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The crucial difference between the middlegame and endgame is that the latter, with fewer pieces cluttering the board, gives greater possibility of exact calculation. In the middlegame - except where some tactics allow a forced gain of material or immediate mating attack - all thought is fuzzy and calculations end in a vague "White stands better" or "with advantage to Black". In the endgame, such imprecision is not good enough. Sometimes you must work out with certainty whether you are winning, losing or drawing. Today's position, from a game Cruz-Seirawan played in the Moscow Olympics last year, is a good example.

It is Black to play and he has a crucial decision to make. He can win a pawn with 1...Rh5, but after 2.Kb4 Rxh2 3.c5, the c-pawn becomes dangerous. That line needs to be analysed further before even a fuzzy assessment is reached, but first of all there is something more important to look at. With 1...Ra5+, Black can force a king and pawn endgame, and such positions ought always to be calculable.

Any lazy player (which covers most of us) would decide against the rook exchange on general grounds: After 1...Ra5+ 2.Kb3 Rxa2 3.Kxa2 White has a "distant passed pawn" on c4. White's king and c-pawn will keep the black king occupied on the Q-side, then, at the right moment, the white king will dart over to feast on the black pawns.

That's how it usually goes, but this position is different thanks to the pawn on g4. After 3...Kd6 4.Kb3 Kc5 White has no pawn moves. Black is free to advance his K-side pawns.

In playing the first of those four moves Seirawan must have calculated 20 moves ahead. Here is what happened next: 5.Kc3 e5 6.Kd3 f5 7.Kc3 e4! (Restricting the white king to c3 and b3) 8.Kb3 h6!! (A delightfully subtle move to ensure that White's king is out of phase when the crucial breakthrough arrives.) 9.Kc3 h5 10.Kb3 f4! 11.gxf4 e3! 12.fxe3 (With White's king on c3, 12.Kd3! would save the game) 12...h4 (Now a black pawn must queen, but the fight is not over) 13.f5! Kd6!! (13...g3 leads only to a draw after 14.hxg3 hxg3 15.f6 Kd6 16.c5+! Ke6 17.c6) 14.Kb4 Ke5!! (14...g3 15.hxg3 hxg5 16.c5+ Kd7 17.f6 g2 18.c6+ again lets White save a draw) White resigned. After 15.c5 Kxf5 16.c6 Ke6 17.Kc5 g3 18.hxg3 h3! 19.c7 Kd7 20.Kb7 Black's pawn queens with check. A magnificent ending by Seirawan showing just how far it is possible - and sometimes necessary - to calculate.