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At the halfway point in the eight-game "Brains in Bahrain" match, Vladimir Kramnik is leading 3 to 1, having won two games and drawn two. To turn the match around, his opponent, the German computer Deep Fritz, must win three of the last four games — a daunting but not impossible challenge. Kramnik has played well, but the wildcard is his stamina. "The world champion suffers from a debilitating disease," said Frederic Friedel, founder of ChessBase, the maker of Fritz. "He gets tired, depressed, and discouraged. Deep Fritz has nerves of steel."

What follows is a blow by blow description of the games so far.

Game 1, October 4
Berlin Wall

Lucena, the fifteenth-century chess theoretician, would be happy. His advice to distract the opponent with blinding light was unwittingly followed in Bahrain. According to match director Malcolm Pein, on Oct. 3, the day before the first game, world-champion Kramnik asked to examine the pieces. To the surprise of the match organizers, he pronounced them unacceptable because he said they were too shiny and reflected the stage lights. He left the playing area, and the organizers were dismayed, worried that he might refuse to play. "First we got some sandpaper," noted Pein, "but this ruined the pieces." They then bought some dark varnish and hastily painted the pieces to try to reduce the glare. But the next day, the pieces were too sticky to touch. "We faced the prospect of Kramnik picking up his king’s pawn and being unable to let go," said Pein. "Frankly I was panicking and I was not alone." Just before the game, someone had the clever idea of placing the pieces in the refrigerator to hasten the drying. Kramnik then found them to be acceptable. Deep Fritz, of course, was oblivious to all the fuss.

In the first game, Fritz was White, which meant that it had the advantage of moving first. The game ended in a draw in a disappointingly short two and half hours, after only 28 moves. But what the game lacked in longevity, it made up for in intrigue. In reply to Fritz's "Ruy Lopez," a sequence of opening moves favored by Garry Kasparov and Bobby Fischer, Kramnik adopted a defense known as the Berlin Wall, appropriate for a match against a German computer. The queens were swapped early, depriving Fritz of the chance to guide the game into the kind of tactical free-for-all in which computers thrive. For the first half of the game, Fritz strangely repeated the moves of a game that Kasparov had once played against Kramnik when the older K was dethroned as world champion. Everyone expected the computer to have prepared a stunning improvement on Kasparov's play — otherwise, why would it repeat the moves that had gotten him nowhere? — but it didn't unleash a stronger move. After they swapped all pieces except for the dark-squared bishops and seven pawns apiece, the game came down to an endgame in which the computer had a slight advantage and could have taxed Kramnik's defensive skills. But instead Fritz threw away its advantage with a lemon of a move, and Kramnik easily equalized into a sterile position where the pawns were locked, stopping progress by either side. They promptly agreed on a draw. After making such a horrible a move, "a human would brood about it, and probably suffer for the rest of the match," Russian grand master Peter Svidler said. "The computer, however, feels no shame."

Deep Fritz- Kramnik
Game 1
1.e4 e5 2.Nf3 Nc6 3.Bb5 Nf6 4.0-0 Nxe4 5.d4 Nd6 6.Bxc6 dxc6 7.dxe5 Nf5 8.Qxd8+ Kxd8 9.Nc3 h6 10.b3 Ke8 11.Bb2 Be7 12.Rad1 a5 13.a4 h5 14.Ne2 Be6 15.c4 Rd8 16.h3 b6 17.Nfd4 Nxd4 18.Nxd4 c5 19.Nxe6 fxe6 20.Rxd8+ Kxd8 21.Bc1 Kc8 22.Rd1 Rd8 23.Rxd8+ Kxd8 24.g4 g6 25.h4 hxg4 26.Bg5 Bxg5 27.hxg5 Ke8 28.Kg2 _-_

Game 2, October 6
Swapping the Ladies

Kramnik drew first blood in the second game. The computer played the Queen's Gambit Accepted, a good choice because it leads to wide-open, street-brawling positions in which machines excel. But the twenty-seven-year-old human managed to swap queens early, on the seventh and eighth moves, just as he had in Game 1. By eliminating the strongest piece in the game, Kramnik reduced the chance that he would make a miscalculation and steered the game toward the ending, which requires long-term positional jockeying, at which humans still outperform machines. On the twelfth move, Fritz made an incredible blunder, the passive retreat of its dark-squared bishop to its home square. This is a move even third-rate human players would avoid. But the computer had its peculiar reasons. It apparently evaluated the position as precisely even, so it planned to shuffle its bishop back and forth. It figured that Kramnik would also regard the position as even and shuffle one of his own pieces, a knight, back and forth. Then they'd agree to a draw. But that was a near-fatal misjudgment: Kramnik just pushed forward, taking advantage of the wasted bishop retreat. After a series of exchanges, each side was down to a single rook and six pawns. Kramnik's rook was more actively placed and the computer made the classic endgame mistake of passively positioning his rook to defend a pawn rather than jettisoning the lowly foot soldier and activating the rook so that it could penetrate into Kramnik's side of the board. After 57 moves and more than six hours of play, Fritz resigned rather than wait for Kramnik to march one of his pawns to the eighth rank, where it could be promoted into a queen. Kramnik and his large entourage — a masseuse, a kickboxing bodyguard, assorted computer and chess experts — went off to celebrate.

