Endgame Series - Part 7

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Hello, dear chess friends!
So far we have focused on pawns' role in the endgame and hopefully you have understood pawn race, breakthrough, "electric" pawns, outside passed pawn, and other ideas we have discussed in the first part of the Endgame series. At the end of the day, most endgames are won by promoting one's pawn into a queen, so first and foremost we need to develop a feel for the pawns.
However, in many endgames, passed pawns need help and/or protection of king and this is what we will focus on in the following issues. In addition to helping his own pawns, the king is often a brave attacking piece in the endgame and we also need to know how to maneuver with it in this context.
At the end of the previous issue of Modern chess, we gave a preview of the second part of Endgame series – the role of the king in endgames. We drew an important conclusion about the nature of king's movement on the chess board: "Distance on the chess board is not always equivalent to distance in the "real" world." As we explained on a real-world example (**correction from the previous issue: the distance between two tram stations is 4 minutes, not 2 minutes) diagonal movement towards a certain line on the horizon always takes longer than a straightforward one. In chess, however, it takes king the same time from h1 to reach a8 (moving diagonally) and h8 (moving straight). This gives rise to certain "anomalies" involving king – the only piece on the chess board whose movement is restricted to one square at the time.
This anomaly in king's movement sometimes plays tricks on minds of even the strongest players, the best point in case being the following World Championship game: Bronstein – Botvinnik 

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