Shalgo on Chess

Chess Ngram of the Day

2012-01-12T15:13:00.003-05:00

A Surprising Missed Winning Opportunity in Nakamura-Karjakin

2011-03-24T16:24:00.000-04:00

In yesterday's rapid game between Nakamura and Karjakin, they played on until bare kings in an endgame. It had seemed drawn for a long time, except for a moment of excitement when Karjakin offered a rook sacrifice on move 42 with 42...Rd2+!?. Nakamura declined the offer, seeing that it would allow Karjakin to queen a pawn, and the game wound on to its drawn conclusion.

Karjakin, who was extremely short of time, did not notice that there was an even better version of his idea--one that would have won on the spot. He could have played

44...Rd3!!

Nakamura-Karjakin after 42...Rd3!! (analysis diagram)

The point is to cover b3 so that White can't recapture with his king after 45...b3+. If 45.Kxd3 b3! queens a pawn. White's rook and knight are so out of position, in fact, that they are helpless to stop 45...b3 regardless of White's next move.

Avoiding an Opposite-Colored Bishop Ending Through an Exchange Sacrifice

2011-03-20T13:17:00.000-04:00

Opposite-colored bishop endings are notoriously (or wonderfully, if you are the defender) drawish. One side can frequently have two, or even more, extra pawns but absolutely no chance of winning, because it cannot overcome a blockade on the squares that its bishop does not cover. Dvoretsky gives the following example:

Despite being up three pawns, Black cannot win. White merely moves his bishop along the h3-c8 diagonal.

If there is more material on the board, one way for the side with the advantage to avoid this fate is to sacrifice some material. The Tata Steel tournament earlier this year witnessed two nice examples of this stratagem.

In Navara-Ganguly, from Round 6 of the B Group, is perhaps not the best example, as White is probably winning even in the rooks plus opposite-colored bishops ending that arose in the following position:

Navara-Ganguly, after 34...Rxb8

But rather than start pushing his queenside pawns, leaving open the possibility that Black might establish a dark-square blockade, Navara played the elegant:

35.Rxf4!

And Ganguly resigned. After 35...exf4, either 36.a6 or 36.b4 will force Black to sacrifice his rook for one or two pawns, leaving White with an easy win.

Next L'Ami-Wang Hao, from Round 10 in Group A, reached the following position:

L'Ami-Wang, after 45.Bb5

Black is up two pawns, but White has just played 45.Bb5, blocking the b-file and intending to win back one pawn on b3. There is again the prospect of a long struggle to grind out a win despite the opposite-colored bishops. Black avoided this by playing:

45...Rxb5! 46.axb5 a4!

L'Ami-Wang, after 46...a4!

Now the connected passed pawns paralyze the White rooks. The White passed b-pawn is easy to stop.

47.b6 Rb4 48.Ra1 Otherwise Black plays ...Rxb6. 48...Bd6 Covering the b-pawn's queening square and also threatening Be5, skewering the rooks. 49.b7

White can't rearrange his rooks. If 49.Rab1, then 49...a3! 50.Rxb3 Rxb3 51.Rxb3 a2 and the pawn can't be stopped. If White tries for activity by 49.Rd1, then again 49...a3 50.Rbb1 a2, again winning.

L'Ami-Wang, after 49.b7

49...Kh7

Wang plays it extra safe, not allowing even a hint of counterplay or risk. But the more direct 49...Kf8 and 49...Be5 would also have won. For example, after 49...Be5, White has to give up a rook for the pawns: 50.Rxa4 Rxa4 51.Rxb3 Bb8. This variation required a bit of calculation, to make sure that White can't get his rook to the back rank or support the b-pawn with his king after the exchange of rooks, but Black wins easily in all variations:

a. 52.Rc3 Rc4 53.Rxc4 dxc4 54.Kf3 Kf8 55.Ke4 Ke7 and the Black king arrives in time.
b. 52.Re3 Kf8
c. 52.Kf3 Kf8 53.Rd3 Rb4 54.Rxd5 Rxb7

Wang's move also wins, however.

50.f4 Kg6 Black simply walks his king to the queenside to capture the b-pawn and then support his own pawns. 51.Kf3 Kf6 52.Ke3 Ke6 53.Kd3 Kd7 0-1

L'Ami had had enough, and resigned. Play could have continued 54.Kc3 Rc4+ 55.Kd3 Kc7 56.Rxa4 Rxa4 57.Rxb3 Rb4.

A Draw for White in Smeets - Vachier-Lagrave?

2011-01-25T22:13:00.002-05:00

Jan Smeets has had a tough time of it in the Tata Steel tournament this month. (I am sure that I am not the first to mention it, but doesn't "Tata Steel" sound like a porn star name?)

In the eighth round, Smeets had White against Maxime Vachier-Lagrave (who sounds like a Bond villain). Lagrave played a Modern Defense with 4...a6, which I used to consider daring and exciting long ago when I played it with Black, but also slightly insulting when I faced it with White. In any event, Smeets looked, if anything, better out of the opening, and was certainly no worse until he played 21.Rd8? But, in his usual ferocious time trouble, he wound up defending a difficult pawn-down rook ending, which he proceeded to lose.

I want to suggest that at move 38 (when he probably had seconds left on the clock), Smeets missed a good drawing chance. At this point, after some exchanges, the material was even, though Black had a strong passed pawn on the kingside. In the following position,

Smeets played 38.Kb3? and wound up in a very difficult position after 38...Kc6 39.h4 Kd5 40.h5 Ke4 41.hxg6 Rxg6. He may still have had a draw even then, but I think the draw is more likely after:

38.h4!

The idea is simply that Kb3 is a loss of a tempo: White wants to break up Black's kingside pawns and should start doing it right away. I don't claim that this move draws for White in all lines--I haven't looked at the position in that depth--but if Black plays in the same way as in the game, White should hold. Thus:

38...Kc6 39.h5 gxh5

Forced, as Black is too late to protect the f-pawn with his king: 39...Kd5 40.hxg6 Rxg6 41.Rxf5; if 40...Ke4 41.g7 Rg6 White, with his extra pawn, perhaps even has a small advantage, though it is undoubtedly still drawn thanks to Black's active king.

40.Rxf5 Rh6

Smeets - Vachieve-Lagrave (analysis diagram)

The main difference between this line and the game is that Black has an h-pawn rather than a f-pawn. That means that his king will have to move farther away from the queenside to help it advance. White's basic drawing plan is to get a passed pawn on the queenside, sacrifice his rook for the h-pawn, and then force Black to exchange his rook for White's remaining passed pawn. Thus:

41.Rf3 h4 42.Rh3 Kd5 43.Kb3 (only now!) 43...Ke4 44.c4 Kf4 45.cxb5 axb5 46.a4 bxa4+ 47.Kxa4 Kg4 48.Rh1 h3 49.b5 Kg3 50.Ka5 Kg2 51.Rb1 h2 52.b6 h1=Q 53.Rxh1 Rxh1 54.Ka6

And Black's king is too far away to stop the b-pawn. Therefore, it is a draw.

This is a very rough and incomplete analysis, so I can't say with certainty that White draws after 38.h4, but he does seem to have good drawing chances. Please indicate corrections to the analysis, or questions, in the comments.

Ruan-Hou (Game 2): the Rook Endgame

2010-12-21T17:08:00.003-05:00

Today in the second game of the final of the Women's World Chess Championship, Ruan Lufei and Hou Yifan reached a rook ending in which Black had a substantial advantage:

Ruan Lufei - Hou Yifan

Women's World Chess Championship, Round 6.2 (2010)

Position after 36...Rxa4

Black is up two pawns, which would normally be an easy win, but rook endings are notoriously drawish. Here, White's slim chances of a draw are enhanced by the passive position of the Black rook (tied to the defense of the b4-pawn), the active positions of the White king and rook, and the facts that (1) if the b-pawn were removed, the game would be a draw and (2) an ending with just Black's f- and h-pawns will usually be a draw.

37.h4 Kf8 38.Re4 f6 39.Rd4 Ke7 40.Rd4 Ke6 41.Ke4 Ke7 42.Kf4

White is asserting that Black cannot make any progress. She will just shuffle her king between e4 and f4. Black can try to make progress by taking one of these squares away from the White king: if she plays h6 and g5, then f4 is off limits. Thus 42...h6 43.Ke4 Ke6 (so that ...g5 comes with check, preventing White from answering it with h5) 44.Kf4 g5+ 45.hxg5 hxg5+ 46.Ke4 Ke7, and White has to give way, either allowing the rook to shift away from a4 with check or allowing the Black king to advance to the queenside.

42...h6 43.h5?!

Position after 43.h5?!

While Black was making progress after 43.Ke4 (as described above), this is a forced win for Black.

43...gxh5

Another attempt was 43...g5!? If White plays actively with 44.Kf5?, Black wins: 44....Ra5+ 45. Kg6 Rb5 46.Re4+ (46. Kxh6 b3 47. Kg7 [47. Rd1 b2 48. Rb1 Kf7 -+] 47... b2 -+) 46... Kf8 47. Kxf6 b3 48. Re1 b2 49. Rb1 Rb6+ 50. Kf5 Kf7 and Black wins.

