Chapter 3

Rook versus Two Knights Endgames

This can be complicated and tricky; it is not well explored in the literature. The rook usually wants dynamics and clear targets and the knights aim for static control.

(a) The rook plays for a win

Usually the rook needs strong trumps to harbor real hopes to win. So we omit the discussion with only one pawn and start with two extra pawns.

(a1) R+2Ps vs. 2Ns

Often the knights either try to set up a blockade or to generate active play, which is surprisingly sometimes the right defense as there are several techniques against a passive blockade.

(a11) Two connected passed pawns

When the passed pawns both safely reach the fifth rank they usually win. If they have reached the fourth rank, a critical situation arises. If the defender is passively placed, the rook usually wins, but this can take a lot of time as the pawns can only advance when no solid blockade can be constructed:

03.01 Gavrikov – Piesina

USSR 1981

White is winning in the long run: 72…Ke7?! (DTC 21 moves) 72…Nh6!? is much more tenacious (DTC 31 moves) – see the main line below. 73.Rf1 This cut off is the best move. 73…Nd6+ 74.Kd5 Of course not 74.Ke5? Nc4+ 75.Ke4 Nd2+= 74…Nc7+ 75.Ke5 Ne6 76.Re1 Nf7+ 77.Kd5 Nfd8 78.g5 Kf7 79.Rf1+ Kg7 80.Ke5 Nf8 81.Kf5 Nf7 82.Rd1 Ng6 83.h5

Now the pawns have reached the fifth rank and Black is passive, so this is of course even better for the attacker. 83…Nf8 83…Ne7+ 84.Kf4 (84.Ke6?! Ng6 85.hxg6? Kxg6=) 84…Ng8 85.Rd7 Kf8 86.g6 Nfh6 87.Kg5+– 84.Ra1 Nh7 85.g6 Nh6+ 86.Ke5 Nf8 86…Ng4+ 87.Kf4 Nhf6 88.Kg5+–; 86…Nf6 87.Ra7++– 87.Ra7+ Kg8 88.Kf6 Ng4+ 89.Kg5 Ne5 90.Ra8 Nf3+ 91.Kf6 1-0

03.01A

White wins in 31 moves:

72.Rf1+ 72.Kf3 is also DTC 31 moves. 72…Kg6 73.Kf3!! 73.Rg1? Nc5+! 74.Kf3 Nd3!= 73…Nf7 Now White is in zugzwang. 74.Re1 Kf6 75.Kg3! Nd6 76.Re2 or 76.Re3 76…Nf7 77.Rf2+! Kg7 78.Rf1! Now Black is in zugzwang. 78…Kg6 79.Rf5! Nf8 80.Ra5 Ne6 81.Kf3! Nc7 82.Ra7! Ne6 83.Ke4! Kf6 84.Ra5! Black is in zugzwang again. 84…Nd6+ 85.Kd5! Ne8

Finally, after all the preparations, White can now advance a pawn: 86.h5! Nf8 87.Kc6! Nh7 88.Kd7! Kf7 89.g5! Nf8+ 90.Kc6!! Ng7 91.Ra7+!! Kg8 92.h6!! Nf5 93.Kd5! Nh4 94.Ke5! Nf3+ 95.Kf6 Nh7+ 96.Kf5! Nd4+ 97.Kg6 Ne6 98.Ra8+! Nef8+ 99.Kf5! Kf7 100.Rb8 Nd7 101.g6+! Ke7 102.gxh7+– 1-0

When advancing a pawn, great care is required:

03.02 Henrichs – Ball

Oberhausen 2007

White can advance directly: 47.h5+ Nxh5+ 47…Kg5 48.Rh1 (48.Rf7? Nxh5+ 49.gxh5 Nf6=) 48…Kh6 49.Kh4+– 48.gxh5+ Kxh5 48…Kg5!? 49.Rh1! Nf6 50.h6! Nh7 51.Rh4+– and Black is in zugzwang. 49.Rf7! Nb6 50.Rc7 Na4 50…Nd5 51.Rc5+– 51.Kf4 Kg6 52.Ke4 Kf6 53.Kd4 Ke6 54.Rb7 Kd6 55.Rb4 1-0

