Chess
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Your support makes all the difference.When Nigel Short reached the diagram position as Black against Veselin Topalov in the first round at Madrid, he had already been defending a miserable looking rook and pawn endgame for an hour or two. He had just moved his rook to d6, offering an exchange of rooks, and it was the moment of decision. White can continue with 1.Re4 Rf6 2.Rc4, though it is difficult to see how he then makes progress. But can he win the pawn ending if he exchanges rooks instead?
After 1.Rxd6 Kxd6, White will lose his c-pawn next move. Any attempt to bring his king into play via h2 and g1 is hoplessly slow, so the only other chance is 2.g3, but after 2...Kxc6 (2...fxg3 3.Kxg3 Kxc6 4.Kf4 White wins easily) 3.gxf4 Kd5 4.Kg3 Ke6 (to stop White from breaking through with f5 and Kf4) can White win? That is what Topalov had to decide before exchanging rooks. Try to work it out for yourself before reading on.
Topalov did exchange rooks, and here is how the game continued after the moves already given: 5.Kf2 Kf6 (planning to meet 6.Ke3 with Kf5) 6.Ke2 Ke6 7.Kd3 Kd5 8.Ke3 Ke6 9.Ke4.
This is precisely the position White would have reached if Black had played 5...Kf5 6.Ke3 Ke6 7.Ke4. There now followed 9...Kf6 10.f5! g5 (The best chance, since 10...gxf5+ 11.Kd5! is an easy win for White) 11.hxg5+ Kxg5 12.Ke5 h4 13.f6 Kg6 (or 13...h3 14.f7 h2 15.f8=Q h1=Q 16.Qf6+ Kh5 17.Qh8+) 14.Ke6 and Black resigned. After 14...h3 15.f7 h2 (or 15...Kg7 16.Ke7) 16.f8=Q h1=Q White picks up the queen with checks on g8 and h8.
The only question that remains to be answered is whether Black would have done better with 5...Kf5 6.Ke3 Kf6 7.Ke4 Ke6, reaching the same position as in the game, but with White to play, not Black. But here White plays 8.f5+! gxf5+ 9.Kd4 Kd6 (or 9...Kf6 10.Kd5) 10.f4! Ke6 11.Kc5 squeezing in to win the f-pawn.
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