Analysis Diagram

White seems to hold the draw, however, with 44.Ke4 Ke6 45.Rc4 Kd6 46.Kd4. If Black tries to break through with 46...f5!?, then White can just hold the draw: 47.gxf5 g3 48.Ke3 g3 49.Kf3 Ke5 50.Kxg3 Kxf5 51.Rc5+! Ke4 52.Rc6 b3 53.Rxh6 Rb4 54.Rf6 Ke5 (54...b2?? 55.Rf4+ +-) 55.Rf1 b2 56.Rb1 Kf5 57.Kg2 Kg5 58.Kg3 Kxh5 59.Kg2 Kg4 60.Kf2 Kh3 61.Rh1+ Kg4 62.Rb1 and Black can't break through.

Analysis Diagram

44.gxh5 Kf7 45.Re4 Kf8

Position after 45...Kf8

46.Kg4? This move makes things too easy for Hou. It would have been more tenacious to play waiting moves that don't allow Black to get the rook behind the b-pawn: 46.Rc4 Ke8 47.Rd4 Ke7 48.Rc4. Another possibility was the direct 46.Kf5!, which seems to hold the draw: 46...Ra5+ 47.Kxf6 Rb5 48.Re2 b3 49.Rb2 Rb6+ 50.Ke5 Kg7 51.Kd4 Kf6 52.Rg2! Rb5 (52...b2?? 53.Rg6+ +-; 52...Kf5 53.Kc3 Kf4 54.Rg6 Rb5 55.Kb2 Rxh5 56.Kxb3 is a tablebase draw) 53.Kc3 Kf5 54.Kb2 Ke4 55.Rg6 Rxh5 56.Kxb3 is another tablebase draw.

46...f5+! 47.Kxf5 Ra5+ (The point: the rook gets behind the passed b-pawn.) 48.Kg6 Ra6+ 49.Rh7 Rb6

Position after 49...Rb6

Now it is all over.

50.Rf4+ Ke7 51.Rf1 b3 52.Kg7 b2 53.Rb1 Ke6 54.Kxh6 Kf5+ 55.Kg7 Kg5 56.Kf7 Kxh5 57.Ke7 58.Kd7 Kf3 0-1

UPDATE: Analysis at Chessdom suggests that White could have drawn with 48.Kf6!: 48... Rb5 (48... Ra6+ 49. Ke5 Rb6 50. Kd4 b3 51. Re1 ) 49. Re2 Rxh5 (49... b3 50. Rb2 Rb6+ 51. Ke5 Kf7 52. Kd4 Kf6 53. Rg2! Rb5 54. Kc3 Kf5 (54... b2 55. Rxb2 = ) 55. Kb2 Kf4 56. Rg6 Rxh5 57. Kxb3 is a theoretical draw ) 50. Ra2! (this wouldn't work with the white king somewhere else) 50... Ke8 51. Ke6! Kd8 52. Kd6! Kc8 53. Kc6! Kb8 54. Ra6! Rh4 55. Rb6+ Ka7 (55... Kc8 56. Ra6! ) 56. Rb7+ Ka6 57. Rb8! Rc4+ 58. Kd5 Rf4 59. Kc6 =

The Hou-Koneru Bishop Endgame

2010-12-20T16:32:00.001-05:00

In the ongoing Women's World Chess Championship, a key encounter came in the semifinal, as the two highest-rated players, Humpy Koneru and Hou Yifan, met. In the first game of the two-game match, Hou had white, and Koneru played the Berlin Defense to the Ruy Lopez, clearly aiming to achieve a draw so that she could play for a win of the game, and the match, with white in the second game.

At move 28, they reached the following position:

Hou Yifan - Humpy Koneru,

Women's World Chess Championship, Round 5.1 (2010)

Position after 28.Kxd3

Hou has a large advantage here. The pawn formation is the classic one from the Ruy Lopez Exchange Variation (although, as mentioned above, this game actually started as a Ruy Lopez Berlin Defense), where White has a mobile pawn majority on the kingside while Black's queenside pawn majority is useless because of the doubled c-pawns. Here Black might appear to have some compensation because White's kingside pawns are on the same color as her bishop, but White can (and, indeed must) advance those pawns so her bishop is by no means "bad."

More important is the difference in king activity: White's king can take up a powerful position in the middle of the board, while Black's is stuck on the 7th and 8th ranks, in part because of her earlier mistake 25...g6?, blocking the king's path from f7-g6-f5. Black may already be lost but at the very least she is in for a long and painful defense.

28...Be7 29.Be3 c5 30.Ke4 b6 31.Kf3 Bf8 32.g4

Position after 32.g4

White needs to open up the position to invade with her pieces and the queenside and center are closed. She also needs to make something of her extra pawn on the kingside, of course. She doesn't play h3 followed by g4, however, because that would make it harder for her king to advance.

32...Be7 (32...hxg4 33.Kxg4 is easy for White because Black cannot use the bishop to protect the queenside pawns, as she does in the game. Either White will start picking up the queenside pawns, or the bishops will get exchanged, either way with a simple win for White. Thus 33...Be7 34.Bf2 Bd8 35.Bh4 Bxh4 36.Kxh4 c6 37.Kg5 Kg7 38.h4 +-

Analysis Diagram

If instead 33...Bg7 34.Bf2 Bf8 35.Bh4 Ke8 36.Bf6 Bh6 37.h4 Kd7 38.Bg5 Bf8 39.h5 gxh5+ 40.Kxh5 Ke8 41.Kg6 +-)

Analysis Diagram

33.Kg3 c6 34.Kh3

Position after 34.Kh3

Now that she is ready to set up her defensive formation with the bishop on c7, Black ought to play 34...hxg4 (or 35...hxg4 on the next move). Then there could follow 35.Kxg4 Bd8 36.Bf2 Bc7 37.Bh4 Kf8 38.Bf6 Kf7, reaching the same position that arrives in the game line after move 38 (and 40). But Black would thereby avoid a strong alternative that White missed on move 36.

34...Bd8 35.Bf2 Bc7?! 36.Bh4?!

(36.gxh5! gxh5 37.Bh4, with the idea that Black cannot successfully defend against White's three threats: taking on h5, capturing on b6 with the bishop, and gaining a passed pawn with f5. A sample line:
37...Kg6 38.Kg3 Kf5 39.Kf3 Kg6 40.Ke4 Kg7 41.f5 Kf7 42.Bf6 exf5+ 43.Kxf5 +-

Analysis Diagram

The h-pawn will fall, leaving White with two passed pawns.)

36...hxg4+ 37.Kxg4 Kg7 38.Bf6+ Kf7 39.Bh4 (repeating moves to reach the time control) Kg7 40.Bf6+ Kf7 41.Kg5

Position after 41.Kg5

(Black is now in semi-zugzwang. If the king moves, the g-pawn falls. And if 41...Bb8 42.Bd8 Ba7 43.Bc7 Kg7 44.h3 Kf7 45.Kh6 +-)

41...b5 42.Kh6 bxa4 43.bxa4 Bb6

We are now at the key moment in the game. Hou plays what she thinks is a winning move, but there is a flaw in her calculations.

44.Be7?

Position after 44.Be7?

A spectacular move, but one that gives up the win. Hou had the right idea, but as indicated in the Chessbase report, she should have advanced her h-pawn first. Thus 44.h4! Bc7 45.Bg5! wins. 45...Bb6 46.Be7! Kxe7 47.Kxg6 and the Black bishop cannot get around to stop the h-pawn: 47...Kf8 48.h5 Bd8 49.h6 Kg8 50.h7+ Kh8 51.Kf7 Kxh7 52.Kxe6 Kg7 53.Kd7 Bh4 54.f5+-

44...Bc7?

Koneru, in her turn, doesn't see the flaw in Hou's calculations. 44...Kxe7! draws, as shown in the Chessbase report: 45.Kxg6 Bd8 46.h4 Kf8 47.h5 Kg8 48.h6 (48.f5 exf5 49.Kxf5 Kg7 50.Ke6 Bc7=) 48...Bh4! 49.h7+ Kh8 50.Kf7 Kxh7 51.Kxe6 Kg7 52.Kd7 Kf8 53.f5 (53.Kxc6 Bg3 54.Kxc5 Bxf4=) 53...Bg3 54.e6 Bh4 55.Kxc6 Kg7! 56.Kxc5 (56.Kd7 Kf8; 56.Kb5 Kf6 57.Kxa5 Kxf5 58.Kb6 Kxe6 59.Kxc5 [59.a5 Bd8+ 60.Kb5 Kd6 61.a6 Kc7 62.Kxc5 Kb8=] 59...Kd7=) 56...Be7+ 57.Kb5 (57.Kd5 Kf6 58.c5 Bd8! 59.c6 [59.Kc6 Be7=] 59...Bc7=) 57...Kf6 58.Kxa5

Analysis Diagram

In this amazing position, White has four pawns for the piece, but it is still a draw: 58...Kxf5 59.Kb6 Kxe6 60.c5 (60.a5 Bd8+ 61.Kb5 Kd7=) 60...Kd7=.

These lines were, of course, very difficult to calculate in a real game. After Koneru's move, Hou is winning.

45.Bxc5 Bd8 46.Bf2 Be7 47.c5! Bf8+ 48.Kg5 Be7+ 49.Kg4 Ke8 50.Be1 Bxc5 51.Bxa5 Be7

Here Hou missed the clearest win.

52.Kf3?! (52.Bc3 Kd7 53.h4 Ke8 54.h5 gxh5+ 55.Kxh5 Kf7 56.a5 Bc5 57.a6 Be3 58.Kg4 Kg6 59.Kf3 Bb6 60.Ke4 Kf7 61.Bd4! c5 62.Bf2 Kg6 63.Be3 Kf7 64.f5! exf5+ 65.Kxf5 and, despite the limited material and having the "wrong" rook's pawn, White is winning. For example, 65...Ke7 66.e6 Kd6 67.Kf6 Bd8+ 68.Kf7 Kc6 69.a7 Kb7 70.Bxc5 Bh4 71.Bd4 Bd8 72.Bf6+-) This again would have been extremely difficult to calculate, and you can understand Hou's decision to leave more pawns on the board.

