compare with your work. But so far the only sources I've actually studied are Soltis, Mednis and Silman.
  
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Re: Practical Knight Endgame 4 pawns vs. 3
Reply #7 - 01/09/11 at 16:29:51
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By all means use the 'N' Micawber - it's a compact way to show what is new, original analysis.

Fantastic work and a great service to the ChessPub community! But you really are messing up my study plans here - I was planning to work on queen endings and rook endings before knight endings...  Wink
  
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Re: Practical Knight Endgame 4 pawns vs. 3
Reply #6 - 01/09/11 at 15:04:16
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@Smyslov-Fan:
You have my solemn promise not to use the Novelity sign again.  Wink

This post is a prelude to the final example before we are ready to tackle Fine's endgame study.
To appreciate the next example, I present two positions for you to study (not endgame studies).

[3.2] A little technique

Study Position 1
Diagram 18
* * * * * * * *
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* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

I believe the positions with this pawn formation to be drawn.
Black also draws if his knight is on c7.

In the present position White has several tries:
[a] Try to move his king to the queenside d6/d7
This will almost certainly fail because black will play g5 followed by Kg6, or
Play his knight to f5 threatening g3.
Try to put his king on g5 and knight on f4.


variation A
[b][1]Ke3
1.Ne2,Ke6 =
-- 2.Nd4+, Kf7 repeats the position
-- 2.Nf4+, Kf7 3.Ke3,Nf5+ 4.Kf3,Kg7=
     (no further progress can be made)
-- 2.Kd4, Kf5! And black threatens Kg4
[1]            Nd5+!

[1]....Nc8?? 2.Kf4!,Ne7 3.Kg5,Kg7 4.Ne6+,Kf7 5.Nf4
Diagram 19 Black to move
* * * * * * * *
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* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

5....Kg7 5.e6 +- Black is in Zugzwang!


[2]Kd3      Ne7
[3]Ke4=      

The position has been repeated this time
with Black to move. We will come back to this position later (see study 2)

Variation B
[1]Kf4      Nd5+
[2]Kg5      Ne7
[3]Ne2      Kg7
[4]Nf4      Kf7=

We have seen this position already in the note to Black's first move in variation A.(diagram 19)
Black to move, White wins.
White to move, Black draws
(white can not strengthen his position and has no useful tempo moves):
[5]e6,Kg7= or 
[5]Kh6,Ng8+ [6]Kh7,Ne7=

Study Position 2
Diagram 20
* * * * * * * *
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* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

The same position as study position 1, but this time with Black to move.
If you studied diagram 19, you noticed that one tempo may make an important difference

[1]            Kg7!
[2] Kf4!
This is the most dangerous try.
--[2] Ne2,Kf7= (White has made no progress)
--[2] Nf3, Nf5 [3]Kf4, Kf7 [4]Ng1!?,Ke6
----- [5] Ne2, Kd5!= ([5]...Kf7?? [6] Kg5!,Kg7 +- (and  white reaches diagram 19)
--[2] e6, Kf6!=
[2]            Nd5+!

[2]....Kf7 [3]Kg5!, Nd5 [4]Ne2!,Ne7
-- ([4]....Kg7 [5]Nf4,Ne7 [6]e6+- see diagram 19)
[5]Nf4!,Kg7 [6]e6 +- (see diagram 19)      

[3] Kg5
[3] Kf3 Kf7! [4] Ke4,Ne7= And we are back in study postion 1.
[3]...Nc3? (iso 3...Kf7!) [4]Ne6+,Kg7 [5]Nf4,Kg7 [6]Kd3!,Nb1
[7]e6!,Kf6 [8]Kc4 +- and white breaks through on the queenside, while the black knight is only a spectator.

[3]            Nc7!!
[3]....Ne7 [4]e6! +-
[4] e6
[4] Kf4,Nd5+! [5]Ke4,Ne7!=
Black repeats the position after 1....Kg7.
[4]      Nd5!
Now e7 is prevented and the White King can hardly move.
[5] Ne2,
[5] Nc6,Nc7! [6]Nd8,Nd5! And white can not make any progress.
[5]            Nf6!
[5]....Ne7? [6]Nf4!+- 

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

[6]Kf4            Ng4!=
And Black is ready to play Kf6 eventually followed by the knight manoeuvre Ng4-h6-f5.

It was clear that with the tempo difference Black time and again had to avoid the position shown in diagram 19.
The pgn files for these study positions will be posted together with our next practical example.

By now it is perhaps useful to indicate where I am going with this thread. In the previous examples there was always a win for the stronger side. But if there is a class of reasonable normal positions with g/h-pawns and a passed e-pawn that is drawn, it becomes possible to reshape Black's strategy in 4 vs. 3 to aim for exactly these positions.

     
  
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Re: Practical Knight Endgame 4 pawns vs. 3
Reply #5 - 01/09/11 at 02:44:11
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Smyslov_Fan wrote on 01/08/11 at 17:12:01:
This is indeed fascinating. I do have a quibble tho. You gave an improvement over a Mednis line as "N", signifying that it's a novelty.