Kramnik - Deep Fritz
Game 2 1.d4 d5 2.c4 dxc4 3.Nf3 Nf6 4.e3 e6 5.Bxc4 c5 6.0-0 a6 7.dxc5 Qxd1 8.Rxd1 Bxc5 9.Kf1 b5 10.Be2 Bb7 11.Nbd2 Nbd7 12.Nb3 Bf8 13.a4 b4 14.Nfd2 Bd5 15.f3 Bd6 16.g3 e5 17.e4 Be6 18.Nc4 Bc7 19.Be3 a5 20.Nc5 Nxc5 21.Bxc5 Nd7 22.Nd6+ Kf8 23.Bf2 Bxd6 24.Rxd6 Ke7 25.Rad1 Rhc8 26.Bb5 Nc5 27.Bc6 Bc4+ 28.Ke1 Nd3+ 29.R1xd3 Bxd3 30.Bc5 Bc4 31.Rd4+ Kf6 32.Rxc4 Rxc6 33.Be7+ Kxe7 34.Rxc6 Kd7 35.Rc5 f6 36.Kd2 Kd6 37.Rd5+ Kc6 38.Kd3 g6 39.Kc4 g5 40.h3 h6 41.h4 gxh4 42.gxh4 Ra7 43.h5 Ra8 44.Rc5+ Kb6 45.Rb5+ Kc6 46.Rd5 Kc7 47.Kb5 b3 48.Rd3 Ra7 49.Rxb3 Rb7+ 50.Kc4 Ra7 51.Rb5 Ra8 52.Kd5 Ra6 53.Rc5+ Kd7 54.b3 Rd6+ 55.Kc4 Rd4+ 56.Kc3 Rd1 57.Rd5+ 1-0

Game 3, October 8
Scotching the Scotch

Fritz had White again. To avoid Kramnik's "Berlin Wall," which had served the champion well in Game 1, the computer played the Scotch opening. White blasts open the center to secure free and easy development. For the third time in a row, Kramnik contrived to swap queens early, but the exchange left him with a slightly inferior position because his pawn structure was fractured. His weak pawns, however, could not be immediately exploited but required subtle long-term maneuvering that he thought would be beyond the machine's capability. He was right. The machine frittered away its advantage and entered a losing endgame. Fritz's programmers were dismayed when they watched the machine's once-comfortable position "spoil like date pudding in the Bahraini sun. The problem," they said, "was that like the eunuch who walked into the harem Fritz had no idea what to do when he got there." At the post-game press conference, Kramnik said he was pleased with how he had ground Fritz down. “If the computer is to win, it has to be through tactics," he said. "In this game, the computer could not grasp many of my ideas because they were too abstract.”

Deep Fritz - Kramnik
Game 3
1.e4 e5 2.Nf3 Nc6 3.d4 exd4 4.Nxd4 Bc5 5.Nxc6 Qf6 6.Qd2 dxc6 7.Nc3 Ne7 8.Qf4 Be6 9.Qxf6 gxf6 10.Na4 Bb4+ 11.c3 Bd6 12.Be3 b6 13.f4 0-0-0 14.Kf2 c5 15.c4 Nc6 16.Nc3 f5 17.e5 Bf8 18.b3 Nb4 19.a3 Nc2 20.Rc1 Nxe3 21.Kxe3 Bg7 22.Nd5 c6 23.Nf6 Bxf6 24.exf6 Rhe8 25.Kf3 Rd2 26.h3 Bd7 27.g3 Re6 28.Rb1 Rxf6 29.Be2 Re6 30.Rhe1 Kc7 31.Bf1 b5 32.Rec1 Kb6 33.b4 cxb4 34.axb4 Re4 35.Rd1 Rxd1 36.Rxd1 Be6 37.Bd3 Rd4 38.Be2 Rxd1 39.c5+ Kb7 40.Bxd1 a5 41.bxa5 Ka6 42.Ke3 Kxa5 43.Kd4 b4 44.g4 fxg4 45.hxg4 b3 46.Kc3 Ka4 47.Kb2 f6 48.Bf3 Kb5 49.g5 f5 50.Kc3 Kxc5 0-1

Game 4, October
10 Surviving the Crash

The fourth game, a Tarrasch Defense, was drawn after forty-one moves. Eight moves earlier the computer had crashed. The programmers panicked but were able to restart Fritz fifteen minutes later. The machine still had sufficient time on its clock — each side had two hours to make forty moves — to finish the game. When Fritz resumed play, it was running on only one processor, instead of the usual eight, and yet for the first time in the match it did not botch the endgame. The Fritz team was also encouraged by Kramnik's seemingly indecisive and wobbly play. He took more than thirty minutes on his twenty-second move and the grand masters watching were not sure that even after his deep think he had made the best move.

Kramnik - Deep Fritz
Game 4
1. d4 d5 2. c4 e6 3. Nf3 c5 4. cxd5 exd5 5. g3 Nc6 6. Bg2 Nf6 7. O-O Be7 8. Nc3 O-O 9. Bg5 cxd4 10. Nxd4 h6 11. Bf4 Bg4 12. h3 Be6 13. Rc1 Re8 14. Nxe6 fxe6 15. e4 d4 16. e5 dxc3 17. exf6 Bxf6 18. bxc3 Qxd1 19. Rfxd1 Rad8 20. Be3 Rxd1+ 21. Rxd1 Bxc3 22. Rd7 Rb8 23. Bxc6 bxc6 24. Rxa7 Rb2 25. Ra6 Bd2 26. Rxc6 Bxe3 27. fxe3 Kf7 28. a4 Ra2 29. Rc4 Kf6 30. Kf1 g5 31. h4 h5 32. hxg5+ Kxg5 33. Ke1 e5 34. Kf1 Kf5 35. Rh4 Kg6 36. Re4 Kf5 37. Rh4 Kg5 38. Kg1 Kg6 39. g4 hxg4 40.Rxg4+ Kf5 41. Rc4 _-_

• Paul Hoffman
• Paul Hoffman on the Man vs. Machine chess match between Vladimir Kramnik and the German computer Deep Fritz