The next case is special as White’s king is imprisoned, but this does not save Black:

03.03 Analysis of D.Gurevich – Gerilstein

USSR 1976

12.Ra7+ 12.Re4? Nhg6 13.Rb4 Kh7 14.Rb7+ Kg8= (ECE) 12…Nhf7 13.Re7 Kf8 14.Re6 Kg7 15.Re8 15.g6? Nd3= 15…Kh7 16.Re7 Kg7 17.Re6

Finally Black is forced to open the prison door because of the threat g5-g6. 17…Nd3 18.Kg4 Nde5+ 19.Kg3 Ng6 20.h5 Nf8 21.Re7 Ng6 22.Rc7 Nge5 23.Kf4 Kg8 24.g6 Nd3+ 25.Ke3 Nfe5 26.h6 Nxg6 27.Kxd3+–

An active set up draws:

03.04 Hawkes – Yanofsky

Canada 1986

Black’s king cannot participate and the pawns cannot advance safely: 82.Ne6 82.Nd3 Rc8 83.Nc5 b4 84.Kc4 b3 85.Kb5 b2 86.Nc3= 82…Rh6 82…a4 83.Kc5 a3 84.Nc3! (After 84.Nb4?, the blockade can be broken by violent means: 84…Rh5+ 85.Kc6 Rh4 86.Na2 Rh2 87.Nb4 Rb2 88.Kc5 Rxb4 89.Kxb4 a2-+) 84…Rc8+ 85.Kb4 Kb6 86.Na2= 83.Nec7? 83.Ke5 b4 84.Nc5 Rh3 85.Kd4 b3 86.Nc3 b2 87.Nd3 a4 88.Nxb2 a3 89.Nb5+=; 83.Nc5 Rh4+ 84.Ke5= 83…b4 84.Kc5?! 84.Kd3 Kb7 85.Nb5 Rh4 86.Nd4 Ka6! 87.Nc7+ Kb6 88.Nd5+ Kc5 89.Nf4 Rg4 90.Nb3+ Kc6 91.Nd4+ Kb6 92.Nfe2 a4-+ 84…Kb7 85.Nb5 85.Kb5 b3 86.Kxa5 b2 87.Nc3 Kxc7 88.Ka4 Rc6-+ 85…Rc6+ 86.Kd4 Rc1 87.Ne7 Kb6 88.Nd6 Rd1+ 89.Ke5 b3 90.Ne4 b2 91.Nc3 b1Q 92.Nxb1 Rxb1 93.Kd4 Rf1 94.Nd5+ Kc6 95.Nc3 Rh1 96.Kc4 Rh4+ 97.Kb3 Rb4+ 98.Ka3 Kc5 99.Na4+ Kc4 100.Nb2+ Kc3 101.Na4+ Kc4 102.Nb2+ Kb5 103.Nd1 Rc4 104.Kb3 a4+ 105.Ka3 Rc1 0-1

An example with b- and c-pawns follows:

03.05 Ivanchuk – Rogers

Istanbul 2000

Black is so active that he could have drawn: 67…Ne6? This allows the pawns to advance safely. 67…Nd6! is forced, e.g., 68.Rh8 Ne4 69.Re8+ Ne6 70.Re7 (70.Ka4 Nd6=) 70…Kd6 71.Rh7 Ke5 72.b5 N6c5+ 73.Kb4 Nd3+ 74.Ka5 Nd2 75.Rh4 Nb3+ 76.Kb6 Kd6 77.Rh3 Ndc5 78.Rh6+ Kd7=; 67…Ng5? 68.b5 Nge6 69.Rd1 Nc5+

Black has a blockade now so White must be careful: 70.Kc3! (70.Kb4? Nfd3+ 71.Kc3 Ke4=) 70…Ke6 71.Rf1 Ne2+ 72.Kb4 Nd3+ 73.Kb3 Nc5+ 74.Ka3 Nc3 75.Kb4 N3e4 76.Rd1+– 68.Rd5+ Kf6 69.c5 Nf4 70.Rd4 Ke5 71.Kc4 Nf6 72.b5 N6d5 73.Rxf4 1-0 in view of 73…Nxf4 74.b6 Nd5 75.b7+–

