Some comments given by Mig during the live broadcast at Playchess.com are included.
1.e4 c5 2.Nf3 d6 3.d4 cxd4 4.Nxd4 Nf6 5.Nc3 a6 6.f3 e6 7.Be3 Nc6 8.Qd2 Be7 9.0-0-0 0-0 10.g4 Nxd4 11.Bxd4 b5 12.g5 Nd7 13.h4 Qc7 14.Kb1 b4 [ 14...Bb7 15.g6 fxg6 16.h5 Ne5 17.Bxe5 dxe5 18.Qd7 Bd8 19.Qxe6+ Qf7 20.Bh3 Bc8 21.Qxf7+ Kxf7 22.hxg6+ hxg6 23.Bxc8 Rxc8 24.Rd7+ Kg8 25.Rh3 Rc6 26.Nd5 g5 27.c3 g4 28.Rg3 Rh6 29.Rxg4 g6 30.Kc2 Kh8 31.Rd6 Kh7 32.Rd7+ Kh8 33.Kb3 a5 34.a4 b4 35.Kc4 bxc3 36.bxc3 g5 37.Rg3 Rh1 38.Kb5 Rg8 39.c4 Rb1+ 40.Kc6 Rg6+ 41.Rd6 Kg7 42.c5 Rc1 43.Rxg6+ Kxg6 44.Kd7 Rxc5 45.Kxd8 Rc4 46.Nb6 Rb4 1-0 Cioara,A-Efimov,I/Porto San Giorgio 2002/CBM 89 ext (46). ]
15.Na4 Bb7 16.b3 Bc6 17.Nb2 a5 18.h5 Ne5 19.Be2 a4 20.Nc4 Bb5 21.Nb6 Rab8 22.h6 Bxe2 23.Qxe2 g6 24.f4 Nc6 25.Nxa4 Nxd4 26.Rxd4 e5 27.Rc4 Qa5 28.f5 Bxg5 29.Rc6 Rfd8 30.Qg4 Be7 31.Rd1 Qa7 32.c3 Bf8 33.fxg6 hxg6 34.h7+ Kh8 35.cxb4 Rxb4 36.Qf3 Rdb8 37.Nc3 Qb7 38.Rcxd6? Rxb3+! 39.Ka1 [ 39.axb3 Qxb3+ 40.Kc1 Qb2# ]
39...Rxc3 [ 39...Rb2 ]
40.Qf6+ Kxh7 41.Rb6 Spectacular, but the only move.
41...Qc7 42.Rh1+ Bh6 43.Rxb8 Rc1+ 44.Rxc1 Qxc1+ 45.Rb1 Qc3+ 46.Rb2 Qe1+ 47.Rb1 Qc3+ 48.Rb2 Kg8 49.a4 Bc1 50.Qb6 I think this is a clear win now. The white king is just too open. His e-pawn gets picked off in many lines and black will still have two reserves! Like most endgames, it's all a question of time. Since white has to lose a move to break the pin and move his king, there is no point in capturing on b2 yet.
50...Kg7 So Kasparov used his 'extra move' to get his king off the back rank and away from queen check and also safe from the white a-pawn queening with check. "The more you look, the harder it is to find a concrete winning line for Kasparov. I'm sure he found that out himself long ago! Just pushing the pawn is not enough.
51.Ka2 [ 51.Qb4 Bxb2+ 52.Qxb2 Qe1+ 53.Qb1 Qd2 54.Qb5 Qc1+ 55.Ka2 Qc2+ 56.Ka3 Qxe4 57.a5 g5 58.a6 g4 59.Qb7 ]
51...Bxb2 52.Qxb2 Qc4+ 53.Ka3 Qxe4 54.a5 g5 55.Qd2 Watch one trick in these endgames. If Black plays his king to g6 and there is a pawn race, white queens the a-pawn, black queens the g-pawn, and Qg8+ wins the black queen. This is either winning or it isn't. Computers need evals in order to decide what to play, so their move suggestions are interesting. BUT, it is not relevant to evaluating the position. There are many +3 positions that are dead draws (or theoretical wins) computers don't understand.
55...Qf4 56.Qd8 Now black catches up in "queening time" because if the white pawn goes to a7, Qe3+ puts it back in the box. So white will have to lose another move with his queen to protect the a-pawn.
56...Qc1+ Hmm, interesting choice by Kasparov. Not sure how the queen can be better on c1 than on f4. Too subtle for me. [ 56...g4! 57.a6 g3 58.a7 Qf3+ Now the queen covers the h5 square, so there is no perpetual check! 59.Kb4 g2-+ 60.a8Q Qxa8 61.Qxa8 g1Q-+ ]
57.Kb4 Qb2+ 58.Kc5 Qc3+ 59.Kb5 So the queen gets back to the right diagonal with Qe3+ and THEN g4. I hope!
