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This position was reached in semi-final game 1 of FIDE world cup 2021. With black to play the players agreed to a draw. The white is up a pawn and looks to be winning? I am not able to figure out a drawing continuation for black.
[FEN "8/8/4k3/6K1/8/7P/8/8 w - - 0 1"]
In these rook-pawn endgames the key rule is that if the defending king reaches the queening square (h8 in this case) then the game is a draw. If the attacking king manages to control it (but not occupy it), however, then it can be a win. You can see this by looking at the key positions
[FEN "7k/8/6KP/8/8/8/8/8 w - - 0 1"]
White cannot stop Black from playing ...Kg8-h8 ad infinitum, and h7 leads to an immediate draw by stalemate. Similarly if
[FEN "7K/5k2/7P/8/8/8/8/8 w - - 0 1"]
This position is also drawn because White cannot extract the king from in front of the pawn.
In the game, Black to play goes ...Kf7, and White cannot stop Black from playing ...Kh8 eventually, reaching the first position. Hence the position is drawn.
If it were White to play in this position, then 1. Kg6 wins. 1...Ke7 2. Kg7! (any other move allows 2...Kf8 and again Black reaches the first position) followed by h4-h5-h6 leads to a promotion that Black cannot stop.
Ke6-f7-g8-h8 and then the black king shuffles between h8 and g8. If white pushes the pawn to h7, it will lead to stalemate. The pawn can't be promoted. This is basic endgame theory and very useful to know!