With c- and d-pawns, it is also about avoiding an active set up by the knights:

03.06 Korchnoi - Tolush

Leningrad 1956

62…Rc2+? This careless check forces White’s king forward. 62…Rg4 wins, e.g., 63.Nh3 (63.Nf3 Rg8 64.Nge1+ (64.Nf4+ Ke4 65.Nh3 Re8 66.Ke2 c4 67.Ne1 d5-+) 64…Kc3 65.Ke2 d5-+) 63…Ke4 64.Ne1 c4 (64…d5?! wins as well as given by the guideline but is bad technique) 65.Ke2 Rg3 66.Nf2+ Kf4 67.Nc2 d5 68.Nd4 Ra3 (68…Rg2 wins faster in DTC metric) 69.Nd1 (69.Nc2 Ra2 70.Kd1 Kg3 71.Nh1+ Kf3 (71…Kg2? 72.Ne3+ Kxh1 73.Nxd5=) 72.Nd4+ Ke3 73.Nc2+ Rxc2 74.Kxc2 Kf3-+) 69…Ke5 70.Nc6+ Ke4 71.Nf2+ Kf4 72.Nd1 Rg3 73.Nf2 Rb3 74.Kd2 Rb2+ 75.Ke1 Rb6 76.Nd4 Ke5 77.Nf3+ Kd6 78.Nd1 Rb3 79.Nd4 Rd3 80.Ne2 Kc5 81.Nf4 Ra3 82.Ne6+ Kb4 83.Ke2 Ra6 84.Nd4 Kc5 85.Nc2 d4-+ 63.Kf3 Ra2 64.Nf4+ Kc4 65.Nf7 Rd2 66.Ke3 Kc3 67.Ng5 d5

White can draw directly now because of his activity: 68.Nf3 d4+ 69.Ke4 Rd1 70.Ne6 Kb4 71.Nexd4 cxd4 72.Nxd4 Kc4 73.Nf3 Rd8 74.Ne5+ ½-½

Exercises

E03.01 Velimirovic – Ivanisevic

Belgrade 1998

Black to move and draw

E03.02 Tregubov – J.Polgar

Yerevan 2014

Where should the rook go?

(a12) Two isolated close passed pawns

Here the knights have drawing chances when they can set up a solid blockade which cannot be broken by zugzwang:

03.07 Saric – Sokolov

Sibenik 2011

62…Rh8? Now White’s fortress holds. 62…Ra3! 63.Ndc2 Ra2! 64.Ke3 Rb2! is mutual zugzwang with White to move: 65.Kf3 Rb3+ 66.Kg4 Rb1 67.Nf3 Rc1 68.Ncd4 e1Q 69.Nxe1 Rxe1 70.Kg5 Re4 71.Nf3 Re3 72.Kf4 Kf2 73.Ng5 Ra3 74.Nh7 Rg3 75.Ng5 Kg2 76.Ne4 Ra3 77.Kg5 Re3 78.Nf6 (78.Kf4 Rxe4+ 79.Kxe4 Kg3-+) 78…Rg3+ 79.Kf4 g5+ 80.Kf5 Kh3-+ 63.Nd3 Rh2 63…Ra8 64.Nc2 Ra2 65.Nde1 g5 66.Ke3 Rb2 67.Kf3 Rb3+ 68.Kg4 Rb1 69.Nf3 Rc1 70.Nfd4= 64.Ne1 g5 65.Ndc2 Rh3 66.Nd3 g4 67.Nf4 e1Q+ 67…Rh2 68.Ne3+= 68.Nxe1 Rh2+ 69.Kd1 g3 70.Ned3 Ra2 71.Kc1 g2 72.Nxg2 Kxg2 73.Nb2 Kf3 74.Kc2 Ke3 75.Kc3 Ra3+ 76.Kb4 Ra8 77.Kb3 Kd4 78.Kc2 Rb8 79.Nd1 Rh8 80.Nb2 Rh3 81.Nd1 Rh2+ 82.Kb3 Rg2 83.Nb2 Rd2 84.Na4 Rd3+ 85.Kc2 Rg3 86.Nb2 Rg2+ 87.Kb3 Rxb2+ ½-½

