Late Knight by Richard Forster Late Knights' Tango: The Troitzky Endgame For years I have been wondering about the famous 'Troitzky Endgame', i.e. Two Knights versus Pawn. Like, probably, so many other players, all I knew was the familiar "demarcation line". For White that is a4-b6-c5-d4-e4-f5-g6-h4. If a knight can block the enemy's pawn on one of these squares, or further back, then he is bound to win the endgame. The winning plan then consists of driving the opposing king into a corner (with appropriate manoeuvres by the king and the free knight), and eventually lifting the pawn-blockade and hurrying with the other knight to the corner to administer mate. If Black did not have a pawn, he would be safe because of the stalemate possibility, but as things stand, his only hope is to promote the pawn and disturb White's plan. This type of endgame was first analysed by Chapais in 1780, but a full and comprehensive examination of all possible positions was only realised by the famous study composer A. A. Troitzky in the first half of the 20th century. His extensive analysis was published as an appendix in his Sbornik Shakhmatny Etiudov (1935). In the English edition (Collection of Chess Studies, 1937) it takes up almost sixty pages, which not only make a fascinating and entertaining reading (as far as this is possible with endgame analysis) but are also 'astonishingly accurate' according to the endgame database specialist John Nunn in Secrets of Minor-Piece Endings (1995). As a matter of fact, the 'Troitzky Endgame' is the only one that he excluded from his comprehensive three volume treatise on five piece endings because hardly any new 'contributions' were possible, which is certainly a deep honour to Troitzky! Queen and pawn versus queen is the other exception, by the way, but for completely different reasons (too numerous and too difficult!). Of course, it is impossible to give a full account of the whole ending in this article, but I would like to present some practical examples, old and new, and try to point out a few guidelines on how to play these positions. I imagine that many of you cannot even imagine how to drive the opponent's king to the rimwith only king and knight (at least I could not until a few weeks ago). Going through some sample positions will give you an idea. But be warned: it is far from easy. Let us start with a very recent and prominent example: Topalov Karpov, Amber Rapid Tournament, Monaco 2000 DIAGRAM: 8/8/8/3K4/3N2p1/3k2N1/8/8 b - - 0 61 Karpov had just sacrificed his last knight for a white pawn on d4 (one of the usual ways of reaching this endgame). With his pawn two squares outside the danger-zone, he probably counted on an easy draw. However, Rule 1: There is no easy draw in this ending. Even if the pawn stands further on than the demarcation line, there are still many positions which are lost! The diagrammed position is actually a draw, but Black must know what he is doing. Question: Two of the four corners of the board are safe for Black's king and two are deadly. Which must he head for? 61...Kc3 62.Kc5 Kd3 63.Nde2 Kd2 64.Kc4 Kc2?! Not yet a real mistake, but a clear sign that Karpov is not familiar with the peculiarities of the ending. 