52...Kd7 53.Ke4 c5 54.Kd3 Kc6 55.Kc4 Bh4 56.Bd2 Bf2 57.h3 Bg1 58.Bc1 Bf2 59.Bd2 Bg1

Position after 69...Bg1

60.Kd3?! Here the breakthrough 60.f5! works: 60...gxf5 (60...exf5 61.e6 Bh2 62.a5 Bd6 63.a6 Kb6 64.Be3 +-) 61.h4 Bh2 (60...Bd4 61.Bf4 +-) 62.h5! Bxe5 63.h6 Bf6 64.a5 e5 65.Be3 f4 66.Bxc5 e4 67.h7 e3 68.a6 e2 69.Bf2 Bg7 70.Kd3 f3 71.Ke4 +-

60...Bf2 61.Be3 Be1 62.Kc4 Bb4 63.Bf2 Kb6 64.Be3 Kc6

As is common in this type of ending, Hou is maneuvering with her bishop to try to put Koneru into zugzwang.

65.Bg1 Kb6 66.Bf2 Kc6 67.Bh4 Bd2 68.Bg5 Be1 69.Be7

69...Bf2?! After 69...Bb4, Hou still had to find a clever triangulation to win: 70.Bf8 Kb6 (70...Ba3 71.a5 Bc1 72.Bxc5 Bxf4 73.Bd4 Bg5 74.a6 Bd8 75.a7 Kb7 76.Kb5 Bh4 77.a8=Q+ Kxa8 78.Kc6+-) 71.Bd6 Kc6 72.Be7! Kb6 73.a5+! Kxa5 (Black would like to keep her king closer to the center, but the point of White's maneuvering is that 73...Bxa5 allows 74.Bd8+) 74.Bxc5 Bd2 75.Bd4 Bxf4 76.Kc5 +-. Now the win is more straightforward.

70.a5 Be3 71.Bg5 Bf2 72.h4 Bg3 73.a6 Bf2 74.h5! A nice breakthrough. 74...gxh5 75.f5 exf5 76.e6 Bg3 77.e7 Kd7 78.a7 1-0

Hou held the draw with black in the second game, thereby advancing to the final.

Ulf Andersson's Dynamic Endgame Play (Part 1)

2010-12-19T20:27:00.070-05:00

For a certain type of chess player, I imagine, there exists the following hierarchy: First, there are boring chess games; second, there are incredibly tedious chess games; and last, somewhere between somnolence and apathy, there are the games of Ulf Andersson.

This reputation for boring play is not entirely undeserved as Andersson, especially in recent years, has had a tendency to agree to many short draws. Witness Andersson-Ruck, Banja Luka 2007:

1.Nf3 g6 2.c4 Bg7 3.Nc3 c5 4.g3 Nc6 5.Bg2 e6 6.e3 Nge7 7.O-O O-O 8.d4 d6 9.b3 d5 10.cxd5 cxd4 11.Nxd4 Nxd4 12.exd4 Nxd5 13.Nxd5 exd5 14.Be3 1/2-1/2

In that tournament, Andersson scored 4.5/9, a perfect record of nine draws with no wins and no losses. His games with White, in particular, consisted of draws of 14, 25, 14, and 11 moves.

I don't know Andersson's reasons for agreeing to so many short draws, but I can speculate, based in part on his recent tendency to drop out of open tournaments before they are over, that perhaps he feels with particular acuteness the phenomenon, known to so many chess players, that the pain of a loss far outweighs the pleasure of a victory.

But Andersson's games were not always like the one quoted above and, indeed, in the past a simplified position like the one reached at the end of Andersson-Ruck would have been the starting point for a long attempt to grind out a win, rather than the time to shake hands.

In this post and its sequels, I will discuss some of Andersson's fascinating wins in the endgame. In addition to showing that Andersson's games are not all boring, I want to make another point about the nature of good endgame play. For some players--probably including many of the ones who find Andersson boring--endgame play is a matter of slowly and patiently grinding away with a static advantage (like a knight on a strong outpost) or against a static weakness (like a weak pawn). The exploitation of static advantages is of course a key component of good endgame play, but very often, to win in a simplified position, one must play dynamically. As there come to be fewer pieces on the board, the differences in their activity can assume decisive significance. Andersson is a master of such dynamic endgame play.

Let's start with a simple example:

Andersson-Robatsch

Munich 1979

1.Nf3 Nf6 2.c4 c5 3.g3 b6 4.Bg2 Bb7 5.O-O g6 6.b3 Bg7 7.Bb2 O-O 8.Nc3 d5 9.Nxd5 Nxd5 10.Bxg7 Kxg7 11.cxd5 Qxd5 12.d4 cxd4 13.Qxd4+ Qxd4 14.Nxd4 Bxg2 15.Nxg2 a6

What position could appear more drawish than this one? The pawn structure is symmetrical and the queens and three minor pieces have been exchanged. The only apparent difference is in the relative activity of the knights--White's is in the middle of the board (though not on an unassailable square, since Black can attack it with ...e5) while Black's remains on b8, interfering with the coordination of the rooks. This difference might not seem like much--and, indeed, a draw is perhaps still the most likely result--but one lesson from this game is that the importance of a difference in activity between a single pair of pieces is greater in the endgame than in the middlegame.

16.Rac1

A year earlier, in Andersson-Hort, Niksic 1978, Andersson preferred 16.Rfc1, though it is not clear that the choice of rook makes much of a difference, since White's plan is to double the rooks on the c-file. Andersson achieved a substantial advantage in that game, but was not able to put it away.

16...Ra7

White's threat to invade on c7 already forces this awkward move. If 16...Nd7 17.Rc7 Rfd8 18.Rd1 (threatening Nc6) and Black is already somewhat tied up, although no immediate win is obvious.

17.Rc2

17.f4, creating an artificial support point for the knight and gaining space, is another approach to the position, played by Korchnoi, among others. Andersson's move is more direct and shows that he does not fear further simplification. Still, 17.f4 might well have been better.

17...Rd8 18.e3 e5

This move shows one reason that White might have preferred to play 17.f4. The knight gets chased back from its active post.

19.Nf3 f6 20.g4 Rd6?!

Black is trying to find a way to coordinate his rooks and get his knight out, but this move is not the best way to do it. 20...Rad7 21.Rfc1 Kf7 looks better. The knight actually plays a useful function at b8, preventing the White rooks from invading at c6, and Black can afford to coordinate his other forces before moving the knight, especially now that the White's knight is ineffectively placed.

21.Rfc1 Nd7 22. Rc6! (Not fearing advantageous simplification.) Rxc6 23. Rxc6 Kf7 24. Nd2!

White's advantage is now reaching serious proportions. The knight is threatening to go to c4 or e4, targeting the weaknesses on b6 and f6.

24...Ke7 25. Ne4! Rb7 26. b4 Rb8 27. Nc3! f5?! Black has virtually no useful move, but a waiting move like 26...Rb7 was probably better than this pawn advance, which only creates new weaknesses on the kingside dark squares.

28.Nd5+

White's rook and knight completely dominate their Black counterparts.

28...Kf7 29. Kg3 Now the White king advances into the fray.

28... h5? Under pressure, Black drops a pawn.

30. gxf5 gxf5 31. Rd6 Rb7 32. Kh4 Kg7 33. Kxh5 1-0

Black is helpless to avoid additional material losses. Every one of Andersson's pieces is vastly more active than its Black counterpart.

In future posts, I will look at other examples of Andersson's dynamic play in the endgame.

Google Books Ngram Viewer -- Chess Searches

2010-12-16T15:49:00.002-05:00

Google launched a new service today called Google Books Ngram Viewer. It allows you to see how the frequency of different words changes over time in the millions of books that Google has scanned and digitized.

You can graph the trends for a single word or compare different words. For example, the following diagram compares the frequency of the terms "chess" and "baseball" between 1800 and 2008:

It shows that references to chess have remained fairly steady, while references to baseball climbed dramatically around 1880-1920, held steady until 1970, took off again until just past 2000, and then declined in the last few years.

Here is another example, comparing references to "checkmate" and "touchdown":

I also ran some searches involving the names of chess world champions, realizing that I would have to avoid champions with common names, because they would produce too many "hits" that were actually references to somebody else.

The Elusive Win in Kramnik-Carlsen (Part 2)

2010-12-15T11:08:00.002-05:00

As a commenter pointed out, I have not addressed Black's moves other than 69...hxg5 in response to the proposed 69.g5. I attempt to fill that gap here. As a reminder, here is the position we are looking at:

There are two sorts of alternatives to 69...hxg5 to consider here: 69...h5 and various waiting moves with the Black king. Before I begin, though, I should note that I focused on 69...hxg5 because it seemed the most direct way for Black to achieve his goal: eliminating the remaining White pawns. As we will see, however, this is not the only way that Black can achieve a draw in this ending.

a) 69...h5

It seems foolish at first sight to leave White with the advanced pawn on g5, but Black has a very specific goal in mind. If Black can capture the pawn on g2, force White to advance the other pawn to g6, and get his King back in time, then he achieve the following fortress position:

White cannot force Black's king away from e7 and f8: if White's king gets too close, then it is stalemate.