(a13) Two isolated distant passed pawns

Here the rook has good winning chances if both pawns are safe:

03.08 Berg - McShane

Malmö 2003

Black wins, but great care is required: 61…b4? Now White can eliminate both pawns and draw with one knight against rook. #0/0 One winning line runs 61…h5 62.Nf4 Rc5+ 63.Ke4 b4 64.Nd3 Rb5 65.Kd4 b3 66.Kc3 Rb8 67.Nb2 Kd5 68.Nd1 Rf8 69.Nh4 Rf4 70.Ne3+ Kc5 71.Neg2 Rb4 72.Kb2 Kb5 73.Nf3 Ka4 74.Ne3 Rf4-+ 62.Kg6? White misses his chance: 62.Nfe5! Rd4 (62…Rh4 63.Nf7+ Ke7 64.Nxh6=) 63.Nxb4! Rxb4 64.Nf7+= 62…b3 63.Kxh6 Rc3 64.Nfe1 Kd5 65.Kg5 Ke4 66.Nb2 Re3! 67.Nc4 Rxe1 68.Nd2+ Kd3 69.Nxb3 Kc3 0-1

(a2) General case

Usually the rook has a passed pawn, which ties the knights down. Then the rook opens another front to win:

03.09 Kamsky – Piket

Monte Carlo 1996

White’s d-pawn either wins material or allows a win on the kingside: 49.Kf4 Ng6+ 50.Ke3?! 50.Kf5!? Nh4+ 51.Kg4 Ng6 52.g3+– is more precise 50…Nf6 51.Kd4 Kf7 52.Ra6 Nf4?! 52…Ne7 53.Ra7 (53.d6?! Ng6 makes White’s task more difficult) 53…Ke8 54.g4 Nfxd5 55.Kxe4 Nf6+ 56.Kf4 Kf8 57.Rb7 Ke8 58.f3 Nd7 59.h4 Nd5+ 60.Kg3 N7f6 61.g5 hxg5 62.hxg5 Ng8 63.Kg4+– 53.Ra7+ Ke8 53…Kg6 54.d6 Kf5 55.g4+ Ke6 56.d7 Nxd7 57.Ra6+ Kf7 58.Rxh6 Nf6 59.g5 Ne8 60.Kxe4+– 54.Ke5 N6xd5 54…N4xd5 55.Ra5+– 55.Ra5 e3 56.fxe3 Nxg2 56…Nxe3 57.Kxf4 Nxg2+ 58.Kg3+– 57.Kxd5 Nxe3+ 58.Ke6 Kf8 59.Re5 Ng2 60.Re4 h5 61.Kf6 Kg8 62.Kg5 Kf7 63.Re2 1-0

The next case is similar:

03.10 Gelfand – Karpov

Sanghi Nagar 1995

Black counterplay on the queenside is not quick enough and the knights cannot actively help: 31.d7 Nb7 32.Re8 Nbd8 32…a5 33.Kf2 b4 34.axb4 axb4 35.Ke1! Nc5 36.Rc8 Nxd7 37.Rxc6 Ne5 38.Rb6+– 33.Kf2 a5 34.Ke3 Kf6 35.g4 Kg5 36.h3 b4 37.axb4 axb4 38.Kd2 Kf6 38…Kh4 39.Rg8 Kxh3 40.Rxg7+– (Ftacnik in CBM 45) 39.h4 g6 39…Kf7 40.g5+– 40.fxg6 Kxg6 41.h5+ Kh6 42.Kc1 Kg5 43.Rh8 Kf6 43…Kxg4 44.h6 Kg5 45.h7 Kg6 46.Rxd8+– (Ftacnik) 44.Rg8 Kf7 45.Re8 1-0

Finally a passed a-pawn decides the day:

03.11 Bacrot – Bartel

Germany 2010

42.Re2! Black’s a-pawn will be lost and then the knights cannot deal with White’s passed a-pawn: 42…Nf5 43.Re5 Kg6 44.Rxa5 N1e3 45.a4 Nd1 45…Nd4 46.Rc5 Ne6 (46…Nb3 47.Rb5 Nd4 48.Rb7+–) 47.Rc6 Nd5 48.a5 Kf5 49.a6 Nec7 50.Kg2 Ke5 51.a7 Kd4 52.Rd6 g5 53.Rd8 g4 54.Kf2+– 46.Rb5 Nfe3 A nice joke 47.Kg1 Of course not 47.a5? Nf2+ 48.Kg1 Nh3+ with perpetual check 47…Nc3 48.Rb6+ f6 49.a5 Ned5 50.Rb7 Ne2+ 51.Kh1 and 1-0 because of 51…Nec3 52.a6 Na4 53.a7 Nab6 54.Kg2 f5 55.Kf3 Kf6 56.Rd7+– 56.Rb8+–

(b) The two knights play for a win

As two knights cannot force mate alone, the case when the opponent still has a pawn is very important. So we bring it separately first in a short discussion.

(b1) The Troitzky endgame:

2Ns vs. P

It is called this as Trotizky’s analysis was extremely accurate. Before him, Chapais (1780) and Guretzky-Cornitz had work on solving the mysteries of this intriguing endgame and reached several results. But the true master of this endgame is doubtlessly the great Russian analyst A.A.Troitzky. We can neither give all his results nor a full proof of them here. We will concentrate on techniques which shall help a practical player understand the ending better:

The endgame K+2Ns vs. K is surprisingly drawn, as the attacker cannot avoid a stalemate defense when the defending king is imprisoned in a corner. But an additional defending pawn opens Pandora’s box as it can provide the desired tempi. The attacker should try to securely blockade the pawn as soon as possible to be able to win tempi for the blockading knight to approach the enemy king and to help his pieces in the mating process. But how far advanced can the pawn be, so that White can still force a mate regardless of where all the men are (the pawn must be securely blockaded by a knight, of course)? Troitzky answered this question as follows:

03.12A A.Troitzky

The line is a4-b6-c5-d4-e4-f5-g6-h4. If the pawn is securely blockaded by a white knight no further down than the line, then Black loses, regardless of where the kings are.

If the pawn has advanced beyond the line, there is usually a drawing and a losing zone for the defending king, which was also analyzed by Troitzky. But there is one caveat: This explanation does not take the 50-move-rule into account. So over the board, you may not be able to win some of the “won” positions, e.g., many positions with Black’s pawn on d4 are not won with respect to the 50-move rule. For example, the following position, with Black to move, is won in 82 moves.

Helmut Conrady found the “second Troitzky line” with Rafael Andrist’s program Wilhelm, which analyses the Nalimov tablebases:

03.12B Second Troitzky

The second Troitzky line is a5 then c5-f5 and finally h5. When the 50-move rule is taken into account, and there is no blockade on the b- or g-file, it always wins. There is a “pseudo-drawing zone” for Black’s king even with a pawn blocked on g7.

(210) 03.12C Longest Win DTM

By the way: the longest win in the ending K+2Ns vs. K+P lasts an amazing 115 moves!

Black starts with 1…Ne7! and mates in 115 moves!

03.12D Troitzky 1935 - The spiral

Before we start with a real case, we want to look at typical technique for the free knight and king without the blockading knight and pawn. Michel de Saboulin thinks that it is as important as the white maneuver for the mate with bishop and knight:

White can force Black’s king into one of the corners or to the seventh rank:

1…Ke1 1…Kc1 is met by 2.Ke2 2.Nc2+ Kd1 After 2…Kf1 3.Kf3 Kg1 4.Ne3 Kh2 5.Kg4 Kg1 6.Kg3 Black’s king is imprisoned near the h1-corner. 3.Kd3 Kc1 4.Ne3 Kb2 5.Kc4 Ka3 After 5…Kc1 6.Kc3 Kb1 7.Nd1 Kc1 8.Nb2 Kb1 9.Nd3 Ka2 10.Kb4 Kb1 11.Kb3, Black’s king is imprisoned near the h1-corner. 6.Nd1 Ka2 7.Kb4 Kb1 8.Kc3 Ka2 8…Kc1 9.Nb2 and the king is caught in typical fashion near the a1-corner.