65.Nd4+ Kb2?? This is losing, as against accurate play the king can no longer escape from the deadly a1 corner. Correct was 65...Kd2 which first of all avoids the immediate imprisonment of the king, and secondly is a step in the right general direction. Both a8 (in which case the g3 knight is too far away) and g2-h1 would have been safe. Intuitively one is probably averse to bringing one's king to the blockading knight, but there is hardly ever a mate in this corner, because as soon as the blockade is lifted, the advancing pawn disrupts White's manoeuvres by covering some important squares or giving check. Also, the presence of the pawn and the blockading knight obstructs White's king's mobility. Rule 2: With the pawn advanced far enough, the defending side is often safe in the corner right in front of the pawn. (Note that this rule is not valid for rook pawn endings, which are governed by special rules.) 66.Kb4 Ka2 (DIAGRAM) 67.Ndf5? A technical mistake, which again gives Black the opportunity to draw. To drive the king further down to the corner the following instructive manoeuvre was necessary: 67.Nb5! Kb2 68.Na3! Kc1 (trying to escape to the kingside since 68...Ka2 69.Nc4 is hopeless) 69.Kc3 Kd1 70.Nc2! and Black's flight is stopped. Note that this only works thanks to the blockading knight covering e2. Without the occasional passive help of the other knight, there is no chance of catching the king in a particular corner. After 70.Nc2 the king must return to the corner (zugzwang!), when 70...Kc1 71.Ne3 Kb1 72.Nc4! leads to a typical winning position. Rule 3: Once the attacker has a king on c3 and a knight firmly established on c4 or d3, then the enemy king can no longer escape from the corner. There follows either 72...Ka2 73.Kc2! Ka1 74.Ne4! g3 75.Nc3 g2 76.Nd2 g1Q 77.Nb3 mate or 72...Kc1 73.Nb2! (going from c4 to d3) Kb1 74.Nd3 Ka2 75.Kb4! Ka1 76.Kb3 Kb1 77.Ne4 and mate in three moves. We see in these variations why a1 is a bad corner for the king: Black's new queen on g1 does not interfere with White's mating plans. With the king on a8 there would be no mate because the queen covers b6, on which either the knight or the king must stand in a mating position. The (big!) difference with h8 is, that although the new queen covers g6, with precise play White can force a mating pattern by putting his king on f7 and one knight on g5, where it prevents ...Qxg6! 67...Kb2? As anticipated by Topalov, but Karpov had a (difficult to spot, admittedly) draw with 67...Kb1!!, and if 68.Ne3 Kb2! as White is in zugzwang and must release the grip on Black's king. Neither can he keep the king cornered by 68.Kb3 Kc1 69.Kc3 Kd1 etc. or 68.Kc3 Ka2! 69.Nd4 Ka3! 70.Nc6 Ka4 71.Kc4 Ka3, and all White can do is 72.Kc3 or 72.Nd4, when 72...Ka4 leads to a repetition of the position. Rule 4: In positions with wKb4 versus bKb2 and the knight covering c2 (e.g. from d4 or e3) reciprocal zugzwang often occurs. Having the move often means another twenty or so extra moves for White, if not worse (i.e. a draw instead of a win). Reaching these positions with White to move is an important defensive technique for Black. After Black misses this chance, everything goes smoothly for White: 68.Ne3 Ka2 Or 68...Kc1 69.Kc3 Kb1 70.Nc4! as in the note to White's 67th. 69.Nc4! (DIAGRAM) Occupying one of the crucial squares c4 and d3. 