Really?  Are we now going to start calling endgame ideas "novelties"?


Why not? It's true, isn't it?

We've got opening books that put "N" on moves in an endgame. Just sayin'.
  
2288 USCF, 2186 FIDE.

FIDE based on just 27 games.
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Re: Practical Knight Endgame 4 pawns vs. 3
Reply #4 - 01/08/11 at 17:12:01
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This is indeed fascinating. I do have a quibble tho. You gave an improvement over a Mednis line as "N", signifying that it's a novelty.

Really?  Are we now going to start calling endgame ideas "novelties"?
  
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Re: Practical Knight Endgame 4 pawns vs. 3
Reply #3 - 01/07/11 at 05:59:13
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Part [3] The pawn structures matters.
[3.1] The stronger side has far advanced g/h-pawns

I took a break the last two weeks. But I am ready to continue.
In this post, I have also included a pgn with the examples so far.



The positions with e/g/h vs g/h pawn deserve some extra attention. 
They follow logical from 4 vs. 3 after white has pushed its e-pawn and exchanged it against Black's f-pawn.
Are these positions always won? Averbakh promises good winning chances.

We will present two examples where Black can make White's life very hard, and the win seems in doubt.
One of them is won after all. But the other, with a slightly less favourable pawn structure is probably a draw (even though White won the actual game).
Actually both games where won by the stronger side, but Black missed his chances.

Diagram 15
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

[74] Nb3      
[74]            e4?

I have come to the conclusion this move is only good if the King of the weaker side is on the 2nd rank or can be pushed back immediately.
Otherwise this move must be prepared.
We will come back to this position and show that [74]....Nd5! Would have won.

[75] Nd4+!

[75] Ke4?,Kf4 -+ And Blacks king breaks through (Mednis)

[75]            Ke5
[76] Nc6+      Kd6

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

[77] Nd8!=      
[77]            Kd5
[78] Nf7!      [Mednis]

Black can make no further progress. 
(i) Black is denied an ideal set-up with Ke5/Nd5+
(ii) Blacks e-pawn now turns out to be weak. Since [78]...Nd7 (with the aim to play Ne5-c4+ to drive the king from e3) is answered by Ng5 and Black is forced to defend it with either Nc5 or Nf6 and again he can not hope to make progress.


In the game Rosetto missed this chance
After
[77]Nd4+,Kd5 [78]Ne2,Ke5
Black's king was safe from checks, and Black was once more ready to push back White's king with Nd5+.
[79] g3,g5 [80]gxh,gxh [81]Ng1,Nd5+ [82]Kf2,Kd4
And eventually White lost his pawn on h3
and the game. 
For the final moves refer to the next line after move 80.

Diagram 15  Repeated
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

What Mednis overlooked was that there was indeed a win

Analysis
[74] Nb3      , Nd5!N (Analysis)
Black should first push White's king back to the second rank before moving his e-pawn.

[75] Kf2!

[75] Kd2, Nf4!  -+ and White will lose his king side pawns.
[75] Kf3, e4+! [76]Kf2,Kf4 -+
Black has pushed his e-pawn with tempo, and is now ready for e3+ - Ke4 – Nf4

[75]            Kf4
[76] Nc1      

[76] Nd2,e4 [77]Nf1,e3+ -+

[76]            e4!

[76] ...Nb4 would have won as well.

[77] Ne2+      Ke5
[78] g3

[78] Kf1,Nf4 [79]Nc3,e3 -+

[78]            g5!
[b]This leads to a position where both sides have an isolated h-pawn. But only White's h-pawn is really weak, since it will soon be under attack, while White lacks the means to attack its Black counterpart.
[79] gxh
[/b]
[79] Nc1,Kd4 [80]Nb3,Kc3 -+

[79] .....,      gxh
[80] Ng1

Diagram 17
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*
We actually now have transposed to the position of the original game after White's 82th move!, but without allowing white any counter play.

[80]            Kd4!
[81] Ne2+      Kd3
[82] Nc1+      Kc2
[83] Ne2      Kd2

Diagram 18
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
*

Black's remaining task is to push his e-pawn all the way. 

[84] Nd4      Nf4
[85] Nf5

[85] Nb3+,Kd3 [86]Nc5+,Kd4 [87]Nb3+,Ke5-+
and the h-pawn drops (Mednis)

[85]            Nxh3
[86] Kf1      e3!
[87] Nxh4      e2+
[88] Kg2      Ng5+ 0-1

Retrospect.
In the actual game. White could have saved his game with an active knight, that operated "behind enemy lines" counter attacking the stronger sides pawns.
But a passive defence was doomed.

The next post will present an example where the stronger sides pawn structure is less favourable. And that will make all the difference between a win and a draw.


  
Knight_endgames_1.pgn ( 11 KB | Downloads )
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