15.exd5 cxd4 This was Fritz's last move from its opening book and it now began to "think" on its own. Kramnik would also go into a deep think after his next move. 16.Bb4 Re8 Again keeping pieces on, instead of ..Be7. There are many tactical chances here for both sides, just what the Fritz team was aiming for. Way back in 1978 the great Tony Miles played ..Be7 and went on to win. 17.Ne4 exd5 18.Nd6 dxc4 Fritz had been expecting this position and was prepared to give up a rook for a knight. Black would have good compensation thanks to the protected passed d-pawn.

19.Nxf7?! After 42 minutes Kramnik comes up with this shocker. We had briefly looked at this but couldn't believe that anyone would ever dare to play such a sharp and aggressive move against Deep Fritz! Kramnik said afterwards that he understood the risks but just couldn't resist the beauty of the sacrifice. Objectively Bd5 was a better move, but we must thank Kramnik for his courage as it led to a thrilling battle. 19...Kxf7 20.Bd5+ Kg6 White is down a piece but black's king is under heavy fire. Long-range tactics of this sort are often a weak spot for computer programs. If they don't see a mate they are happy to be ahead in material. They don't mind having their kings under seige just because it looks horrible to us! But Fritz has it all worked out and as we'll see it was the world champion who had missed a reply as stunning as his original sacrifice. 21.Qg4+ Bg5 22.Be4+ Rxe4 Black is forced to do this to avoid a repetition of position draw. 23.Qxe4+ Kh6 24.h4 Bf6 25.Bd2+ g5 26.hxg5+ Bxg5 Fritz spent a long time on this move and meanwhile Kramnik discovered that his original idea did not work.

27.Qh4+ A critical moment. When Kramnik played 19.Nxf7 he thought that White would be completely winning after Qe6+ here. With little time remaining he changed plans, but analysis shows Qe6+ was still the best chance. [ 27.Qe6+ Nf6 28.f4 ( 28.Qh3+ Nh5 ( 28...Kg6 Kramnik pointed out this move in the post-mortem. White gets back the piece but his position is losing thanks to Black's powerful pair of passed pawns. 29.f4 Bh6 30.f5+ Kf7 31.Bxh6 c3) 29.f4) 28...Bh4!! The move Kramnik failed to foresee and you really cannot blame him. Black gives up the bishop to open the g-file for a queen check! Incredible, but in such complex positions such possibilities are bound to exist. 29.gxh4 Qg8+ 30.Qxg8 Rxg8+ 31.Kh2 Ng4+ 32.Kg3 Ne3+ 33.Kf3 Nxf1 34.Rxf1 c3 35.Rf2 cxd2

27...Kg6 28.Qe4+ Kg7 The black king makes good its escape and Black keeps an extra piece. But White is still fighting here; the rooks can be dangerous. 29.Bxg5 Qxg5 30.Rfe1 cxb3 31.Qxd4+ Nf6 32.a5 Qd5?! Fritz is eager to swap queens, having seen that it's b-pawn will soon ascend to the throne. But even with a queen the endgame that now arises is not at all easy. With that in mind, perhaps ..Qc5 is indicated. 33.Qxd5 Nxd5 34.axb6 axb6 0-1

Kramnik resigned, seeing that Fritz gets a new queen if he takes the proffered bishop on a6. But in what may turn out to be the most shocking thing of all about this amazing game, this final position is very close to being a draw!! Black will have a queen, knight, and passed b-pawn versus two rooks. But the black king is without shelter and the white rooks run amok.

Also important is that if there is a win for Black it requires very deep planning that does not seem possible for a program, at least from what we've seen so far. So it is a very real possibility that Kramnik resigned in a position he could have drawn. With this he follows in the footsteps of the man he succeeded in the throne, Garry Kasparov. In the second game of his rematch against Deep Blue in 1997, Kasparov resigned in a hopeless position only to later be told that with best play he could have drawn the game. It will certainly be a shock to Kramnik if that turns out to be the case here as well.

34...axb6 35.Rxa6 b2 36.Ra7+ Kg6 This leads to a position in which Black has a queen, knight, and passed b-pawn versus two white rooks. An easy win, right? Kramnik and Fritz thought so. But Fritz's evaluation was "only" +3.3, an advantage of three pawns. If it had seen a clear win it would have been much higher. (36...Kf8 This move allows white to give up a rook for both black b-pawns. There might be some way to win the resulting position for Black, but it is very obscure. Without any pawns the ending is completely drawn, and the black h-pawn is not impressive. Remarkably, however, this is probably the best winning try for Black!. 37.Rd7 Nc3 ( 37...Rc1 transposes to main line) 38.Rd2 ( 38.Rb7?! Winning the h-pawn instead of the dangerous passed b-pawn is unnecessarily risky. 38...Rc6 39.Kg2 b1Q 40.Rxb1 Nxb1 41.Rxh7) 38...b1Q 39.Rxb1 Nxb1 40.Rb2 Nc3 41.Rxb6 Black has winning chances but this is very hard to win. GM Danny King: "Don't dismiss this as a draw just yet. I've won this position and there are many tricks. Maybe it should be drawn, but it's the best chance from the final position.)