69...Kb1 70.Kc3! Kc1 71.Nb2 Kb1 72.Nd3 Ka1 73.Kb3 Kb1 74.Ne2 1:0. To find out more about this endgame I checked various old magazines, endgame manuals and big databases. All in all I discovered about one hundred games in which the Troitzky Endgame occurred and in which some play took place (i.e. I excluded immediate draws and positions in which the draw was more than obvious). The players with the advantage turned out to be quite successful: of the winning positions they converted close to 80 percent, whereas of the theoretically drawn positions they still managed to win about a third. Most of the material comes from recent practice, but I also examined some older examples. Jaenisch Shumov Match game, St Petersburg 1854 1.e4 e5 2.f4 exf4 3.Bc4 Qh4+ 4.Kf1 g5 5.Qf3 d6 6.g3 Qh6 7.gxf4 gxf4 8.d4 Qf6 9.Qxf4 Nc6 10.c3 Bd7 11.Nf3 Qxf4 12.Bxf4 f6 13.Nbd2 Bh6 14.Bxh6 Nxh6 15.Ke2 0 0 0 16.Rae1 f5 17.exf5 Bxf5 18.Kd1 Bg4 19.Be6+ Bxe6 20.Rxe6 Ng4 21.Rhe1 Kd7 22.Ng5 Rde8 23.Rxe8 Rxe8 24.Rxe8 Kxe8 25.Nxh7 Nxh2 26.Nf6+ Ke7 27.Nd5+ Kd7 28.Ne3 Ne7 29.Ke2 Ng6 30.Kf2 Nf4 31.Kg3 Nd3 32.b3 Nc1 33.Kxh2 Nxa2 34.Nd1 Ke6 35.Kg3 c5 36.dxc5 dxc5 37.Kf4 b5 38.Ne4 Kd5 39.Ne3+ Kc6 40.Ng4 a5 41.c4 Nc1 42.Ne5+ Kb6 43.Nd7+ Kc6 44.Ndxc5 Nxb3 45.cxb5+ Kxb5 46.Nxb3 (DIAGRAM) 46...Kb4 47.Nc1 a4 48.Na2+ Kc4 49.Ke3 a3 and the game remaineda draw. (Deutsche Schachzeitung, January 1855, p.20-21) Black's pawn is already too far advanced and his king is in the safe zone, which for a pawn on a3 consists of the area towards the corner h8. Rule 5: In the case of a rook pawn, the king should head for the diagonally opposite corner of the board! Unlike positions with other pawns, Black must avoid being driven to the corner next to his pawn, because against a rook pawn White is able to force a mate, often by sacrificing one knight and achieving a position like this: DIAGRAM: 8/8/8/8/8/p7/k1KN4/8 White wins White wins with the well-known manoeuvre 1.Nf3 Ka1 2.Nd4 Ka2 3.Ne2 Ka1 4.Nc1 a2 5.Nb3 mate. Apart from being the oldest example, Jaenisch - Shumov is of interest because it leads to one of the longest win situations if Black plays 48...Ka5? instead of 48...Kc4. With optimal play White then has a win in 95 moves, starting with 49.Ke5 Kb6 (The king must try to get out of that area. That's why 49...a3 50.Nec3! Ka6! 51.Ke6! loses.) 50.Kd6 Kb5 51.Kd5 Kb6 52.Nec3! Kb7 53.Kc5! (Zugzwang. If 53...a3 54 Nd5, and wins.) Kc8 54.Kd6 Kd8 55.Nb5! (Intending to cut off the king with 56.Nc7.) Ke8 56.Na3! with a theoretical win. The next example is straightforward: Zukertort N.N., Simultaneous game, Sheffield 1885 DIAGRAM: 8/6k1/3N4/5K2/2p5/2N5/8/8 w Zukertort won as follows 1.Kg5 Kf8 Or 1...Kh7 2.Nf5 Kg8 3.Kf6! and wins (see Rule 3). 2.Kf6 Kg8 3.Nf5! Again a typical winning situation as in the Topalov-Karpov example. 