30 September 2007

The Most Famous Positional Sacrifice?

The first position in the series on Petrosian's Exchange Sacrifice, one of the most famous positional sacrifices of all time, is shown in the diagram.

Zurich 1953
Petrosian, Tigran

Reshevsky, Samuel
(After 25.Rf1-e1)
[FEN "3rq1k1/4rppp/2n3b1/pp2P3/2pP1QB1/P1P1R3/1B4PP/4R1K1 b - - 0 25"]

In a wonderful example of verbal analysis, Petrosian wrote:

The situation is very tense and complicated, materially balanced. So-called dynamic balance exists, with even chances for both sides in attack and defense. White has a strong Pawn center which would smash Black's position if put into motion. On the other hand, it is not easy to advance White's central Pawns; no use of e5-e6 and no sense of d4-d5. Therefore I was satisified with this position until I reached it. But when it stood on the board I realized that Black's position is rather difficult. You may ask, why? Because Black's pieces are posted passively, limited strictly to defense. White can prepare the advance of his d-Pawn to d6, throwing Black's pieces back and achieving a winning position. On the other hand, White has the possibility of advancing his h-Pawn: h2-h4, threatening h4-h5-h6. If Black reacts h7-h5 or h7-h6, he creates weaknesses on his Kingside giving White a good attacking opportunity; the Bishop will go to c1 and join the main forces.
I realized that by moving my Knight to d5 I would change the situation completely so as to make it very favorable instead of difficult. White's Pawns would be blockaded; his Bishop on b2 would be very poor; after an eventual b5-b4 Black could obtain a passed, very powerful Pawn supported by Nd5 and Bg6. However, it is very difficult to bring the Knight to d5. This could be done via b6, c7, or e7, but a Knight maneuver to b6 or c7 would take a lot of time; White plays Bg4-f3 and d4-d5, obtaining a winning position. Of course the idea of moving the Knight to e7 is highly welcome, but how to do it? First I should go away with the Rook, but where?
I spent a good deal of time thinking over this position, and when I found the right move I felt kind of amused. The move was so simple that there was no doubt about its correctness. I overcame the psychological barrier and put my Rook under the fire of White's Bishop. (Petrosian's Legacy p.68)

Petrosian played 25...Re6. In the tournament book, considered one of the best chess books ever written, Bronstein summarized the positional ideas this way:

Black must block the White Pawns, and Petrosian immediately offers the exchange in order to free his e7 for the transfer of his Knight to d5. True, Black gets serious compensation: his Knight on d5 will be exceptionally strong, as will his Bishop, which will lack a light square opponent. Notice that now or on his last move White could have started a direct Kingside attack by h2-h4-h5 and Re3-g3, getting good winning chances; but he counts on winning in another way.

Reshevsky delayed the capture for one move with 26.a4 Ne7, but finally played 27.Bxe6 fxe6, and was unable to win. To play through the complete game see...

Samuel Reshevsky vs Tigran Vartanovich Petrosian, Zurich 1953

...on Chessgames.com.

28 September 2007

WCC Mexico - Opening Ceremony

Opening ceremony 1 • I'm not sure what the first sequence in this clip shows, chess in an aquarium? • From Europe Echecs; see their many other videos from Mexico City.

Opening Ceremony 2 (4:59) • Ceremonie d'ouverture du championnat du monde du Mexique (Opening ceremony of the World Championship in Mexico)

The second clip shows the drawing of lots to determine the pairings for the tournament.

26 September 2007

K + 2N vs. K + P

The strange looking diagram shown below is a continuation of Tablebase 1 - Botvinnik 0. There I pointed out that Botvinnik had incorrectly analyzed a position in an endgame of two Knights against a Pawn. The simpler endgame of two Knights without other pieces is a theoretical draw, because the Knights can't contruct a mating position without first stalemating the enemy King. The extra Pawn allows the Knights to play through the 'stalemate' position because the weak side has a Pawn move and isn't stalemated. It is the trickiest of the 'elementary endgames'.

Not all positions with 2N vs. P are won for the strong side. Ignoring for a moment the blue symbols, an example is the diagram. The position of the five pieces, with White to move, is a draw. It is an exception to a clever, but faulty, schema developed by the famous endgame composer Alexey Troitsky (1866-1942). Botvinnik relied on the schema to reach his erroneous conclusion that the 1941 game Smyslov - Lilienthal was a win for Black.

White to Move

Looking at the diagram, I started to wonder how sensitive the result was to the position of the Knight on c2, the only piece that has real freedom of movement. The Knight on h7 is tied down to blockading the Pawn until the critical moment and the Black King must stay near the White King to restrict its space.

Keeping the position of the other pieces fixed, always with White to move, I shifted the Nc2 to its available squares and recorded the results. A square marked 'D' means the position where the Knight starts on that square is a draw. For example, placing the Knight on h4 is an obvious draw, because White plays Kxh4. A square marked 'S' indicates an immediate stalemate, with no further play possible.

