From this day on, I will post a weekly endgame column on my blog. The positions are from new and old games, and endgame studies are included as well.
This week: The knights inability to lose a tempo, and how to compensate for that.
V. Bron 1948: White to move and win.
Take your time and try to solve the study. I have already indicated a clue by pointing out the knight’s inability to lose a tempo as it changes color with every move – and thus is unable to make a waiting move and keep the same squares under control.
Pawns are not good at waiting moves either, unless they are in the starting position, with the option of moving 1 or 2 squares forward.
Therefore, the king will have to lose the tempo, and this is done by a king triangulation.
The next position stems from my own analysis. However, a reader of the blog made me aware that Karsten Müller has treated the position in his DVD Chess Endgames 4 (Centurini 1887).
The clue here is not a king triangulation, but rather it is the White rook that loses a tempo at a crucial point in the analysis. One expects the long range pieces such as queen, rook and bishop to easily make waiting moves, but it is surprising when it happens on an open board featuring an enemy rook.
By the way, this is a special case of the endgame R+N vs. R that wins for the attacker, and the solution is instructive and pretty.
I hope you found this week’s material interesting, and you are welcome to contact me for future ideas for the column.
The solutions follow here:
1.Kf8? Nh6= and White is to move.
Black must return to g8 with the knight.
2…Ng8 3.Ng4 h6
3…Nh6 4.Ne5! with 5.Nf7+ mate next move.
4.Kf7 Kh7 5.Ne5 Kh8
A curious position where White to move needs to lose a tempo. However, knights cannot lose a tempo, so White needs to use the king – and the way to do it by a king triangulation. However, this needs to be prepared.
The knight is on the way to e8.
6.Ng6+?! Kh7 shows White’s dilemma: White would love it to be Black to move, when the 2nd player would be in zugzwang and lose.
6…Kh7 7.Nd6 Kh8 8.Ne8
From e8, the knight controls the squares g7 and f6 and thereby keeps the Black king trapped in the corner, and the Black knight off the f6–square. The White king then only needs to keep the e7–square under control. However, White can more than just keep this square under control, he can make a king triangulation around it and lose a crucial tempo, before returning to diagram position. The triangulation will be on the squares e6–d6–d7–e6. Meanwhile, the Black king can only move forth and back between h8 and h7.
8…Kh7 9.Ke6! Kh8 10.Kd6! Kh7 11.Kd7! Kh8 12.Ke6!
White has lost the crucial tempo by triangulation and the king now returns to f7.
12…Kh7 13.Kf7 Kh8
Same position as above, but with White to move. Now the White knight can return to g6 (or f8).
14.Nc7 Kh7 15.Ne6 Kh8 16.Nf8+-
16.Nf4 Kh7 17.Ng6+– also works.
To begin with, I would like to mention that only a limited number of positions with R+N vs. R are in fact winning for the attacker. Even if the defender is forced onto the back rank with the king. This position wins for White (to move) only because the Black king is close to the corner. In this position with rooks on the board, it is not the White king who loses a tempo, but instead the rook. Again, knights are not able to lose a tempo as they change color with every move they make, and thus are unable to make waiting moves to keep the same squares under control.
For a start, we notice that the Black rook needs to stay on the f-file. The best squares are on the 1st and 2nd rank (f1/f2) so as to stay outside the range of the White knight. If the rook is forced onto the 4th rank (f4), Black will be in trouble – and with a rook triangulation, this is exactly what White can achieve.
If Black moves first, the king can escape the h8-corner with 1…Kf8!=
1…Rf8 2.Ra1! Rf2!
The best defense at this point (the 2nd rank). The worst defense: the 4th rank.
2…Rf4?! 3.Ne6! Threatening back rank mate, and after 3…Rg4+ 4.Nf6+– there is no check on f4. White has reached this position 7 moves earlier compared to the main line.
2…Rb8 Black defends the back rank and does not try to give checks from behind, on either the f- or g-file. 3.Nh7! Defending f8, and preparing to set up mating threats once the knight lands on f6. (3.Ne4? Kf8=) 3…Rb6+ 4.Nf6+ Kf8 5.Ra7! (Threatening 6.Rf7#) 6.Nd7++– and White can safely pick up the black rook (6.Rxb7?? is stalemate).
3.Ne4! Rg2+ 4.Kf6
f2 is defended, and this is why the 2nd rank is worse than the 1st rank. White now threatens 5.Ra8+ Kh7 6.Ng5+ Kh6 7.Rh8#
Good defense by Black. With the last move, Black prepares to defend against the back rank checks by interposing the rook on g8. However, if Black were to move, the rook would have to move from g2 to g4 – a clear worsening of the position. White can hand over the move to Black with a rook triangulation.
5.Ng5 Rf2+ 6.Kg6 Kg8 leads to the position at move 2 in the main line.
A move like 6.Rc1! is also possible – it is not vital if the White rook is on a1, b1, c1 or d1 at the end of the triangulation. The important point is that the rook can stay flexible and deliver checks on both the back rank and the h-file.
Same position, but with Black to move.
Black was forced onto the 4th rank.
7…Rg7 8.Ng5+– and Black is soon mated: 8…Rb7 (8…Kg8 9.Ra8#; 8…Rg8 9.Rh1#) 9.Ra8+ Rb8 10.Rxb8#
8.Ng5 Rf4+ 9.Kg6 Kg8
Compared with the position on move 2 in the main line, the Black rook is now on the 4th rank, not the 2nd.
10.Ne6! Rg4+ 11.Kf6
Now Black has no check on the f-file (f4).
With the knight on e6, White also covers the important g7–square. White is closing in on the Black king. Now mate on the h-file is a threat.
And now mate on the back rank is threatened!
With the king on h8 instead of g8, there is no reasonable way to prevent back rank mate.
You can also find and play through the detailed solutions here.
I would like to mention some similarities to the endgame R+B vs. R:
- The idea of rank priorities: in our R+N vs. R, we saw rank 1-2-4, in R+B vs. R we shall see 2-1-3. More of that in a later blog post!
- The idea of the Black king being ‘out of balance’: with the kings opposed (say, g6-g8), Black is ready to answer checks on the back rank with Rf8. If ‘out of balance’ (on h8), this is no longer an option. In R+B vs. R, the attacker has ways to force the defender’s king ‘out of balance’ – usually a disturbing rook check on the 7th rank.