3...Kf8 4.Ng7! Kg8 5.Ne6 Kh7 6.Kg5 Kg8 7.Kg6 Kh8 8.Ne4 c3 9.Nf6 c2 10.Ng5 c1Q 11.Nf7 mate. Here Black's pawn was further advanced than the drawing line. Still he lost; why? The answer is that with a pawn on c4 (or f4) the only drawing area for Black's king is right in front of the pawn, i.e. in the a1-b2-c2 area (see Rule 2!). Therefore, many positions with the pawn on c4 are won, especially if the superior side can create a safe starting formation with knights on c2 and c3, followed by slowly chasing the Black king into one of the other corners. Rule 6: A pawn on bishop's 5th only draws if the king is in the same corner. From the above example we can also see why a bishop pawn is less useful than a knight pawn: the queen on c1 does not cover any of the squares which are important for the mate on h8 (there would be no mate with a queen on b1!). This is a little different for a8, when the queen covers the c-file, but still White has a mating set-up with Kc7, Nc6 and Nb6. Similarly, we can grasp why the centre pawns can be allowed to advance even farther: a new queen on e1 or d1 can hardly prevent any of the usual mating patterns in this ending which is even more important than the fact that the blockading knight can reach its goal faster from the central squares d3 or e3 rather than from one of the wings. Of the games in which the superior side missed a theoretical win, we find a relatively large number of strong players involved on both sides. Perhaps this is an indication that the defence is usually even more difficult than the attack. Here are a few notable examples: Nijboer Sadler, Arnhem 1999 (DIAGRAM: 8/8/1n6/K1k2n2/5P2/8/8/8) 64.Ka6 Nc4 65.Kb7 Kd6 66.Kc8 Both sides play the correct moves. Black wants to catch the white king in the corner, whereas White tries his best to escape. 66...Na5! In ChessBase Magazine 71 Atlas recommends 66...Ke7, but this would be a mistake, prolonging the win by more than twenty moves. Driving the king to h8 is fine, only later Black fails to find the mate. 67.Kd8 After 67.Kb8 Black wins by 67...Kd7 68.Ka7 Kc6! 69.Kb8 and now the quickest win is 69...Nd6! 70.Ka7 Kb5 71.f5 Nc6+ 72.Ka8 Kb6 and wins. 67...Nb7+ 68.Ke8 After 68.Kc8 Kc6 the win is easy. 68...Ke6 69.Kf8 Nbd6 70.Kg8 Ke7 Bringing the knight to c7 with 70...Ne8 or 70...Nb5 would have been a little faster, but in principle Sadler's play has been perfect so far. 71.Kh7 Kf7 72.Kh8 (DIAGRAM) A critical position. So far everything has gone according to plan, but now Black faces the problem of how to mate the king. As we noted above, the pawn's promoting corner is usually quite a good place for the king to hide, because once set free the pawn can disrupt Black's forces. Here lines like 72...Ne4 73.Kh7 Nf6+ 74.Kh8 demonstrate the problem: 74...Kf8 is stalemate, and 74...Ne7 fails to 75.f5 and the win has gone. Sadler probably had a long think here, and finally concluded that there was no mate in this corner. As a consequence, he started to drive the kingout of this corner again, but he had already spent too much time to win under the fifty move rule. However, there was a mate. It required a little trick, though. A logical way to win (albeit not the fastest) was first to transfer the knight to e6 with 72...Ne4 73.Kh7 Nc5 74.Kh8 Ne6 75.Kh7. The second stage is a triangularmanoeuvre to achieve the same position with White to move. This is done as follows: 75...Kf6 76.Kg8 Ke7! 