59...Qb3+ In his infinite wisdom, Garry decided e3 was better than f4 for the queen. From e3 it covers the critical a7 square.
60.Kc5 I'm still not sure if it really gains a tempo over the immediate 56...g4 line, but I'm willing to give him the benefit of the doubt! Mostly I think he wanted to make move 60 and get more time.
60...Qc3+ 61.Kb5 Qb3+ 62.Kc5 Qe3+ All those checks were exactly what the principles of endgame play tell you NOT to do! The white king was less active back on a3. But it shouldn't really matter in this line where the white king is.
63.Kb4 Qe4+ f3 was a key square for the black queen. It eliminated the perpetual. Now black doesn't have access to that square with check. From f3, the black queen covered the h5 square, so no perpetual. Now it looks like a draw.
64.Kc5 Qc2+ 65.Kb5 Qe2+ 66.Kb6 Qe3+ 67.Kc6 g4 68.a6 g3 69.a7 g2 70.a8Q Qe4+ Kc7 Qxa8 Qg5+ draw. And we should note that it's because of the active king on c7
70...Qe4+ 71.Qd5?? [ 71.Kc7 Qc4+ 72.Kb7 Qb3+ 73.Kc6 Qc2+ 74.Kb5 Qe2+ 75.Kc6 Qe4+ 76.Kc7 Qxa8 77.Qg5+ Kh7 78.Qh5+ Kg8 79.Qg5+ Kf8 80.Qh6+ Ke7 81.Qd6+ Thanks to the active white king, white has a perpetual check!]
71...Qc2+? [ 71...Qxd5+ 72.Kxd5 g1Q 73.Kxe5 A ChessBase program with tablebases will now happily inform you that this position is mate in 62! But that would almost certainly be harder for Black to win than the queen endgame with two black pawns. 73...Qg5+ 74.Kd4 Qd2+ 75.Kc5 Qe3+ 76.Kb5 f5 77.Qd5 Kg6 78.Qg8+ Kh5 79.Qf7+ Kg4 80.Qg6+ Qg5 81.Qe6 Qf4 82.Kb6 Kg3 83.Qb3+ Qf3 84.Qg8+ Kf2 85.Qh8 f4 86.Kc7 Qe3 87.Qb2+ Kf3 88.Kb8 Qe8+ 89.Kb7 Qe7+ 90.Ka8 Qf8+ 91.Kb7 Kg3 92.Qd4 Qe7+ 93.Ka8 Qa3+ 94.Kb7 f3 95.Qg1+ Kf4 96.Qd4+ Kf5 97.Qd5+ Kg4 98.Qd4+ Kh3 99.Qh8+ Kg2 100.Qg8+ Kf1 101.Qc4+ Ke1 102.Qe4+ Kd2 103.Qd4+ Kc2 104.Qb6 Kc1 105.Qg1+ Kb2 106.Qg3 Ka2 107.Qf4 Ka1 108.Kc6 Qd3 109.Qc1+ Ka2 110.Qc5 Kb2 111.Qb4+ Qb3 112.Qh4 Qc2+ 113.Kd7 f2 114.Qd4+ Kb1 115.Qb4+ Kc1 116.Qa3+ Qb2 117.Qa6 Qd2+ 118.Ke7 Qe1+ 119.Kd6 f1Q 120.Qa1+ Kc2 121.Qa2+ Kc3 122.Qa3+ Kc4 123.Qc5+ Kb3 124.Qd5+ Qc4 125.Qb7+ Kc3 126.Qf3+ Qd3+ 127.Qxd3+ Kxd3 128.Kc6 Kc4 129.Kc7 Qe6 130.Kb8 Qd7 131.Ka8 Kb5 132.Kb8 Ka6 133.Ka8 Qe8# Yep, that's 62!]
72.Kd6 Qg6+ 73.Kc7 g1Q 74.Qxe5+ Qf6 [ 74...f6 This move offered the last of the winning chances, although very difficult to prosecute. Both players were down to their last minutes.]
75.Qh8+ Kxh8 76.Qxf6+ Qg7 77.Qh4+ Kg8 78.Kd6 Qg6+ 79.Ke5 Kg7 80.Qe7 Dead draw now.
80...Qg3+ 81.Kf5 Qg6+ 82.Ke5 Qh6 83.Kf5 Qg6+ 84.Ke5 Kh7 85.Qh4+ Kg8 86.Qd8+ Kg7 87.Qe7 1/2-1/2