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Basic Endgame Technique

This is a must know ending. Can you describe white's winning method?

8/2p5/8/8/8/8/k6P/4K3 w - - 0 1

1.Kd2 Kb2
2.Kd3 Kb3
3.Kd4 Kb4
4.h4 c6
5.h5 c5+
6.Ke3 c4
7.h6 c3
8.h7 c2
9.Kd2 c1=Q+
It's a winning position for white

Alena, why would black simply waste a tempo with 4. ....c6?

1.Kd2 Kb2
2.Kd3 Kb3
3.Kd4 Kb4
4.h4 c5+
5.Ke3 c4
6.Kd2 Kb3
It's doesn't matter c6 or c5 for me because I know how to win this position.

It should matter to you, Alena, even if black can't force a draw with either move. Let me ask you this- if you were on the black side of this problem in a game, which move would you play at move 4? Surely you don't resign the position every time you know your opponent already has a winning position.

Of course c5+.