Unfortunately for Black, however, White seems to be able to avoid this result. The simplest way is to attack the g7-pawn with the King:

70.Kf4

Now Black can either attack the pawn on g2 or start pushing his h-pawn, but neither achieves the draw:

a1) 70...Ke2 71.Kf5 Kf2 72.Bd5 a2 73.Bxa2 Kxg2 74.Kg6 h4 75.Be6

The bishop will capture Black's h-pawn, the White king will capture on g7, and the White pawn will promote.

a2) 70...h4. The trick here is that in some lines Black's king is going to attack the g5-pawn instead of the g2-pawn. White has to be careful.

71.Kf5 Ke3 72.Kg6 Kf4

Now if White waits with, say, 73.Ba2, there is probably no win: 73... Kg3 74.Kxg7 Kxg2 75.Bd5+ (or 75.Kh6 h3 76.g6 h2 77.Bd5+ Kf2 78.g7 a2 79.g8=Q h1=Q+ 80.Bxh1 a1=Q. We now reach an endgame of queen and bishop versus queen, which is very complicated, but where the defending side can usually draw.) 75...Kf2 76.Kh6 h3 77.g6 h2 78.g7 a2 79.g8=Q h1=Q+ 80.Bxh1 a1=Q, again reaching the drawish Queen and Bishop versus Queen. In fact, this position is a tablebase draw.

To avoid this outcome, White needs to play:

73.Kh5!

73...Kg3 (or 73...Ke5 74.Ba2 Kf5 75.Kxh4 Kf4 [75...g6 76.g3 Ke5 77.Kg4 Ke4 78.Bb3 Ke5 79.Kf3 Kf5 80.g4+ Kxg5 81.Kg3 wins] 76.Kh5 Kf5 [76...Kg3 77.Kg6 Kf4 78.g3+ Kg4 79.Be6+ Kxg3 80.Kxg7 wins] 77.g3! g6+ [77...Ke5 78.Kg6 wins] 78.Kh6 Kg4 79.Kxg6 wins.]

74.Bd5 h3 (74...a2 75.Bxa2 Kxg2 76.Kg6 h3 77.Kxg7 h2 78.Bd5+ wins) 75.gxh3 Kxh3 76.g6! (The only winning move).

76...Kg3 77.Kg5 Kf2 78.Kf5 Ke3 79.Ke6 Kd4 80.Ba2 and White wins.

Better yet, and much simpler than these lines, White could diverge earlier with a waiting move like 72.Bf7!

This prevents the Black king from reaching f4 and after 72...Kf2 73.Bd5 Kg3 (73...a2 74.Bxa2 Kxg2 75.Kg6 h3 76.Kxg7 h2 77.Bd5+ wins) 74.g6! (or 74.Ke6!) h3 (74...a2 75.Bxa2 Kxg2 76.Ke6 h3 77.Kf7 h2 78.Bd5+ wins) 75.gxh3 Kxh3 76.Ke6 Kh4 77.Kf7 wins.

Now let's look at what happens if Black plays a waiting move with his king at move 69.

b) 69...Kd4 70.Kf4 Kd3 71.Kf5 Kd4 (...hxg5 or ...h5 at any of these moves will transpose to lines I have already looked at) 72.Ba2 (or another bishop move, but not 72.Kg6? Ke5! 73.Ba2 Kf4 and Black draws) Ke3 73.g6! h5 74.Ke6 h4 75.Kf7 and White wins.

In sum, it appears that White wins in all lines, though it is far from easy to achieve in some of them.

The Elusive Win in Kramnik-Carlsen

2010-12-14T15:47:00.017-05:00

Today at the London Chess Classic, Vladimir Kramnik and Magnus Carlsen played a fantastic game. At move 62, Kramnik exchanged down into what he must have thought would be an easily-winning piece-up endgame. At move 65 the players reached the following position:

Carlsen saw a clever drawing idea, however: he would send his king deep into White's position. If White tried to push his own king forward, Black would attack the White pawns from behind. There thus followed:

65...Kd4 66.Kf3 Kd3 67.g4 Kd2 68.Be6 Kd3

Here Kramnik played 69.Kg3 and Carlsen defended marvelously to achieve the draw.

In this post, I want to examine the alternative 69.g5, which I believe was winning.

69.g5! hxg5 70.Kg4 Ke2 71.g3!

This is the key move. If instead 71.Kxg5 Kf2 72.g4 Kg3, White cannot win. For example, 73.Kf5 g6! 74.Kg5 (74.Kxg6 a2! 75.Bxa2 Kxg4) Kf3!

But after 71.g3!, White is winning:

71...Ke3 (71...Kf2 72.Bd5 Ke3 73.Kxg5 transposes) 72.Kxg5

a) 72...Kf2 73.Kf4! (Not 73.g4, which transposes into the drawing line given above.)

73...g5+ 74.Kg4 Kg2 75.Bb3 (or any other square along the a2-g8 diagonal except d5) Kf2 76.Bd5! Ke3 77.Kxg5 and White wins

b) 72...Ke4 73.Kg4 Ke3 (73...Ke5 74.Bb3 Ke4 75.Ba2 Ke5 (75...Ke3 76.Bb1!) 76.Kf3 and White wins, as the king escapes.)

74. Bb3 Ke4 75.Ba2 Ke3 76.Bb1! (The key move in this line! The bishop needs to leave the a2-g8 diagonal to cut off the e4-square while still covering a2. This tablebase move was mentioned out at chessgames.com by "Kinghunt.")

76...Kd4 77.Kf4 and White wins.

It would of course have been virtually impossible for Kramnik to see all of this over the board, but it is nevertheless a beautiful win.

UPDATE 12/16/2010: Karsten Mueller has posted an explanation of the position after 69.g5! on the Chessbase website, based on an analysis by Hiarcs 13. It confirms that 69.g5! wins, and adds that 70.g3, rather than 70.Kg4 followed by 71.g3, is apparently the most precise line. The winning idea is the same, however, and some of the lines transpose.

Stalemated Knight

2010-05-05T11:42:00.014-04:00

I happened to be looking at the otherwise unremarkable game Rodriguez Crespo (1904)-Kolar (2196), August Open Cambre ESP 2006, when I arrived at the following position:

White has been trying to make something of his good-bishop versus bad-bishop advantage in a typical French ending, but Black seems to be holding. (A couple of moves earlier, White made the mistake of allowing the Black bishop to get out to h5.)

Now things start to get interesting, however.

44...Nf7? (44...Kf7 45.Ng2 Ng6 and Black should be fine.)

45.Ng2! Aiming for f4, forking the h5-bishop and the e6-pawn. Now Black is in trouble.

45...Bg6? (45...Ng5 46.Nf4 Bf7 47.h4 Nh7 48.Kg4 Nf8 seems to hold for Black. White has no way of breaking through.)

46.Bxg6 Kxg6 47.Kg4? (47.h4! wins, not letting the Black knight out via g5. Black is running out of moves and the White knight will start to eat up his pawns. For example, 47...Kf5 48.Kf3 Nh8 49.Ne3+ Kg6 50.Ng4 Kg7 51.Nf6 Ng6 52.Kg4 Nf8 53.Kh5. Now it is a draw again.)

47...h5+ 48.Kf4 Ng5 49.h4 Ne4 Wait a minute, you must be asking, how can this be a draw? Isn't White going to lose his pawn on a4?

50.Ne3 Nc3

51.Nc2?? The losing move! White has the amazing drawing resource 51.Kf3! Nxa4 52.Nd1!!

Now the Black knight cannot move without being captured and the Black king has no way to break through. White has established a fortress and the game is a draw! For example, 52...Kf5 53.Ne3+ Kg6 54.Nd1 and Black has made no progress. If the Black king goes to the queenside, hoping perhaps to play ...Nc5 and pick up a couple more pawns for the knight, then White just captures the pawn on h5.

After missing this chance, White goes down to defeat in a couple of moves.

51...Nxa4 52.Na1 Nc3 0-1

Sacrificing the Queen for Two Minor Pieces (Part 2)

2009-05-15T10:00:00.015-04:00

Ehlvest goes berserk! Nakamura's queen sacrifice in the second round of the U.S. Championships must have made a strong impression on his opponent, Jaan Ehlvest. A mere, three rounds later Ehlvest himself sacrificed his queen for bishop and knight against Varuzhan Akobian. Unfortunately for Ehlvest, his moment of inspiration did not work out very well.

Jaan Ehlvest-Varuzhan Akobian
U.S. Championship (5) St. Louis 2009

1. e4 e6 2. d4 d5 3. Nd2 Nf6 4. Bd3 c5 5. e5 Nfd7 6. c3 Nc6 7. Ngf3 Qb6 8. O-O cxd4 9. cxd4 Nxd4 10. Nxd4 Qxd4 11. Nf3 Qb6 12. Qa4 Qb4 13. Qc2 Nc5 14. Bd2 Qa4 15. b3 Qd7 16. Nd4 Qd8 17. Rac1 Bd7 18. Be2 Ne4 19. Nb5 Bc5

Ehlvest has sacrificed a pawn in a French Tarrasch, but does not appear to have much compensation in this position. The only thing he really has going for him is that Black's king is still in the center. White's knight is ready to harass the king from d6, but Black's dark-squared bishop and knight are both covering that square. But how can White deflect them from the defense of d6? 20. Be3 seems like a plausible move. There are then a lot of potential variations to evaluate:

a. 20...a6? 21. Bxc5 Bxb5 22. Bxb5+ axb5 23. Bb4 gives White a nice advantage, with the Black king stuck in the center, strong dark-square control, and the Black knight in danger of being trapped.

b. 20...Rc8 21. Bxc5 Rxc5 22. Nd6+ Kf8 23. Qb2 Rxc1 24. Rxc1 Nxd6 25. exd6 Bc6 26. Qe5 and White has good compensation for the pawn, because Black's rook isn't in play.

c. 20...Bxe3 21. Nc7+ Ke7 22. fxe3 Rc8 23. Bd3 Bc6 24. Bxe4 Qxc7 (24...dxe4?? allows 25. Qc5+ Kd7 26. Qd6 mate!) 25. Bd3 Qxe5 26. Qc5+ Ke8 27. Qxa7 seems unclear. Black is up a pawn but his king is stuck in the center. White queen is off-side while Black's is nicely centralized. White also has to watch out for his king's position.

