Phase one: reduce one black piece to passivity. 21.Nd2 Ne8 22.Nb1 Bb7 23.f4 f6 24.Nc3 Kf7 25.Na4. Now at least the knight cannot move from d7.
Phase two: advance in the centre: 25...Ke7 26.d4 Kd8 (he cannot let the bishop attack b6 from d4) 27.d5 exd5 (27...e5 28.Bh3 leads to the loss of the b6-pawn) 28.exd5.
Now Bh3 is seriously threatened, so Black needs another way to defend b6. He played 28...Nc7 29.Bh3 Na8 when it was time for phase three: increase K-side space: 30.Be6 Nf8 31.f5 Bc8 32.Kf2 Bd7 33.g4 Ke7 34.g5!
Now 34...fxg5 35.Bxg7 is good for White while 34...Be8 leaves the b6- pawn in dire trouble after 35.Bc8 Nd7 36.Bb7 Nc7 37.Bc6. Illescas decided to get rid of the bishop: 34...Nxe6 35.fxe6 Be8 36.gxf6+ gxf6.
Phase four: get the bishop and knight to their best squares without losing the c-pawn: 37.Ke3 Bg6 38.Kd2 Be4 39.Bc1 Bg2 40.Kc3 Bf1 41.Bh6 Bg2 42.Bf4 Bf1 43.Nb2 Nc7 44.Nd1 Bg2 45.Ne3 Be4 46.Bh6 Ne8.
Phase five: bring the king to f4 to enable Nf5+: 47.Kd2 Nc7 48.Ke2 Ne8 49.Kf2 Nc7 50.Kg3 Bd3 51.Kg4 Ne8 52.Kf4 Bb1 53.Nf5+. Now 53...Bxf5 54.Kxf5 Nc7 55.Bg7 Ne8 56.Bh6 leaves Black without a move.
Phase six: more driving back: 53...Kd8 54.Bf8 Bd3 55.Be7+ Kc7 56.Ne3 Kc8 57.Kg4 Kc7 58.Kh5 Ng7 59.Kh6 Ne8 60.h4 Kc8 61.h5 Kc7.
Phase seven: the only way to make progress - a piece sacrifice: 62.Ng2 (thanks to his h-pawn advance, 62...Bxc4 63.Kxh7 now wins for White) 62...Kc8 63.Nf4 Bc2 64.Bxf6!! Nxf6 65.Kg7 Ne8+ 66.Kf7 Nc7 67.e7 h6 (67...Kd7 68.Ne6 Bd1 69.Nf8+ is even worse for Black) 68.Ne6 Bd1.
Now all it needs is phase eight: hair-raising tactics: 69.Kg6! (not 69.Nxc7?? Bxh5+) 69...Ne8 70.Nf8 Be2 71.Kxh6 Bxc4 72.Kxg6 Bxd5 73.h6 c4 74.h7 Be4+ 75.Kf7 Bxh7 76.Kxe8! Bg8 77.Nd7 and Black lost on time. The threats of Kf8 or Nxb6+ cannot be met.
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