The long-reigning world champion Mikhail Botvinnik once memorably described chess as a combination of sport, art, and science. In examining the playing styles of the world’s top grandmasters, we can see elements of each of these three components. Usually, in a given player, one element predominates. Vladimir Kramnik and Peter Leko, who faced each other in the 2004 match for the world championship, both have a decidedly scientific approach to the game. It was demonstrated again most recently in their eight-round rapid-game match in the Hungarian city of Mishkolc. In this round, the struggle was fought over a deeply analyzed opening variation. Mr. Kramnik won the game and the match by a score of 4. 5 to 3.5.

KRAMNIK VS. LEKO (white) (black) Catalan

1.d4 Nf6 2.c4 e6 3. Nf3 b6 4.g3 Ba6 5.b3 Bb4+ 6. Bd2 Be7 7. Bg2 c6 8. Bc3 d5 9. Ne5 Nfd7 10. Nxd7 Nxd7 11. Nd2 0-0 12.0-0 Rc8 13.e4 c5 14. exd5 exd5 15. dxc5 dxc4 16.c6!? This variation has been exhaustively examined at the highest levels. Leko as black defended against it in 2006 and after 16. cxb6 Nxb6 17. Re1 against Radjabov, black was worse after 17…Bf6 18. Bxf6 Qxf6 19. Ne4 Qg6 20. Qd6 Qxd6 21. Nxd6 Rcd8 22. Nf5 , but Leko proved that black can still draw here. 16… cxb3 17. Re1 b2!? This is a more popular method of defense than 17…Bb5 which in 1996 gave Kamsky an advantage over Karpov: 18. axb3 Bxc6 19. Bxc6 Rxc6 20. Rxa7 Bf6 21. Nc4 Bxc3 22. Rxd7 Qf6 23. Re4 with eventual victory. 18. Bxb2 Nc5

(See Diagram)

19. Nc4 Bxc4 20. Qg4 Bg5 21. Qxc4 Nd3 22. Be5 Topalov vs. Anand 2005 entered a position without the exchange: 22. Ba3 Nxe1 23. Rxe1 Re8 24. Rxe8+ Qxe8 25. Bd5 and white obtained strong pressure. But practice proved that the move played in this game is even stronger . 22… Nxe1 23. Rxe1 Bf6 24. Bxf6 Qxf6 25.c7 Qd6 26. Rc1 b5 27. Qc2 b4 At the tournament in Monte-Carlo, Levon Aronian defended this position twice. Against Radjabov he tried 27…g6 28. Bb7 a5?! 29. Qc5! Qxc5 30. Rxc5 b4 31. Kf1 Rfe8 32. Bxc8 Rxc8 33. Ke2 a4 34. Kd3 b3 and lost the endgame after 35.a3! In this game, Leko tried the move which allowed Aronian to reach a draw against Ivanchuk. But it appears that this position is also not particularly safe for black. 28. Bb7 g6 29.h4 Rfe8?! Now Leko deviates from the previously mentioned Ivanchuk-Aronian, which had proceeded 29… h5 30. Kf1 a5 31. Qc5 Qxc5 32. Rxc5 a4 33. Ke2 b3 34. axb3 axb3 35. Kd3 Rfe8 36. Kc3 Kf8 37. Kxb3 (Here white missed victory by 37. Ba6! and the black king can not leave the corner: 37… 37…Ke7 38. Re5+ Kd7 39. Bb5+) 37…Ke7 38. Kc4 Kd6 and black achieved a draw. A final attempt to rehabilitate this variation might be connected with the immediate 29…a5!? but after 30.h5! white can add threats on the king side, especially if the white h-pawn will reach the h6 square. 30. Qa4! Qd2 The only move not to lose material immediately. 31. Qc6 a5 32. Bxc8 Rxc8 33. Kg2! Kg7 Both sides hide their kings from the last ranks to avoid sudden checks. For example in the case of 33…a4? 34. Rc2 Qd3 35. Qb7 Qd7 36. Qxb4 white wins the rook by checking on b8. 34. Rc2 Qd3 Now black loses the pawn and white’s task becomes technical. Black could keep material balance playing 34…Qe1!? 35. Qb7 Qe6 36. Rc5 Qd7 but after 37.h5! he hardly could endure pressure on both sides of the board. 35. Rc5! a4 36. Qxa4 Qe4+ 37. Kh2 Qd4 38. Qc2 h5 39. Kg2 Qd6 40. Qb2+ f6 This weakens the black kingside, buy Leko didn’t have anything better. For example, he would lose his queen after 40…Kh7 41. Qxb4 Rxc7 42. Rxh5+ 41. Qc2 Kf7 42. Qc4+ Kg7 43. Rc6 Qd7 44. Qc5 Kf7 45. Kh2 Immediately winning was 45. Rd6 Qxc7 46. Qd5+ Kf8 47. Rxf6+ Kg7 48. Qe6. The move actually played did not delay matters for long. 45… Kg7 46. Qb6 Qf5 47. Qd4 Kf7 48. Rxf6+ Qxf6 49. Qd7+ 1-0