In any event, 20. Be3 seems playable, although there were a lot of complicated variations to evaluate. Ehlvest's way of breaking through to the d6 square is more elegant:

20. Qxc5?!?! Nxc5 21. Nd6+ Ke7 22. Rxc5

What does White have for the queen? Materially, a bishop and a knight, though White is also a pawn down. Black's king is stuck in the center, White's knight is an octopus in the middle of the board at d6, and Black is weak on the dark squares. It doesn't seem like enough and, in the rest of the game, Akobian calmly defends and brings home the full point. But, as we will see, Ehlvest might have had a chance or two to make things messier.

As an aside, we are dealing here with a very different kind of sacrifice from those seen in Spassky-Bronstein or even Ehlvest-Nakamura. In those games, Black's compensation was largely material and structural. Here, Ehlvest's compensation is based on his temporary initiative against Black's weakened king. If he doesn't break through soon, he will be lost. It is thus actually an older style of sacrifice. For example, the oldest example in my database of the material imbalance Queen + Two Rooks + Two Minor Pieces vs. Two Rooks + Four Minor Pieces is the following game:

Louis Charles Mahe De la Bourdonnais - Alexander McDonnell
London Match 4 (4) 1834

1. d4 d5 2. c4 dxc4 3. e4 e5 4. d5 f5 5. Nc3 Nf6 6. Bxc4 Bc5 7. Nf3 Qe7 8. Bg5 Bxf2+ 9. Kf1 Bb6 10. Qe2 f4 11. Rd1 Bg4 12. d6 cxd6 13. Nd5

13...Nxd5!

Black, already up two pawns, sacrifices his queen for bishop and knight. He also gets a knight on e3 and White's king is stuck in the center. I won't comment on the rest of the game, except to point out how Black repeatedly eschews chances to win back material in favor of pursuing his initiative (16...Rd8 instead of 16...Nxd1; 19...Rac8 instead of 19...Nxg2+; 20...b5 instead of 20...Bxd2+).

14. Bxe7 Ne3+ 15. Ke1 Kxe7 16. Qd3 Rd8 17. Rd2 Nc6 18. b3 Ba5 19. a3 Rac8 20. Rg1 b5 21. Bxb5 Bxf3 22. gxf3 Nd4 23. Bc4 Nxf3+ 24. Kf2 Nxd2 25. Rxg7+ Kf6 26. Rf7+ Kg6 27. Rb7 Ndxc4 28. bxc4 Rxc4 29. Qb1 Bb6 30. Kf3 Rc3 31. Qa2 Nc4+ 32. Kg4 Rg8 33. Rxb6 axb6 34. Kh4 Kf6 35. Qe2 Rg6 36. Qh5 Ne3 0-1

A marvelous game. Incidentally, in Part 3 I will discuss a couple of games by Larsen and Tal that also feature Nxd5 followed by Ne3 as the key moves in a sacrifice of queen for two minor pieces.

Back to Ehlvest-Akobian.

22...f6

This may not have been the best move. Engines favor 22...b6 or 22...Kf8. After the move in the game, Ehlvest seems to have missed a strong move.

Here Ehlvest could have played 23.Bb4! This move highlights Black's weakness on the dark squares and his stalemated king. The position is incredibly complicated.

The concrete idea behind Bb4 is to make Nxb7 more of a threat, because it sets up a powerful discovered check on the next move. For example, if 23...h6 24. Nxb7 Qb8 25. Rxd5+ Kf7 26. Rxd7+ and White is winning.

So Black should play something like 23...Qb6, covering b7 and attacking the bishop. White can then play the computer move 24. Rb5!?, when after 24...Bxb5 25. Bxb5 Black can't prevent Nc8+, winning back the queen. The resulting rook and two bishops versus two rooks ending looks safe for White. Better for Black is therefore 24...Qa6, when White doesn't have any effective discovered checks. White's best might be 25. Nc4+ Kf7 26. Rxd5 (setting up the following discovered attack on the queen) exd5 27. Nd6+ Qxd6 28. exd6, but then Black is up a clean exchange. If this analysis is correct (and it probably isn't), then White's sacrifice was unsound, although this line would have made things much harder for Black than the game continuation.

23. Rfc1 fxe5!

Akobian offers to return the queen.

24. Nxb7

White's initiative leads to nothing after this move, but the alternative 24. Bg5+ Kxd6 25. Bxd8 Raxd8 just leads to a lost ending down two pawns.

24...Qb6 25. Bg5+ Ke8 26. Rc7 Rb8 27. Bb5 Rxb7 28. Bxd7+ Kf7 29. Be8+ Kxe8 30. Rc8+ Kf7 31. Rxh8 h6 32. Bh4 Rc7 33. Rf1 Rc2 34. Bg3 Qc7 35. h4 d4 36. Kh2 d3 37. f4 Qc6 38. fxe5+ Kg6 39. Bf2 d2 40. Rd8 Rc1 0-1

Cool-headed defense from Akobian that put him in a tie for first after the round.

Sacrificing the Queen for Two Minor Pieces (Part 1)

2009-05-11T10:11:00.020-04:00

The long-term positional sacrifice of the queen for two minor pieces is perhaps the most fascinating and difficult to evaluate type of material sacrifice. According to the counting scheme inculcated in all of us from very early in our chess education, two minor pieces (6 points) should be completely inadequate compensation for the queen (9 points). After all, even rook and a minor piece (8 points) is insufficient compensation for the queen.

Some creative players have attempted to show, however, that in the right kind of position, two minor pieces can hold their own against the queen.

One of the earliest, most famous, and most important games to feature this kind of sacrifice was played between Boris Spassky and David Bronstein at the Amsterdam Candidates' Tournament in 1956.

Boris Spassky-David Bronstein
Candidates Tournament (12), Amsterdam 1956

1. d4 Nf6 2. c4 g6 3. Nc3 Bg7 4. e4 d6 5. f3 e5 6. d5 Nh5 7. Be3 Na6

At the time, the normal moves in this position were 7...f5 or 7...O-O. Tal had played the former move against Spassky a couple of months earlier at the 23rd USSR Championships; Spassky won in 38 moves. Ragozin had been the first to play 7...Na6, in a game against Tolush from the same Soviet Championship tournament. Ragozin had reached a passive position, however, after 8. Qd2 Bd7 9. Bd3 c5 10. Nge2 Qh4+ 11. g3 Qe7 12. a3 Nc7 13. O-O-O a6 14. g4 Nf6 15. h4.

Bronstein had a different idea. What if, rather than waiting for White to play Nge2 and cover g3, he played the queen check a couple of moves earlier? Of course, if Black plays ...Nxg3, White can also pin it with Qf2...

8. Qd2 Qh4+ 9. g3

9...Nxg3!!?? 10. Qf2 Nxf1 11. Qxh4 Nxe3 12. Kf2 Nxc4

Black has two bishops and two pawns for the queen, but no trace of an attack. Bronstein later wrote that "I wanted to demonstrate that the two bishop are a great force." It was a revolutionary idea at the time to consider this position even playable for Black. Bronstein ended up losing this game, but improvement were later found for Black and other players have taken up Bronstein's idea with success.

13. b3 Nb6 14. Nge2 f5 15. Rhg1 O-O 16. Kg2 Bd7 17. a4 Bf6 18. Qg3 Nb4 19. a5 Nc8 20. exf5

In "Bronstein on the King's Indian," he wrote that he had not expected this move, "became nervous and took with the bishop." He gives instead 20...Ne7! (a move also proposed by Goldberg in the Russian tournament bulletin) 21. Ne4 (21. fxg6 Nf5 22. Qe1 [22. gxh7? Kh8! 23.Qe1 Nd3 24.Qd2 Nh4+ 25.Kg3 Rg8+! and Black's attack breaks through] Nd3 23. Qd2 Nh4+ leads to a draw by repetition.) Nxf5 22. Nxf6+ Rxf6 23. Qg5 Raf8 and Black "has a very strong position. He has a mass of threats- ...Nd4, ...Nc2, and ...Nd3. It seems to me that here Black's position is considerably better, as his pieces are dominant."

20...Bxf5 21. Ra4

Bronstein says that he became rattled after this move and is very critical of his subsequent play.