77.Kh8 Kf8 78.Kh7 Kf7. Finally, the mating manoeuvre: 79.Kh8 Kg6! 80.Kg8 Ne7+ 81.Kh8 Kh6 82.f5 Nf8 83.f6 Nfg6 mate. Rule 8: Sometimes you must calculate. 72...Kg6? 73.Kg8 Nf7 74.Kf8 N7h6? Consistent, but wrong. After 74...N7d6 the position is still fairly quickly won (if one sees it, of course). 75.Ke8 Kg7 To win in this position against perfect play, Sadler would have had to play 75...Kf6 (or 75...Ng4), when he could have mated exactly on the fiftieth move. His driving the king to h1 in the game is very instructive too, but unfortunately he arrives just too late and Nijboer can claim a draw under the fifty-move- rule. 76.Kd8 Kf7 77.Kd7 Ng4 78.Kc6 Ke6 79.Kc5 Kd7 80.Kd5 Nge3+ 81.Ke5 Ke7 82.Ke4 Kd6 83.Kd3 Kd5 84.Kc3 Nc4 85.Kd3 Ncd6 86.Kc3 Ke4 87.Kb3 Kd3 88.Kb4 Kd4 89.Kb3 Ne4 90.Kb4 Nc3 91.Kb3 Nd5 92.Kb2 Kc5 93.Kc1 Nb4 94.Kd1 Kc4 95.Ke2 Nd5 96.Kf3 Nf6 97.Ke2 Kc3 98.Ke1 Ne4 99.Ke2 Nd2 100.Ke1 Kd3 101.Kf2 Ne4+ 102.Ke1 Nc3 103.Kf1 Kd4 104.Kf2 Ke4 105.Kf1 Kf3 106.Ke1 Ke3 107.Kf1 Ne4 108.Ke1 Nf2 109.Kf1 Nd3 110.Kg2 Ke2 111.Kh2 Kf3 112.Kh3 Nf2+ 113.Kh2 Drawn. After 113...Ng4+ 114.Kh3 Nge3 115.Kh2 Kg4 116.Kh1 Kh3 117.Kg1 Kg3 118.Kh1 Nd4 mate would follow shortly. Another source of trouble for the superior side is positions where the weaker side's king is hanging around the pawn and restricting the opponent's forces by constant attacks on the blockading knight. In our next example even such an expert as John Nunn, although in his pre-database years, does not find a solution. In fact, in the forty moves played he does not make any progress at all! Watson Nunn, Leeds 1991 (DIAGRAM:8/8/8/5n2/5Pn1/3K2k1/8/8) Even with perfect play (44 moves) the win is quite difficult. 77.Ke4 Nge3 78.Ke5 Kf3 Stronger is 78...Kg4. To drive the king away from the pawn, Black must first bring his own king to e6 or g6 and then slowly push back the enemy. Rule 9: To drive the king away from the pawn your own king must go back too! 79.Kf6 Ke4 80.Ke6 Nd5? A fruitless manoeuvre, only hindering the king's route via d5. The correct procedure was 80...Ng4! 81.Kf7 Kd5 82.Kg6 Ke6 83.Kh5 Nge3 84.Kg6 Ke7! 85.Kh5 Kf7! (Not 85...Kf6? stalemate, of course.) 86.Kg5 Kg7 87.Kh5 Ng2! (The knight will defend his colleague from a less active post, but in return the stalemate position is lifted.) 88.Kg4 (Stubbornness does not pay off as after 88.Kg5 Ngh4 89.Kg4 Kh6 90.Kh3 Kh5 91.Kh2 Kg4 Black soon mates in the lower-right corner.) 88...Kf6 89.Kf3 (Or 89.Kh5 Ne1 90.Kg4 Kg6 etc.) 89...Nge3 90.Ke4 Ke6 followed by 91...Kd5, and the white king will be separated from his pawn. 81.Kf7 Nc7 82.Kf6 Nd5+ 83.Ke6 Nb6 84.Kf6 Nc8 85.Ke6 Ncd6 86.Kf6 Kd5 87.Kg5 Ke6 88.Kg4 (DIAGRAM) 88...Nc4 Black should take the square g5, either with 88...Ne4 (89.Kf3 Nf6) or with 88...Kf6 89.Kf3 Nc4!, with lines similar to those in the last note. 89.Kf3? Kd5? 90.Kg4 Nce3+ 91.Kg5 Ke6 92.Kg6 Nd5 93.Kg5 Nf6 94.Kg6 Ne4 95.Kh5 Nf2 96.Kg5 Nd1 97.Kg4 Nde3+ 98.Kg5 Kf7 99.Kh5 Ke7 100.Kg5 Ke6 101.Kg6 Nd1 102.Kg5 Nf2 103.Kg6 Ne4 104.Kh5 Drawn. A final example from recent grandmaster practice. A friend of mine recently remarked how impressed he was to witness Gurevich's quick technique. As we shall see, it was not all that convincing...: Rogers M. Gurevich, Biel 1993 (DIAGRAM:8/8/3K1n2/3n2k1/3P4/8/8/8) In the first stage Black drives White's king away from the pawn. 60.Ke5 Kg4 61.Ke6 Kf4 62.Kd6 Kf5 63.Kc5 Ke6 64.Kc4 Ne4 65.Kd3 65.Kb5 was slightly more stubborn. 