Let's start from scratch and see who is the best player in the world. After all, it's a new year, not to mention a new century or millennium. The traditional tournament in the Dutch sea town of Wijk aan Zee is a good place to begin. Last year, Garry Kasparov played there for the first time and won brilliantly ahead of India's Vishy Anand. This year, Kasparov is in the lead again after seven rounds, but sharing it with Russia's Vladimir Kramnik, both scoring 5 points. They are closely followed by Anand and the Hungarian Peter Leko with 4.5 points.

Kasparov had a few lucky bounces, but his wins are fun to watch. Loek Van Wely made an unfortunate choice, engaging himself in a typical Sicilian slugfest with Kasparov, who simply outnumbered, outcalculated and outplayed the Dutch grandmaster.

Kasparov-Van Wely

1.e4 c5 2.Nf3 d6 3.d4 cxd4 4.Nxd4 Nf6 5.Nc3 a6 6.Be3 e6 7.f3 (After players began to bother Kasparov with the English attack against his Najdorf Sicilian he became a quick study, ready to face it with either color.) 7...b5 8.g4 h6 9.Qd2 Nbd7 10.0-0-0 Bb7 11.h4 b4 12.Na4!? d5 (More popular is 12...Qa5.) 13.Bh3 g5?! 14.Bg2 gxh4? (Kasparov marks this move as a decisive mistake, suggesting 14...Rg8 instead.) 15.Rxh4! dxe4 (Changing his mind after realizing that 15...Nxe4?! would allow a powerful exchange sacrifice 16.fxe4! Qxh4 17.exd5 with a strong attack after either 17...e5 18.Ne6 Rc8 19.Nxf8 Rxf8 20.Qxb4; or 17...exd5 18.Bxd5 Bxd5 19.Nf5 Qf6 [On 19...Qxg4 20.Qxd5 Rd8 21.Rd4 wins.] 20.Qxd5 Rd8 21.Bd4 winning.) 16.g5 Nd5 (After 16...exf3 17.Nxf3 Nd5 18.Bd4 Rh7 19.Qd3 the black rook is in trouble.)

17.Rxe4 (The rook joins the attack and a knight sacrifice on e6 is in the air.) 17...hxg5 (It is too late for 17...Qa5, since 18.Nxe6! fxe6 19.Rxe6+ Kf7 20.Qd3!! leaves the black king in an awkward position and after 20...Kxe6 21.Qe4+ Kasparov would close the game either after 21...Ne5 22.Bh3+ Kd6 23.Bc5+; or after 21...Kf7 22.g6+ Kg7 23.Qe6, threatening decisively 24.Qf7+.) 18.Bxg5 Qa5? (The only way to continue was 18...Qxg5 19.Qxg5 Bh6 20.Nxe6 Bxg5+ 21.Nxg5+ Kf8 22.Bh3 still, with advantage for white.) 19.f4 Rh2 (The pin is tempting. Black loses outright after 19...Qxa4 20.Nxe6 fxe6 21.Rxe6+ Kf7 22.Bxd5 Bxd5 23.Qxd5 winning. But two other moves require Kasparov's genius to break down black's position. After 19...e5!? 20.Nb3 Qxa4 21.Rxe5+!! Nxe5 22.Bxd5 wins. And after 19...N7f6 20.Bxf6 Nxf621.Nxe6 Bxe4 22.Bxe4 Rc8 23.Nxf8 Qxa4 24.Qd6! black is in dire straits.) 20.Nxe6! fxe6 21.Rxe6+ Kf7 22.Qd3!! (A quiet culmination of white's attack-trademark Kasparov.) 22...Bg7 (After 22...Kxe6 23.Bxd5+ Bxd5 24.Qg6+ Nf6 25.Qxf6+ Kd7 26.Rxd5+ Qxd5 27.Nb6+ Kc7 28.Nxd5+ white wins.) 23.Qf5+ (Other way was 23.Bxd5 Bxd5 24.Re7+ Kg8 25.Qg6.) 23...Kg8 24.Rxd5 Qxa4 25.Re7 Black resigned.

Vladimir Kramnik has not lost a game in a long time, but he does not play for draws. His opponents are usually under a great positional pressure, but Kramnik can call on tactics when he needs to as in this game with Nigel Short.

Kramnik-Short

1.Nf3 d5 2.d4 Nf6 3.c4 e6 4.Nc3 Be7 5.Bf4 0-0 6.e3 c5 7.dxc5 Bxc5 8.cxd5 Nxd5 9.Nxd5 exd5 10.a3 Nc6 11.Bd3 Be7 (The usual way to cope with the threat 12.Bxh7+ Kxh7 13.Qc2+ is to retreat the bishop to b6.) 12.0-0 Bf6 13.Qb3 Qb6?! (Miscalculating white's chances on the kingside.) 14.Qxd5 Rd8 15.Qe4 g6 16.Bg5! (Taking care of the unpleasant 16...Bf5 and challenging the only defender of the black king.) 16...Qxb2 (After 16...Bf5? 17.Qh4 white wins, e.g. 17...Bxd3 18.Bxf6 Bxf1 19.Qh6 mating or 17...Bxg5 18.Nxg5 Rxd3 19.Qxh7+ Kf8 20.Qxf7 mate.) 17.Bc4 (Looking at the weak pawn f7.) 17...Kg7 18.Qh4 h5 (Another weakening, but white was ready to chase the black queen from the long diagonal.)

19.Bxf7! (A nasty surprise, winning a pawn.) 19...Bxg5 (After 19...Kxf7 20.Rab1 Qc3 21.Rfc1 the long diagonal suddenly becomes too short for the queen and black is forced to surrender his bishop on f6.) 20.Nxg5 Qf6 21.e4! (Creating an outpost on the square d5 for his bishop, e.g. 21...Ne5 22.Bd5.) 21...Rd4 22.Rae1 Bd7 23.f4 (Concentrating all his forces against the black king.) 23...Rf8 24.Ba2 Qd6 25.Kh1 Qxa3 (Short won a pawn back, but within a few moves the white pieces encircle the black king.) 26.Bb1 Qe7 27.Qg3! (Kramnik frees the square h4 for his knight. The queen has been x-rayed along the 4th rank and 27.e5?! would run into 27...Nxe5!? e.g. 28.Qg3 Qf6 and black pinning game may survive white's attack, e.g. 29.fxe5?? Qxf1+ or 29.Ne4 Qa6.) 27...Kh6 28.Nf3 Rb4 29.Nh4 Be8 30.e5 Rxb1 (After 30...Rg8 31.Nf5+! gxf5 32.Qxg8 wins. And after 30...Qg7 31.Qg5+ Kh7 32.Nxg6 Bxg6 33.Qxh5+ Kg8 34.Bxg6 Rbxf4 35.Rxf4 Rxf4 36.Be4 white is on the way to win.) 31.Rxb1 Nd4? (In time trouble Short speeds up the end. After 31...b6 white wins in a long run anyway.) 32.Qg5+ (After 32...Qxg5 33.fxg5+ Kg7 34.Rxb7+ Rf7 35.Rfxf7+ Bxf7 36.Nf3 Ne6 37.Rxa7 wins.) Black resigned.