21...Nd3 22. Rc4 Nc5 23. Ne4 Na6 24. Nxf6+ Rxf6 25. f4 e4 26. Nc3 Ne7 27. Re1 Raf8 28. b4 c6 29. Nxe4 Bxe4+ 30. Rcxe4 Nxd5 31. Re8 Nac7 32. Rxf8+ Kxf8 33. Kh1 Rf5 34. Qh4 Nf6 35. Qf2 Nb5 36. Qe2 Nd5 37. a6 bxa6 38. Qe8+ Kg7 39. Qxc6 Kh6 40. Qxa6 Nxb4 41. Qb7 Nd3 42. Re7 Nxf4 43. Rxh7+ Kg5 44. Qe7+ Kg4 45. Qe3 Kg5 46. h4+ Kg4 47. Kh2 Nh5 48. Rh6 1-0

Although unsuccessful in this game, Bronstein's idea became an inspiration for later players. For example, Seirawan employed it in a similar position against Kasparov in 1989:

Gary Kasparov-Yasser Seirawan
World Cup Barcelona (4) 1989

11...Nxg3 12. Qf2 Nxf1 13. Qxh4 Nxe3 14. Ke2 Nxc4 15. Rc1 Na6 16. Nd1 Nb6 17. Ne3 Bd7 18. Nh3 f6 19. Nf2 Nc8 20. Rc3 Ne7 21. Rhc1 Rac8 22. Rb3 Rb8 23. Nd3 Rf7 24. Qe1 Nc8 25. Qa5 Nb6 26. Rxc7 f5 27. Rc2 fxe4 28. fxe4 Rbf8 29. Rxb6 axb6 30. Qxb6 Bh6 31. Qxd6 Rf3 32. Nf5 gxf5 33. Qxh6 fxe4 34. Ne1 1/2-1/2

White actually looks better in the final position, and 34. Qg5+ was probably even stronger. Perhaps Kasparov offered the draw in time trouble?

In the type of position seen in these games, Black's compensation is in part material (two bishops plus two pawns are worth almost as much as a queen), in part the power of the two bishops, and in part the fact that the closed position and Black's unbroken pawn formation leaves the White queen with few opportunities to invade the Black position.

From this perspective, far more adventurous is the sacrifice played by Hikara Nakamura in the U.S. Championship over the weekend.

Jaan Ehlvest-Hikara Nakamura
U.S. Championship (2) St. Louis 2009

1. Nf3 Nf6 2. c4 e6 3. g3 b6 4. Bg2 Bb7 5. O-O Be7 6. b3 O-O 7. Bb2 d5 8. e3 c5 9. Nc3 Nc6 10. cxd5 Nxd5 11. Nxd5 Qxd5 12. d4 Rad8 13. Ne5

This is a well-known position from a line of the English that is considered to give White a slight edge. The usual move is 13...Qd6, played, for example, by Carlsen in a rapid game against Ivanchuk last autumn. Nakamura played

13... Qxg2+?!?!

This move is, incredibly enough, not a novelty. It was played in Andrijevic-Jovicic, Belgrade 1980. That game went:14. Kxg2 Nxe5+ 15. f3 Ng4 16. Qe2 cxd4 17. exd4 Nf6 18. Rfc1 Nd5 19. Rc4 Rfe8 20. Kf2 Bg5 21. h4 Be3+ 22. Kg2 Bf4 23. Bc1 Bd6 24. Bd2 h6 25. Kh2 Ba6 26. Qe4 Nf6 27. Qc6 Bxc4 28. bxc4 Bc5 29. dxc5 Rxd2+ 30. Kh3 bxc5 31. Qxc5 Rb8 32. a4 Rbb2 33. Rh1 Rf2 34. Qxa7 h5 35. a5 Rfd2 36. a6 Ra2 37. Qb8+ Kh7 38. a7 1-0.

14. Kxg2 Nxe5+ 15. f3 cxd4 16. exd4 Nc6 17. Qe2 Rd5

Here Black has bishop, knight, and one pawn for the queen. White has an isolated d-pawn and a bad bishop. If Black ever takes the d-pawn, however, the position could open up to the advantage of White's queen. In fact, there are already many open lines that White's queen can use. In short, Black's compensation is much more questionable here than in Spassky-Bronstein. Ehlvest, however, appears rattled by the unexpected turn of events.

18. Rac1 Rfd8 19. Rc4?!

Returning some material. 19. Rfe1 Nxd4 20. Bxd4 Rxd4 21. Rc7 looks good for White.

19...Ba6 20. Qe4 Bxc4 21. bxc4 R5d6 22. Rd1 Bf6 23. Ba3 Rxd4 24. Rxd4 Nxd4

Now Black has a more conventional rook, knight, and pawn for the queen. This material, combined with the weak White pawn on c4, should give him sufficient compensation if he can stabilize the position. In the next couple of moves, White could try to mix things up by invading with the queen at Qb7, but Ehlvest plays it safe. After 25. Qb7! h5 26. Qxa7 Nf5 27. Qxb6 Rd2+, Black's counterplay appears menacing, but the computer shows that White is safe after 28.Kh3 Bd4 29. Bc5.

25. Bc1?! h5 26. g4?! hxg4 27. fxg4 g5 28. Be3 e5 29. a4 Rc8 30. Qd5 Ne6 31. Kf3

Now Black is fine. Nakamura's next move is risky, as it allows White to invade and win a pawn. As compensation, however, White's king becomes exposed. He might have considered instead biding his time with moves like ...Rc7 and ...Kg7.

31...Be7!? 32. Qxe5 Rxc4 33. Qb8+ Kg7 34. Qxa7 Bd8 35. Qd7 Rb4 36. h3 Bf6 37. Qd1 1/2-1/2

It is hard to see how either side can make much progress in the final position.

My Favorite Moves (1)

2009-05-04T10:36:00.007-04:00

I am going to start another series of occasional posts, in which I highlight some of my favorite moves. This is not meant to be a compilation of the "greatest" moves ever made, but is rather a selection of my personal favorites, based on my own subjective, aesthetic criteria. To the extent there is a pattern or theme to the moves, I think they are all moves that have a certain paradoxical quality. Many of them are superficially bizarre or rule-breaking, but on a deeper examination, are in fact completely logical. They are almost all moves that it would never have occurred to me to play.

The first move is justly famous will probably be familiar to most readers. I still remember the thrill I felt when I first saw this game, however, and it still gives me pleasure to watch Short's king creep forward to help the queen deliver the final blow.

Nigel Short - Jan Timman
Tilburg (4) 1991

White has seized control of the d-file and the dark squares around Black's king. But how can he finish Black off? The queen cannot mate alone; White needs one more piece. The knight is immobile because of the mate threat at g2.

White could try to open up the kingside and bring a rook into the attack with a sequence like 31. Rd3 Rc8 32. R7d4 Rce8 33. g4. Then 33...hxg4 34. h5 gxh5 35. Qg5+ Kh7 36. Qxh5+ Kg8 37. Rxg4 is mate. (Other 34th moves for Black also lead to mate in this line, usually on g7 after White plays h6.) But Black can try 33...Qc5! 34. gxh5 Qe7, when White is still better, but there is no immediate win. Pawn-up endgames are not likely to lead to much for White, with his shattered queenside pawn formation.

Short's solution is brilliant: if the knight and the rooks cannot join the attack, he will use the only other piece available: the king!

31. Kh2!! Rc8

If 31...Bc8, White needs to change plans. With the mating threat on g2 gone, White can play 32. Ng5! Bxd7 33. g4! Bc8 34. gxh5 Bb7 35. f3 with mate to follow a few moves later.

32. Kg3! Rce8 33. Kf4! Bc8 34. Kg5 1-0

White threatens Kh6 and mate on g7. If Black blocks this threat with 34...Kh7, then White plays 35. Rxf7+ (or 35. Qxg6+) Rxf7 36. Qxf7+ Kh8 37. Kh6 with mate in 2.

It is amazing that Black was so helpless that he could do nothing about the king's march deep into his position, even with queen, two rooks, and a bishop still on the board.

Great Rivalries: Petrosian vs. Larsen (Part 5)

2009-04-30T23:08:00.006-04:00

Petrosian and Larsen met for the third time at the Nimzowitsch Memorial in Copenhagen. Petrosian dominated the tournament, scoring 11.5/14 against the largely weak opposition. Larsen could finish only fourth, behind Petrosian, Geller, and Stahlberg.

Tigran Petrosian-Bent Larsen
Copenhagen (Nimzowitsch Memorial) 1960

I am not sure about the order of moves at the beginning of this game. Chessbase gives a completely different sequence from that in P.H. Clarke's Petrosian's Best Games of Chess 1946-1963. In any event, Petrosian gained a large advantage with a menacing pawn majority on the kingside after some passive play from Larsen in another Old Indian. The position after 22 moves was:

There followed:

23. Qh5 Rxd3 24. Rxd3 Rd8

25. Nf6+!

Not the only winning move (25.Rg3 and 25.Rh3 also do the trick), but certainly the most pleasing one. The idea is that after 25.Rh3 Black's best, though still inadequate, defense is 25...h6. After 25.Nf6+ gxf6 26.Rh3, that move would just hang the h6-pawn and lead to mate in three.

25...gxf6

If 25...Bxf6, Clarke gives 26. gxf6 Rxd3 27. Qg5 Kf8 28. fxg7+ Kg8 29.Ne4! when Black's best is 29...Qd8 30.Nf6+ Qxf6, which is completely lost after 31.exf6. In this line, 28. Qxg7+ Ke8 29. Qg8+ Kd7 30. Qxf7+ wins even more quickly.

26. Rh3 Kf8 27. Qxh7 Ke8 28. g6! Bf8 29. g7

By this time, almost everything wins: 29. e6, 29. exf6, 29. Ne4.

29...Bxg7 30. Qxg7 Qe7 31. Ne4 Rd1+ 32. Kf2 f5 33. Nf6+ Kd8 34. Rh8+ Kc7 35. Re8 1-0

Once again, Petrosian wins by trapping Larsen's queen.