65...Nd6 66.Ke2 Kf5 67.Kf3 Ne4! 68.Ke2 Kf4 69.Kd3 Nd6 70.Ke2 Kg3 71.Kd3 Kf2! 72.Kd2 Kf1! (DIAGRAM) Gurevich constantly plays the best move. Now White must cede some ground, because 73.Kd1 allows 73...Nc4. For example, 74.Kc1 Ke1 75.Kc2 Ke2 76.Kc1 Nce3 77.Kb2 Kd3 78.Kb3 Nc4 79.Ka4 Nd6! 80.Kb3 (On a8 mate follows even sooner.) Kd2 81.Kb2 Nc4+! 82.Kb3 Ncb6 83.Kb2 Kd1! 84.Kb3 Kc1! and it is obvious that White will be mated shortly. 73.Kd3 Ke1 74.Kc2 Ke2 75.Kc1 Nc4! 76.Kc2 (DIAGRAM) 76...Nce3+? In his notes in Informator 58 Gurevich mentions the correct winning manoeuvre, which consists once again of a pawn- ending like triangle: 76...Ke3! 77.Kc1 Kf3!! 78.Kb1 (or 78.Kd1) Kf2! 79.Kc1 Ke1! 80.Kc2 Ke2 and Black wins as in the note above. Rule 10: If you cannot make progress and your opponent's king is confined to moving back and forward, consider a triangle. It seems that finding these manoeuvres is extremely difficult, even for GMs. In the next phase Gurevich plays aimlessly until more or less the same situation arises again. 77.Kc1 Kd3 78.Kb2 Kc4 79.Ka3 Kc3 80.Ka4 Kc4 81.Ka3 Nd1 82.Ka4 N1c3+ 83.Ka3 Kd3 84.Kb2 Nb5 85.Kc1 Ke2 86.Kc2 Nd6 87.Kc1 (DIAGRAM) 87...Nb4 Overlooking the winning manoeuvre with the triangle 87...Nc4! 88.Kc2 Ke3! (as pointed out above), which would still win just in time, Gurevich decides to allow White's pawn one further move, which gives him another fifty moves to find a win. 88.d5 Delaying this advance with 88.Kb2 Kd2 does not improve White's situation. 88...Ke1 89.Kb1 Gurevich gives a question mark here, but there is no difference between this move and 89.Kb2, at least in theory. 89...Kd2 90.Kb2 Nc2? On the other hand this is a big mistake. The win after 90...Nd3+ 91.Kb3 Nc5+ 92.Kb4 Nd7 93.Kb3 Kd3 takes another thirty- odd moves and is far from simple, but the text move makes things even worse. 91.Kb3 Kd3 (DIAGRAM) 92.Kb2?? No comment by Gurevich, but according to the perfect endgame database, winning the position after 92.Ka4! would require 61 moves (i.e. it would be a draw under the fifty-move- rule). The king cannot be driven to either a8 or a1. 92...Nd4! 93.Kb1 93.Ka3 Kc3 94.Ka4 Nb3 95.Ka3 Nc5 or 93.Kc1 Ke2 94.Kb2 Kd2 and the end is also near. 93...Kd2 94.Kb2 (DIAGRAM) Allowing an immediate mating combination, but after 94.Ka2 Kc2 95.Ka3 Nb3! 96.Kb4 Kb2! 97.Ka4 (The only legal move!) Kc3 98.Ka3 Nc5 99.Ka2 Nd3 100.Ka3 Nb2 101.Ka2 Nbc4 102.Kb1 Kd2 Black wins easily. 94...Nc4+! 95.Kb1 Ne2 0:1. The right combination of the moves Nc3, Kc2 and Nd2-b3 leads to mate. Incidentally, there are two more Gurevich endings of this sort, one by Dimitry and one by Ilya. And they all won! Therefore: Rule 11: Call yourself Gurevich. Further reading: A. Troitzky: Collection of Chess Studies, 1937. A. Chron: Nouveau Trait Complet d'checs, 1952. R. Rey Ardid: Finales de Piezas Menores, 1983. Y. Balashov, E. Prandstetter: Finali Fondamentali di Scacchi, 1992.