37.Rd7 Rc1 38.Rd6+! This is the key move to the entire concept. White forces the black knight to shield the king, otherwise it's a perpectual check draw. This would have been quite hard to find, particularly with just a few minutes on the clock. 38...Nf6 ( 38...Kf7 39.Rd7+ Kf8 40.Rd8+ Kf7 41.Rd7+ Kf6 42.Rd6+ Kg7 43.Rd7+ Kg6) 39.Rdd1 b1Q Other moves draw easily. ( 39...Rc2 40.Kg2 Ng4 41.Kf3 h5 42.Re2) 40.Rxc1

The previous moves were forced after ..Kg6 and this is the position Fritz and Kramnik were expecting. Until we ask him we can't be sure Kramnik bothered to look this far ahead, or if he saw the difficult idea of Rd7-d6+. He may just have believed Fritz, the way Kasparov believed Deep Blue. "The computer wouldn't play this unless it were winning," is the way it goes. As GM Danny King said, "Kramnik wouldn't resign that position against me!" Fritz and Kramnik assumed Black would win easily with such a large material advantage. However, the black king can only be sheltered from checks by the knight, and without the knight's help the b-pawn cannot be advanced. The rooks can attack the knight or the b-pawn, preventing progress by either. Various defensive postures such as placing the rooks on b5 and b4 and just shuffling the king prove impenetrable to Fritz. (And to everyone else so far!)

Also, if given the chance White can give up a rook for the black knight and b-pawn and then the queen versus rook endgame is completely drawn. The variations below are by no means exhaustive, but they give you an idea of how hard it is for Black to make any progress.

40...Qf5 This logical move is refuted directly by 41.Rc6. (40...Qb4 41.Rb1 Qc5 42.Rec1 Qd6 43.Rd1 Qc6 44.Rdc1 Qb7 Another key position. White can harass the black queen until it is behind the pawn. Now white can double rooks on the b-pawn, moving them to attack the black knight when necessary. Black never has time to advance the b-pawn. White is always looking for a chance to sacrifice a rook for the black knight and b-pawn, again creating the fortress draw. Finally, if Black protects the pawn with the king and queen to activate his knight, white can give up both rooks for a drawn endgame of knight+h-pawn vs the two white pawns. Black also risks losing the h-pawn if the king strays too far away. Lots of theory up there, and analysis is backing it up so far.

45.Rb5 Kf7 ( 45...Nd7 46.Rd1 One of the main defensive concepts. White threatens to simply capture the knight and then the b-pawn with a crystal clear fortress draw.( 46.Rcb1 Pressurizing the b-pawn is another tough nut for Black to crack. 46...Qc6 47.R5b3 h5 48.Rb4 Kf6) ) 46.Rcb1 Nd7 47.Rd1 Ke7 Or else Rxd7 draws. 48.Re1+ Kd6 49.Rd1+ Kc6 50.Rdb1 Qa6 51.R5b4 Qe2 52.R1b2 Qd3 53.Kg2 Qd5+ 54.Kg1 b5 55.Rxb5 Qxb5 56.Rxb5 Kxb5 Yet another key position. The drawing concept is to put the white pawns on f4 and g4. If the black king pushes in from the side, the white king runs up the h-file after the black pawn. We don't have our Averbakh collection in Bahrain, but it looks like White holds the draw here. A sample line: 57.Kg2 Kc4 58.Kf3 Kd5 59.Kg4 Ke6 60.Kg5 Kf7 61.Kh6 Kg8 62.g4 Ne5 63.Kg5 Kg7 64.f4 White has to be very precise to avoid zugzwang positions. Pushing either pawn would allow the black king to penetrate. Because the white king has the h-file available Black can't force him away from the pawns.) 41.Rc6 b5 ( 41...Kh5 42.Rxb6) 42.Ree6 b4 ( 42...Kf7 43.Rxf6+ Qxf6 44.Rxf6+ Kxf6 45.Kf1 And the pawn endgame is drawn.)

Back to the main line: 43.Rb6 Kf7 44.Rxf6+ Qxf6 45.Rxb4= Fritz and other programs are convinced they are winning here, but the position is a dead draw. Black has no way through the fortress. We give this as the main line not because it is the best winning try for Black (which is 36...Kf8 according to GM King), but because it is the line that Fritz would have played had Kramnik found the best defense.