Great Rivalries: Petrosian vs. Larsen (Part 4)

2009-04-24T16:55:00.021-04:00

Petrosian and Larsen next met over the board in 1960. In 1959, Petrosian had won the 26th Soviet Chess Championship and had finished third in the Candidates' Tournament, behind Tal and Keres. Larsen had been left with the somewhat humiliating task of serving as the second to the fifteen-year-old Fischer in Yugoslavia, a task that reportedly involved reading Tarzan stories to the teenager.

In the small tournament in Beverwijk, Holland, in 1960 (the predecessor of the great Wijk aan Zee and Corus tournaments of more recent years), Petrosian and Larsen tied for first place. But Petrosian prevailed in their head-to-head encounter.

Tigran Petrosian-Bent Larsen
Beverwijk 1960

1. c4 d6 2. d4 e5 3. Nf3 Nd7 4. Nc3 Ngf6 5. e4 Be7 6. Be2 O-O 7. O-O c6

This is the main line of the Old Indian. White has a small advantage, as Black's position is more passive than in the analogous lines of the King's Indian, thanks to the bishop's position on e7 instead of g7. Nevertheless, Black's position is still very solid.

8. d5

Not the most common move--in fact, Re1, Qc2, Be3, h3, and Rb1 are all seen more often in this position--but perhaps played by analogy to the Petrosian variation in the King's Indian? Petrosian closes the center, stabilizing the position and reducing Black's options. In this position, though, Black is able to establish his knight on c5 and White does not seem to gain any advantage.

8...Nc5

Keene and Simpole, in Petrosian vs the Elite, mention that 8...c5 is a viable alternative. That move would transpose into a well-known line of the Czech Benoni, but a tempo down for Black. Of course, in such a closed position, one tempo is not particularly important. Still, White should have the edge after 9. a3 Ne8 10. b4.

9. Nd2 a5 10. b3 cxd5?

Keene and Simpole prefer 10...Ne8. That move is certainly possible, but Black's problem is not so much that he has the wrong plan but that he uses the wrong move order. Thus 10...Bd7 11. Rb1 cxd5 12. cxd5 b5! gives Black a good position. Indeed, Larsen would later use this idea when he had the position after 10.b3 a tempo down in a game against Polugaevsky in Bugojno 1982. That game went 11. a3 Bd7 12. Rb1 cxd5 13. cxd5 b5 and Black had no problems.

11. cxd5 Bd7 12. a4!

Now ...b5 is impossible and White has a powerful bind on the queenside light squares.

12...Qb6 13. Ba3 Rfc8 14. Rb1 Qa7 15. Rc1 Rc7 16. Bb5

Threatens to pave the way for an invasion of the light squares by exchanging off a key defender of them, the d7-bishop. If, for example, 16...Ne8 17. Bxd7 Nxd7 18. Nb5 Rxc1 19. Qxc1 Qb8 20. Nc4 and Black is completely tied up. Larsen avoids the exchange and also leaves the White bishop blocking the knight's access to b5.

16...Bg4 17. Qe1 Na6 18. h3 Bh5

This removes the bishop from the defense of the queenside, but 18...Bc8 19. Bxa6! bxa6 (19...Qxa6 20. Nb5 Rxc1 21. Qxc1 Qb6 22. Nc4 Qd8 23. Bxd6 wins) 20. Nc4 leaves White with a dominating position. 18...Bd7 19. Bxd7 Rxd7 20. Nb5 Qb8 21. Nc4 is the sort of thing Larsen was trying to avoid with 16...Bg4.

19. Bxa6!

At first sight, a surprising move, but it clears the way for the knights to occupy c4 and b5. If 19...bxa6, then 20. Nc4 wins the a5-pawn.

19...Qxa6 20. Nc4

Keene and Simpole don't analyze any alternatives to Larsen's exchange sacrifice. Petrosian has established such an effective bind, however, that it is hard to come up with ideas for Black. For example, after 20...Ne8 21. Nb5 Rd7 22. Qe3 Bg6 Black is badly tied up, though I don't see an immediate breakthrough for White. Nevertheless, Petrosian is the last player against whom you would want such a position, so Larsen's decision to lash out, even if his compensation for the exchange is ultimately inadequate, is understandable.

20...Rxc4 21. bxc4 Qxc4 22. f3

White could also try 22. Nb5 Qxa4 23. Bxd6 with a powerful passed d-pawn, but Petrosian's decision to keep things under control is also strong, and characteristic of his play.

22...Ne8 23. Qe2 Qd4+ 24. Kh1

Black has a pawn for the exchange, but has no real positional compensation. He has a temporary initiative on the dark squares, but once White's bishop returns to c1, he will have all of the important dark squares covered. White still has control over the queenside light squares, which he will use to organize an invasion along the b- or c-file.

24...Bg5 25. Rfd1 Qb6 26. Rb1 Qc7 27. Nb5

The establishment of a knight on b5 is a key part of White's strategy. It helps ensure his invasion on the c-file and ties Black to the defense of the d6-pawn. Incidentally, in Petrosian's King's Indian games, where he frequently used the same sort of light-square strategy, I count 26 games in which he landed a knight on b5. In those games, he scored a staggering +22 =4!

27...Qd7 28. Bc1 Bd8 29. Be3

Petrosian has beaten back Larsen's attempt at counterplay on the dark squares. Now Larsen is helpless to prevent Petrosian's invasion down the c-file.

29...Bg6 30. g4!

Eliminating any chance of counterplay with ...f5.

30...h5 31. Rbc1 Nf6

If Black exchanges off the dominant White knight with 31...Nc7, White remains in control after 32. Nxc7 Bxc7 33. Qc4 Bd8 34. Rd2 intending Rb2.

32. Rc4 Nh7

Still angling for some counterplay on the kingside dark squares.

33. Rdc1 Bg5 34. Bxg5 Nxg5 35. Kg2 Qd8 36. Qe3!

Another characteristic "short" move from Petrosian. 36. Rc7 was also completely winning after 36...hg 37. hg f5!? 38. gf Bh5 39. R1c3 or 38. ef Bf7 39. Qd3, but Petrosian does not allow Black even a hint of counterplay. Now if 36...hg 37. hg f5? 38. ef Bf7 39. Nxd6 and Black is crushed. White is also threatening 37. Nxd6, which forces the following weakening of the seventh rank.

36...f6 37. Rc7 Kh7

If 37...Rb8, then 38. Qa7.

38. Rxb7 Rc8 39. Rxc8 Qxc8 40. Rc7 Qf8 41. Qc1 Qd8 42. Qc6 Nxe4 43. Rc8

43. fe Bxe4+ 44. Kh2 also wins, but is not as elegant as Petrosian's choice.

43...Qe7 44. Qa8 Kh6 45. Rc7 1-0

The queen is trapped. A beautiful game by Petrosian.

A Prolegomena to a Theory of Drawing Lines (Part 1)

2009-04-24T11:25:00.009-04:00

There are always plenty of reasons to agree to a short, agreed or semi-agreed, "grandmaster" draw. Perhaps you are tired. Or looking for an easy day after a hard defeat. Or preparing to face a difficult opponent the next day. Maybe the round is starting too early in the morning. Or maybe the Real Madrid game is on TV. There are also more sinister reasons.

In any event, the "whys" of grandmaster draws are almost infinite. But that still leaves the question of "how." Even if you and your opponent both know that you are going to agree to a draw, you still need to go out there and play some moves. If you try to agree to a draw on move one, the organizers might not like it.

What follows is my attempt at a survey of a little-studied branch of chess opening theory: the theory of drawing lines. It turns out that there are a great variety of standard lines that lead to short draws, either by producing a perpetual check or a sterile position. Some players even specialize in certain lines.

I propose that it doesn't make sense to classify these openings according to the usual ECO code or the common names of openings (Queen's Gambit, King's Indian, etc.). Instead, I suggest a subjective classification based on the style of "game" that the opening produces. After all, given that the objective result of all of these games is the same--a draw--only the subjective, aesthetic aspects of the openings are relevant criteria for classification.

Symmetrical Exchanging Lines

These lines are perhaps the simplest way to agree to a draw: produce a symmetrical position with no imbalances, trade off some pieces, and sign the score sheets--what could be easier?

The Exchange Slav. Perhaps the most popular drawing line of all. As with so many of these drawing lines, as we shall see in a later post, White can actually play for the win in the Exchange Slav, but if he wants a draw, then he can choose the following line: 1.d4 d5 2.c4 c6 3.cd cd 4.Nc3 Nf6 5.Nf3 Nc6 6.Bf4 Bf5 7.e3 e6 8.Bd3 Bxd3 9.Qxd3 Bd6 10.Bxd6 Qxd6. In my database, 190 games ended as draws in this position. After 11.O-O you get another 105 draws; 11...O-O 274 more 12.Rac1 84 more (alternatively, 12.Rfc1 113 more draws) and so on. In total, I count at least 1335 draws in twelve moves or fewer in this line. Some players are connoisseurs of this variation. GM Ognjen Cvitan, for example, has "played" 36 draws of no more than 16 moves in the Exchange Slav. Other avid practitioners include Ionescu (36 draws), Panchenko (27), Milorad Knezevic (23), Vadasz (23), Naumkin (22), and Kirov (20).
The Symmetrical English (1). Another symmetrical drawing line goes: 1.c4 c5 2.Nc3 Nc6 3.g3 g6 4.Bg2 Bg7 5.Nf3 Nf6 6.O-O O-O 7.d3 d6 8.a3 a6 9.Rb1 Rb8 10.b4 cb 11.ab b5 12.cb ab. This line is not as popular as the Exchange Slav--there is actually a lot of play left in the position--but nevertheless I count at least 170 early draws in this line. Hulak has 9 draws in this line. Our friend Cvitan has 3. (Indeed, if you want to learn the theory of drawing lines, you can do worse than to study Cvitan's games.)
The Symmetrical English (2). 1.c4 c5 2.Nc3 Nc6 3.g3 g6 4.Bg2 Bg7 5.e3 e6 6.Nge2 Nge7 7.O-O O-O 8.d4 cd 9.Nxd4 Nxd4 10.ed d5 11.cd Nxd5 12.Nxd5 ed. I find 62 draws in this position, with dozens more on the moves immediately before or after it, including the classic Hulak-Cvitan, Sarajevo 1988, which continued 13. Be3 Be6 14. Qd2 Qb6 15. Rac1 Rfc8 16. h3 h5 17. Rfd1 1/2-1/2 Hulak is again a frequent player, with at least 12 draws, although he does not match Csom's 19 games in this line. Even Tal played 4 short draws (as Black) from this position.