The squares marked with a number show the number of moves required to win when the Knight starts on that square. For example, shifting the Knight from c2 to g5 allows Black to win in eight moves: 1.Kh4 Kf4 2.Kh5 Kg3 3.Kg6 Kg4 4.Kg7 Kf5 5.Kh8 Kf6 6.Kg8 Kg6 7.Kh8 Nf6 8.h7 Nf7 mate.

The longest win, with the Knight starting on e3, takes 54 moves. It goes like this: 1.Kh4 Kf4 2.Kh5 Nd5 3.Kg6 Ndf6 4.Kf7 Kf5 5.Ke7 Ke5 6.Kd8 Kd6 7.Kc8 Kc6 8.Kd8 Nd7 9.Kc8 Ndf8 10.Kb8 Ne6 11.Kc8 Kc5 12.Kb7 Kb5 13.Ka8 Ka6 14.Kb8 Kb6 15.Kc8 Kc6 16.Kb8 Nc5 17.Ka7 Kc7 18.Ka8 Kb6 19.Kb8 Nd7+ 20.Kc8 Kc6 21.Kd8 Nb6 22.Ke8 Kd5 23.Ke7 Ke5 24.Ke8 Ke6 25.Kd8 Kd6 26.Ke8 Nc8 27.Kd8 Na7 28.Ke8 Nc6 29.Kf7 Kd7 30.Kg7 Ke7 31.Kg6 Ke6 32.Kh5 Kf5 33.Kh4 Kf4 34.Kh3 Kf3 35.Kh2 Kf2 36.Kh3 Ne5 37.Kh4 Kg2 38.Kh5 Kf3 39.Kh4 Nf7 40.Kh3 Nfg5+ 41.Kh2 Kf2 42.Kh1 Ne6 43.Kh2 Nf4 44.Kh1 Kg3 45.Kg1 Ng2 46.Kf1 Kf3 47.Kg1 Ne3 48.Kh2 Kg4 49.Kg1 Kg3 50.Kh1 Kf2 51.Kh2 Ng5 52.Kh1 Ng4 53.h7 Ne4 54.h8=Q Ng3 mate. This variation shows best play for both sides, although there are branches of equal value at many points.

There are several mechanisms at work in the different solutions. Together they show how the simplest chess positions can illustrate attractive geometric patterns. • Reference: Shredder 6 piece tablebase.


Note: For the record, I submitted this to Chess Blog Carnival II, but it wasn't used.

Later: After Jack Le Moine explained that my submission had been lost, not rejected, I tried again. Second time lucky: November Carnival of Chess Blogs.

24 September 2007

Tablebase 1 - Botvinnik 0

The diagram and text on the left is from Botvinnik's 'Soviet Chess Championship, 1941' (p.154). It shows the position after 84.Kf2-f1 in Smyslov - Lilienthal, from rd.16 of the event played in March-April 1941.

Note the concluding sentence: 'The given position is won, since the White King cannot get into the draw area.' Botvinnik continued, 'Lilienthal did not have a very easy task when studying Troitsky's analyses. However, that is no excuse for his further weak play. In general, this endgame is a rare occurrence in practical play. However, if my memory does not betray me, Lilienthal had encountered this very endgame (irony of fate!) twice previously, and on neither occasion could he discover the way to victory.'

In fact, a five piece endgame tablebase shows that the position after Smyslov's 84.Kf1 is a draw. Botvinnik gave 84...Nc2 85.Kg2 Ke3 86.Kg3, with analysis through move 97 to show how Black wins. The problem is that White has the paradoxical 86.Kh3, moving to the side of the board. This draws after 86...Kf3 (86...Ne1 87.Kg3) 87.Kh4 Kf4 88.Kh5 Kf5 89.Kh4, when Black can't make progress.

Lilienthal tried instead 84...Ne6. After 85.Kf2 Neg5 86.Kg3 Ke3 87.Kg4 Ke4 88.Kg3 Nf3, Smyslov continued to play perfectly and held his well earned theoretical draw. After Black's 96th move, Botvinnik wrote that it 'also should not have led to a draw', but he was wrong there as well.

I don't have access to Troitsky's original analysis, so I'm not sure what he overlooked. In the variation given above, after 86.Kh3 through 88...Kf5, I tried the Knight on squares other than c2 and found several other positions where White draws even though the King is outside the 'black line'. Troitsky's analysis was not correct and Botvinnik was wrong to condemn Lilienthal for 'weak play'.

22 September 2007

Petrosian's Exchange Sacrifice

In The Exchange Sacrifice, I quoted Petrosian on the psychological difficulty of sacrificing a Rook for a minor piece. The source of that quote, a chapter titled 'The Positional Exchange Sacrifice' in Petrosian's Legacy, offers seven examples illustrating the theme from Petrosian's own games:-

1953 Switzerland, Reshevsky - Petrosian
1962 Varna, Petrosian - Gligoric
1972 San Antonio, Portisch - Petrosian
1958 Riga, Tal - Petrosian
1946 Leningrad, Dunaev - Petrosian
1953 Bucharest, Troianescu - Petrosian
1971 Moscow, Parma - Petrosian

Kasparov used several of the same key positions in the Petrosian chapter of Predecessors III. These games will be the basis for my next analytical series.

20 September 2007

Vacation Reentry

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