9.Ne3 Ka3 10.Nf5 Ka2 11.Nd4 Ka3 11…Kb1 12.Nb3 Ka2 13.Nd2 Ka3 14.Nb1+ Ka4 15.Kc4 Ka5 16.Nc3 Kb6 17.Kd5 12.Nb5+ Ka4 13.Kc4 Ka5 14.Nc3 Kb6 15.Kd5 Kc7 15…Kb7 16.Kc5; 15…Ka5 16.Kc5 Ka6 17.Nd5 Ka5 18.Nb6 Ka6 19.Nc4 Kb7 20.Kd6 16.Na4 Kb7 17.Kd6 Ka6 18.Kc5 Kb7 18…Ka5 19.Nb6 Ka6 20.Nc4 Kb7 21.Kd6

19.Nc3 Kc7 19…Ka6 20.Nd5 Ka5 21.Nb6 Ka6 22.Nc4 20.Ne2 Kd7 21.Nd4 Vitaly Chekhover coined the term spiral for this method found by Troitzky. For the entire endgame it of course depends, where the blockading knight is.

Two more techniques will follow. The first is old and famous.

03.12E Stamma’s Mate Malmstig – Kiik

Skelleftea 1999 (D)

Unfortunately, White ignored the golden moment when Caissa was smiling at him: 85…Nd5+? The a7-knight can be sacrificed: 85…Ke7 86.Kb6 Kd6! 87.Kxa7 (87.Ka5 Kc5! 88.Ka4 Kc4! 89.Ka3 Kc3 90.Ka2 Kc2

91.Ka3 Nd5! 92.Ka4 (92.Ka2?! Nb5 93.a7 Ndc3+ 94.Ka1 Nd4 95.a8Q Nb3#) 92…Kb2 93.Ka5 Kc3 94.Ka4 Nc7 95.Ka3 Ncb5+ 96.Ka2 Kc2 97.Ka1 Na3 98.Ka2 Nc4 99.Ka1 Kb3 100.Kb1 Nb2 101.Kc1 Kc3 102.Kb1 Nd3 103.Ka2 Kb4 104.Kb1 Kb3 105.Ka1 Kc2 106.Ka2 Nb5 107.a7 Nb4+ 108.Ka1 Nd4 109.a8Q Nb3#) 87…Kc7!

and now Black can deliver Stamma’s famous mate: 88.Ka8 Nd5 89.Ka7 (89.a7?! Nb6#) 89…Ne7 90.Ka8 Nc8 forcing White to put the last nail in his own coffin 91.a7 Nb6#

86.Kb7 Nb5 87.a7 Stamma’s mate is the main reason why the rook’s pawn can be so far advanced in the Troitzky line. Here the pawn has advanced one square farther than the line, White’s pawn on a6 is firmly blockaded by a black knight on a7, so a drawing zone for the defending king must exist. It is around the safe corner h1: c5-f5-g4-h3-h1-e1-d2-c3-c5. If White’s king is inside the zone, then the position is always drawn. If White’s king is caught near the h8-corner, then Black has to force it into the a1- or a8-corner to give mate. ½-½

03.12F After Troitzky

The second method is a typical way to imprison the defending king. The attacker has to be very careful here, as the knight cannot lose a tempo. So White to move would only draw the following position:

1…Kg1 2.Ne3! the first step to imprison Black’s king on g1 and h1 2…Kh1 3.Kg4! the king has to lose a tempo 3.Kg3?! Kg1 would leave White “on the wrong foot” (this term was coined by Nunn). 3…Kh2 4.Kh4 Kh1 5.Kh3! now White is on the “right foot” 5…Kg1 6.Kg3 Kh1

and finally the time has come to release the blockading knight from its duty 7.Nd3 b2 8.Nf2+ Kg1 9.Nh3+ Kh1 10.Ng4 forcing the cursed pawn to seal Black’s fate 10…b1Q 11.Ngf2# the knight’s inability to lose a tempo makes this endings very tricky. No less than 3,124 reciprocal zugzwang positions exist according to John Nunn.

