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My question concerns the final position in the game

Judit Polgar vs Garry Kasparov It (cat.19) (1996) · Sicilian Defense: Najdorf. Amsterdam Variation (B82) · 0-1 

[White "Polgar"]
[Black "Kasparov"]
[FEN ""]

1.e4 c5 2.Nf3 d6 3.d4 cxd4 4.Nxd4 Nf6 5.Nc3 a6 6.f4 e6 7.Qf3 Qb6 8.a3 Nc6 9.Nxc6 bxc6 10.b3 Bb7 11.Bb2 d5 12.Bd3 c5 13.exd5 exd5 14.O-O-O O-O-O 15.Na4 Qc7 16.Bf5+ Kb8 17.Be5 Bd6 18.Qc3 d4 19.Bxd6 Qxd6 20.Qxc5 Qxf4+ 21.Kb1 Rd5 22.Rdf1 Qe5 23.Qc4 Rb5 24.Qxf7 Bd5 25.Qxg7 Rg8 26.Qh6 Bxb3 27.cxb3 Rxb3+ 28.Kc1 Qc7+ 29.Bc2 d3 30.Qf4 Rc8 31.Qxc7+ Rxc7 32.Rf2 Ne4 33.Rf8+ Ka7 34.Rf7 Rbb7 35.Rxc7 Rxc7 36.Rd1 Rxc2+ 37.Kb1 Rxg2 38.Rxd3 Rxh2 39.Rd7+ Kb8 40.Re7 Nd2+ 41.Kc1 Nb3+ 42.Kd1 h5 43.Re3 Nd4 44.Nc5 a5 45.Nb3 Nc6 46.Rc3 Kb7 47.Ke1 Kb6 48.Kf1 Rh4 49.Kg2 Nd4 50.Nxa5 Kxa5 51.Rc5+ Kb6 52.Re5 Kc6 53.Kg3 Rh1 54.Kg2 Kd6 55.Ra5 Rh4 56.Kg3 Rg4+ 57.Kh3 Ne2 58.Rxh5 Rg3+ 59.Kh4 Rxa3 60.Kg4 Ke6 61.Rb5 Rg3+ 62.Kh4 Rg1 63.Rg5 Rf1 64.Ra5 Kf6 65.Ra8 Rg1 66.Rf8+ Ke5 67.Re8+ Kf4 68.Rf8+ Ke4 69.Re8+ Kf3 70.Kh5 Ng3+ 71.Kh6 Nf5+ 72.Kh7 Kf4 73.Rb8 Rg7+ 74.Kh8 Rd7 75.Re8 Kg5 76.Re6 Nd4 77.Re1 Kf6 78.Rd1 Rd5 79.Ra1 Ne6 80.Ra6 Kf7 81.Ra7+ Kg6 82.Ra8 Rd7 83.Rb8 Rc7 84.Kg8 Rc5 85.Ra8 Rb5 86.Kh8 Rb7 87.Rc8 Nc7 88.Rg8+ Kh6 89.Rg1 Rb8+ 90.Rg8 Ne8 0-1

White resigned, but I cannot find a win for Black. As long as Black keeps his R & N on the 8th rank, White shuttles his R between g8 and f8. If Black moves his N, W plays R takes R. If Black moves his R, W plays R x N.

The idea I'm missing must involve moving the Black King. But I would appreciate a detailed explanation.

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2 Answers 2

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15

If white ever trades her rook for black's knight, the game is lost. The only move for her is thus 91.Rf8, which is answered by 92.Kg6 Rg8+ 93.Kf7 resulting in the following position:

[FEN "1r2n1RK/5k2/8/8/8/8/8/8 w - - 66 93 "]

1. Rg1 (1.Rxe8 Rxe8 2.Kh7 Re6 3.Kh8 Rh6#) (1.Rg7 Nxg7 2.Kh7 Rb6 3.Kh8 Rh6#) (1.Kh7 Nf6+) Nf6  2. Rg8 Rxg8#

and now any rook move loses to the discovered mate Nf6# or loses the rook entirely

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2
  • Nitpickery; Nf6 isn't mate, but it's mate next move (1. Rg1 Nf6+ 2. Rg8 3.Rxg8#)
    – Steven Stadnicki
    Commented Nov 21, 2014 at 5:45
  • The question mark for 1.Kh7 seems a bit harsh, seeing as the alternative defenses allow mate in 2.
    – bof
    Commented Nov 22, 2014 at 2:48
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[FEN "1r2n1RK/8/7k/8/8/8/8/8 w - - 0 1"]

1. Rf8 Kg6 2. Rg8+ Kf7 3. Rg1 Nf6+ (3. Kh7 Nf6+ 4. Kh6 Nxg8 (4...Rxg8??)) 4. Rg8 Rxg8#
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