Thursday, August 23, 2007

Nailing Down an Endgame Advantage

This week, at our chess club, we had another fine lesson by our IM who is also the endgame expert of ours. He presented this position:


Black to move.

First, as always, comes this question: Who is better, how much, and why? It is clear that Black is better, even much better, and this should him bring a win. Both have been strong players, and the game was drawn. What went wrong?

Black has not been aware WHY he was better and he missed to nail down the advantage. Black certainly is better because his King is better, his Knight is better and his pawns are more advanced, and his whole army is united whereas White's army is split.

Black too fast pushed forward his plan, that is, an attack on the white pawns. He moved b4 with the idea Nb7-d6-b5-a3 to attack c2. Most of us would have played this way, but it comes out that White manages to save his pawns with Kg4-f3-e2-d1.

The only way to win is by nailing down the advantage of the split white army and move 1.-Ke3!, cutting off the white King from his pawns forever. The plan of attacking the white pawns can wait because White cannot move them, and his Knight already is in his best position to block the black King from intruding.

Take home message: If you are better, always look where your biggest advantage is and try to make it even better.

Update

Glenn Wilson says in his comment that the position is drawn according to a Fritz analysis. So I have done an analysis with Deep Shredder and come to the same conclusion. Thanks Glenn!

Pawn move as played in the game
1.-b4 2.Kf3 Nd6 3.Ke2 Nb5 4.Kd2 drawn because the white King has joined his army.

Knight move
1.-Nd6 2. Kf3 Ne4 3.c4 bxc4 4.bxc4 Kd3 5.Kf4 Nc5 6.Ke5 Kxc4 7.Na3+ Kb3 8.Nb5 a4 9.Kd5 Nd3 10.Kc6 Nf4 11.Kc5 Ne6+ 12.Kc6 Kb4 13.Kb6 this looks also drawn but surely is more critical than the line after the pawn move.

King move
1.-Ke3 2.Kf5 b4 3.Ke5 Nc5 4.Kd5 Ne4 5.Kc6 Nc3 6.Kb6! Nxb1 7.Kxa5 Kd2 8.Kxb4 Kxc2 drawn. It seems our IM has overlooked that the Knight on b1 can be given and that the King has enough time to attack the black pawns from the north side.

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8 Comments:

At 4:36 PM, Blogger Temposchlucker said...

Botwinnik's rule:
A knight endgame is won when the underlying pawnending is won.

But they tend to be very difficult.

 
At 1:50 AM, Blogger Glenn Wilson said...

Interesting endgame. Botvinnik is right, of course. :-)

Knights with pawns on one wing would normally be drawn. But yes, the White king is offside and the white knight is poorly placed. I would have thought this is drawn with correct play but will defer to the IM who has studied the position (and Ke3 is very convincing!).

Thanks.

 
At 9:42 AM, Blogger Christian said...

Indeed, the drawn line of the game has proven Botvinnik's rule. The knights have been traded and Whites's king, after having rushed to the queenside just in time, managed to secure a drawn pawn ending.

 
At 1:28 AM, Blogger Glenn Wilson said...

I no longer defer to the IM who has studied this position. I'd like to see some analysis.

After 1...Ke3 2. Kf5 it looks drawn. I'm looking at it with the assistance of Fritz. Two idiot savants, so maybe we are wrong, but it looks drawn to us. :)

 
At 2:01 PM, Blogger Glenn Wilson said...

I'm not saying the position is drawn (but it might be!). I am saying that after 1...Ke3 2. Kf5 it is. I agree that 1...Nd6 looks like the critical line.

My friend Fritz and I were looking at that last night but things got a little ugly between us. We each had a few beers and were looking at the possible position with black King at a1, black pawn at a2, black Knight at c6; white King at c1 and white pawn at c2.

White to move. I say its a draw. Fritz seems sure he can win this as Black.

He needs a 5-piece tablebase...

 
At 4:22 PM, Blogger SamuraiPawn said...

Great post! Good to see that there are quite a few knights these days, who can make the studies of endgames seem like something so close to...fun!

 
At 8:39 AM, Blogger likesforests said...

Hi Mousetrapper. I also believed this position was won, but when I tried to convert the point against Rybka I discovered it was drawn. I saw 1...Ke3 as the obvious move, so I'm glad to hear that's what your IM endgame expert would pick. :)

{Botvinnik's Rule is that knight endgames are really pawn endgames. In that case, Black is surely winning and it's simply a matter of technique to convert the win.} 1... Ke3 2. Kf5 b4 {Now White's knight is impotent.} 3. Ke5 Ke2 4. Kd4 Kd1 5. c3! {A draw?! All other moves lose.} Kc2 6. cxb4 axb4 7. Kc4 Kxb1 8. Kxb4 Kb2 9. Kc4 Ka3 10. b4 Ka4 11. b5 Ka5 12. b6 Kxb6 1/2-1/2

 
At 8:43 AM, Blogger likesforests said...

"Knights with pawns on one wing would normally be drawn." -- Thanks; I will store away this bit of strategic advice. I've only studied pawn and rook endings with any seriousness.

 

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