The next example shows a typical win, when the pawn is blockaded on or below the Troitzky line:

03.12G Vaculik – Vokac

Budejovice 1999

Black’s aims are as follows: force White’ king near the first rank and imprison it there. Then it is possible to mate White in the h1 or the a1 corner. To reach the first aim, Black has to act very precisely:

46…Ned3+ 47.Ke4 Ke6 48.Kd4 Kf5 49.Ke3 49.Kc4 loses as well, e.g., 49…Ke4 50.Kb5 Kd5 51.Kb6 Ne5 52.Kb5 Nec6 53.Kb6 Nd4 54.Kc7 Ke6 55.Kd8 Nb5 56.Kc8 Ke7 57.Kb7 Kd6 58.Kc8 Nd4 59.Kd8 Ndc6+ 60.Ke8 Ne5 61.Kf8 Ke6 62.Kg7 Ke7 63.Kh6 Kf6 64.Kh5 Kf5 65.Kh4 Nf3+ 66.Kg3 Ng5 67.Kh4 Ne4 68.Kh3 Kg5 and we have reached the game at the 66th move.

49…Ke5 50.Kf3 Nf4 51.Ke3 Nfd5+ 52.Kf3 Kf5 53.Kg3 Nf6 54.Kf3 Ng4 55.Ke2 Ke4 56.Kd2 Kd4 57.Ke2 Ne5 58.Kd2 Nf3+ 59.Ke2 Ke4 60.Kf2 Nd4 61.Kg3

61…Kf5! White’s king should not escape in the direction of the north east corner. 62.Kf2 Kf4 63.Kg2 Nf5 64.Kf2 Ng3 65.Kg2 Ne4 66.Kh3 Kg5 67.Kg2 Kg4 68.Kf1 Kf3 69.Ke1 Ng3 70.Kd2 Ne2

Now White’s king is firmly caught near the right edge. Note that Black’s blocking knight completes the barrier! 71.Ke1 Ke3 72.Kf1 Nf4! Black starts the typical maneuver to imprison White’s king 73.Ke1 Ng2+ (D)

White can now only choose in which corner he wants to perish 74.Kd1 74.Kf1 loses as follows: 74…Kf3 75.Kg1 Ne3 76.Kh2 Kg4 77.Kh1 Kg3 78.Kg1 Nd3 79.b4 Nf2 80.b5 Nh3+ 81.Kh1 Ng4 82.b6 Ngf2#

74…Kd3 75.Kc1 Ne3 76.Kb2 Nec2 77.Kc1 Ke2 78.Kb1 Na3+ 79.Kb2 Nb5

A typical set-up of the knights. White’s king cannot break through their barrier. 80.Kc1 Ke1 81.Kb1 Kd2 82.Kb2 Nd3+ 83.Ka2 Kc2 and White resigned because of 84.b4 Nc1+ 85.Ka1 Nd4 86.b5 Ndb3# Superb technique by Marek Vokac!

We want to end this part of our discussion with a nice promotion to a knight:

03.12H Pervushov – Yanvarev

Toljatti 2000 (D)

94.Ne3 Ka3 95.Nc5 Kb2 96.Kb4 e4 97.Na4+ Kc1 98.Kc3 Kb1 99.Nb2 Ka2 100.Nbc4 Kb1 101.Kd2 Ka2 102.Kc2 Ka1 103.Nd6 Ka2 104.Nb5

Ka1 105.Nf5 e3 106.Nc3 e2 107.Nd4 e1N+ 107…e1Q 108.Nb3# 108.Kb3 1-0

Black is in fatal zugzwang. A very good performance by White! Does every Russian schoolboy know how to win this endgame?

Sources:

Troitzky,A., Collection of Chess Studies, 1937

Balashov,Y. & Prandstetter, Basic Endgames, Prague Chess Agency 1992, pp.55-65

Chéron, Lehr- und Handbuch der Endspiele, Band 2, 2nd edition, Verlag “Das Schach Archiv” 1964, pp.220-250

Forster,R. in his “Late Knight” column 24 at www.chesscafe.com, April 2000 with the title: “Late Knights’ Tango: The Troitzky Endgame”

Nunn,J., Secrets of Minor Piece Endings, Batsford 1995

Speelman,J., Tisdall,J. & Wade,R., Batsford Chess Endings, Batsford 1993, pp.112-115

(b2) 2Ns+P vs. R

This is usually a draw as the rook can be sacrificed for the pawn, but often care is required:

03.13 Benjamin – Timman

Amsterdam 1994

83.Rb3? 83.Kd4? is also wrong because of 83…Nf3+ 84.Kd3 g3 85.Ke2 g2 86.Rxf3+ Kg4 87.Rf1 Ng3+–+ (Timman in Informant); 83.Ra1 Nf3 84.Ra4 g3 85.Rxe4+ Kf5 86.Re3=; and 83.Kc6 Nf3 84.Ra2= draw. 83…Nf3 84.Rb2 Nfd2 85.Rc2 g3 86.Rc1 Nf3 87.Rc2 0-1 because of 87…Ned2 88.Rc1 g2 89.Ra1 Nf1 90.Ra4+ Kg3 91.Ra8 Ne3+ 92.Ke4 g1Q 93.Rg8+ Ng4

(b3) 2Ns+P vs. R+P

The friendly pawn can be the rook’s undoing:

03.14 Galliamova – Danielian

Chakvi 2015 (D)

72…f3! Mate in 90 moves. 73.Rh4 Ng2?! Now it is a draw when the 50-move rule is taken into account. 73…f2 74.Rh2 Nc4 75.a4 Na5 76.Kg4 Ke1 77.Rh1+ f1Q 78.Rxf1+ Kxf1 is mate in 83 moves and also won with 50-move rule. 74.Re4+? 74.Rh1 f2

75.a4 Nb4 76.a5 Na6 77.Ra1 f1Q 78.Rxf1 Kxf1 is mate in 89 moves but drawn with 50-move rule. 74…Kd3 75.Re8 f2 76.Rf8 Ngf4 0-1

(b4) 2Ns+P vs. R+P

This of course is usually also drawn if the knights cannot drum up a mating attack:

03.15 Nakamura – Capo Vidal

Gibraltar 2009

Even this can be defended, but great care is required: 72…Rf6? 72…Re6!? 73.Nd7 Re1 74.Nxb6 Rb1 75.Kc7 Rxb5= 73.Kc7 Ka8 74.Nd7 1-0

(b5) General Case

If the knights have control they have usually good chances to win. A passed pawn helps a lot of course:

03.16 Carlsen – Aronian

Elista 2007

45.Rb1 Kf6 46.Rb7 Ke6 47.Rxa7 Kxd6 48.Kf1 c4 49.Ke2 c3 50.Ra6+ Kd5 51.Kd1 Ne5 52.Ra5+ Kd4 53.Kc2 Nc4 54.Ra8 54.Ra4 Kd5 55.Ra8 Ne3+ 56.Kd3 Nxg2-+ 54…Ne3+ 55.Kb3 Nc5+ 56.Ka2 c2 57.Rd8+ Kc3 0-1

03.17 Movsesian – Swiercz

Wroclaw 2010

White’s passed b-pawns wins, but great care is required: 32.Nbc5! Ke7 33.b5 Ra3 33…Kd6?! 34.b6 e5 35.b7 Kc7 36.Nxe5 Rxc5 37.b8Q+ Kxb8 38.Nd7++– 34.b6 Ra1+ 35.Kf2 Rb1 36.b7 Kd6 37.Ke3

37…g5?! This opens inroads and makes it easy. Black should wait for the time being: 37…Rb5 38.Kd4 Rb1 39.Ne5 Rb4+ 40.Ke3 Rxb7 (40…Rb6 41.Ned7 Rb2 42.Kf3 Rb4 43.Nb8 Rb6 44.Nba6 e5 45.Kg3 Kc6 46.Kg4 Kd6 47.b8Q+ Rxb8 48.Ne4+ dxe4 49.Nxb8 Kc7 50.Na6+ Kb6 51.Kf5 e3 52.Nb4+–) 41.Nxb7+ Kxe5 42.Nd8 Kf5 43.Kd4 Kf6 44.Nb7 Kf5 45.Nd6+ Kf6 46.Ne8+ Kf7 47.Nc7 Kf6 48.Ke3 Ke5 49.Ne8 g6 50.Kf3+–; 37…e5?! 38.Nxe5+–

38.Kd4 Kc7?! 38…h5 39.Ne5 Rb4+ 40.Ke3 Rxb7 41.Nxb7+ Kxe5 42.Nd8+– 39.Ke5 1-0