Incidentally, Csom might be the all-time champion of grandmaster draws. My database has 643 Csom draws of fewer than 20 moves. Cvitan is close behind with 588. By comparison, such supposed "draw masters" as Kramnik and Leko have only 166 and 103 such draws, respectively.

In the next installment, I will turn to the always exciting draw by perpetual check.

Great Rivalries: Petrosian vs. Larsen (Part 3)

2009-04-21T16:48:00.019-04:00

Let's look at some of the Petrosian-Larsen games.

Their first encounter was in the 16th round of the Portoroz Interzonal in 1958, an event whose outcome Larsen described as "the greatest failure of my chess career." He ended up finishing 16th, with 8.5/20. Petrosian lost only one game in the whole tournament and tied for third with Benko, with 12.5/20, thereby qualifying for the Candidates' Tournament. But his one defeat came in his game against Larsen.

Before this game, in the 16th round, Petrosian was leading the tournament. Larsen was near the bottom of the table.

Larsen opened with the Bird (1.f4), a bit of a provocation against Petrosian, who was already establishing a fearsome record against the Dutch Defense as white. According to my (surely incomplete) database, his record at the time was +5, =5, and would eventually grow to +15, =7, including wins over Korchnoi, Bondarevsky, Tolush, Bronstein, Nikolic, and Larsen himself. the Korchnoi game in particular, played when they both were juniors, is a classic demolition of black's old-fashioned Stonewall strategy (7...O-O? instead of 7...Qe7).

Petrosian's disdain for the Dutch is captured by remarks such as "If they want to play the Dutch, there is no reason to prevent it!" and "What a delight! I love playing against the Dutch." (The latter is from Petrosian's annotations to his game against Larsen (!) from the wonderfully-named Church's Fried Chicken First International Chess Tournament, in San Antonio, in 1972. I will come to this game later.

Anyway, to the game:

Bent Larsen - Tigran Petrosian
Portoroz Interzonal (16) 1958

1. f4 Nf6 2. Nf3 d5 3. e3 Bg4

Larsen later wrote that he had intended to play 3...g6 4.b4!? in this game.

He got his chance to play this novelty against Simagin at the Alekhine Memorial in 1959, a 76-move draw. He subsequently employed it four more times, most prominently in his win over Spassky at the 1964 Interzonal.

4. Be2 Nbd7 5. Ne5 Bxe2 6. Qxe2 e6 7. O-O Bd6 8. d4 O-O 9. Nd2 c5 10. c3 Rc8

It is hard to believe that White has any advantage here. It is a standard Stonewall Dutch position in reverse, in which Black has succeeded in exchanging off his bad bishop. Larsen, ever the optimist, nevertheless decides to start pushing his kingside pawns.

11. g4 A committal move. White would like to develop the dark-squared bishop, but 11.b3? cxd4 leaves White with problems on the c-file, while 11.Ndf3 Ne4 looks slightly better for Black.

11...Ne8 12. Ndf3 Ndf6 Perhaps inviting a repetition after 13.Nfd2 Nd7.

13. Bd2 Ne4?! This move leaves Black's other knight without prospects. Better seems to be 13...Bxe5 14.Nxe5 Ne4 15.Be1 f6 16.Nd3 N8d6, with an advantage for Black.

14. Be1 f6 15. Nd3 Be7 16. f5!? Continuing Larsen's risky play Qd7 17. Nh4 Nc7 18. Bg3 Bd6 19. Bxd6 Qxd6 20. Rad1 Rce8 21. dxc5 Nxc5 22. Nf4 b5? Black is fine after 22...e5 23.Nxd5 Nxd5 24.c4 Nc3 25.bc Qc6, but now White gets a strong initiative.

23. Qg2 Rd8 24. b4! Removing a defender of e6 Ne4 25. fxe6 g6 26. Nxd5 Nxd5 27. Qxe4 Nxc3 28. Rxd6 Nxe4 29. Ra6 Rd3 30. Rxa7 White has a clean extra pawn. Re8 31. Ng2 g5 32. Rc1 Rd6? This allows the other rook to invade the seventh rank, which will prove fatal for Black. 32...Nc3 was better. 33. h4! Rdxe6 34. Rcc7 Nd6? 34...h6 was necessary, not only to save the pawn, but to prevent what follows 35. Rxh7 Rc8 36. Rhg7+ Kh8 37. h5 Ne8 38. Rgf7 Nd6 39. Rh7+ Kg8 40. h6 Ne8 41. Rhf7 1-0

Black has to give up a piece to avoid mate. (41...Re4? 42.h7+ Kh8 32.Rf8#) Active play by Larsen, but uncharacteristically weak defense from Petrosian.

After this game, Petrosian closed the tournament by drawing four games in a row, thereby conceding first place to Tal.

Great Rivalries: Petrosian vs. Larsen (Part 2)

2009-04-17T13:13:00.008-04:00

Back to Petrosian and Larsen.

After playing over Larsen's fine victories over Petrosian in Santa Monica (which I will discuss below), a few questions occurred to me:

1. Had any other sitting world champion ever lost two games to the same opponent in a tournament?

2. Had Petrosian, who was so notoriously difficult to defeat, on any other occasion lost two games to the same opponent in a tournament?

3. What was Larsen's lifetime score against Petrosian? Did he always displace such dominance?

1. I found the answer to the first question quickly enough, having a vague memory that Alekhine had lost twice to somebody in AVRO 1938. Sure enough, Fine won both of his games against Alekhine there. Are there any other examples?

2. It also turned out that Larsen was not the only person to win two games against Petrosian in a single tournament. Taimanov had done it in the 1953 Candidates' Tournament, as had Olafsson in the 1959 Candidates' Tournament.

3. Finally, looking up the lifetime score between Petrosian and Larsen revealed an extraordinarily interesting and combative series of contests. Petrosian won the series, +9, -4, =9. These were hard-fought games. They did not draw a game until their tenth encounter. Only 4 of their first 17 games were draws.

To provide some perspective: in the period between 1958 and 1979, when they played those 13 decisive games out of 17 (only 24% draws), Larsen overall had 30% draws and Petrosian had 56% draws.

Great Rivalries: Petrosian vs. Larsen (Part 1)

2009-04-17T11:38:00.001-04:00

I have been reading Larsen's game collection and recently looked at his two victories over Petrosian from the great Second Piatigorsky Cup tournament in 1966.

Incidentally, my copy of this book, the 2003 reprint by Hardinge Simpole, is called "Bent Larsen's Best Games of Chess: Master of Counter Attack." This book was originally published, in Danish, as "50 Udvalgte partier, 1948-1969," in 1969. I believe that a literal translation of this title is "50 Selected Games, 1948-1969." An English translation, called "Larsen's Selected Games of Chess, 1948-1969," appeared the next year. Batsford then reissued it as "Bent Larsen: Master of Counter-Attack: Larsen's Selected Games of Chess 1948-1969," in 1992.

I mention all of this because on page 99, Larsen writes the following: "It is not by chance that the title of this book makes no reference to "best games"--for where do you find two chess players who agree which games are best? Which do you rate highest, courage or foresight? Imagination or precision? Poetry or prose? Music or mathematics?" All of which sounds ridiculous when the book you are holding in your hands in fact does make reference to "best games" in the title. Does a publisher really think that it will sell more copies of a collection of "best games" than of "selected games?"

While I'm on the topic, what is with these "Master of ..." books? The Batsford Larsen book was the predecessor of the recent Everyman Chess series, which includes:

Alexander Alekhine: Master of Attack
Boris Spassky: Master of Initiative
Rudolf Spielmann: Master of Invention

Actually, now that I look at the Everyman Chess web site, I see that the full titles of these books are in fact "The Masters: Alexander Alekhine Master of Attack," etc.

Can a great chess player be summed up in one word? If so, are these words the correct choices?

Having played through the games in the Larsen book, I submit that "Master of Counter-Attack" is a serious misnomer. I have always thought that counter-attacking in chess involved luring your opponent into over-extending himself in an attack and then responding with an attack of your own. In other words, you cannot counter-attack until your opponent has first attacked you. My favorite example of such play is Geller-Euwe, Zurich Candidates' Tournament 1953. Of the all-time greats, Lasker and Korchnoi seem to have the styles best described as "counter-attacking."

Larsen, at least in the games in this collection, is all about fighting for the initiative from the start. I'll post some examples later.

And I will also get back to the alleged topic of this post, the games between Petrosian and Larsen, later.