Interesting situation. can black not now win?
Endgame study 1
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In this game, white had to lost 1 pawn! white can only draw by eat Black one pawn. If Black purpose is h6 pawn, then white can eat e6 pawn.If Black purpose is e5 pawn, then white can eat h7 pawn. We can see, this game will be draw when White king in g5 and Black king in e5, Move the king's purpose is when White king in g5 and Black king in e5 and then let opponent to move! Near e5 square is d5,d4,e4. Near g5 square is h5,h4,g4.When Black king in d5 or d4 square, white king can in h5 or h4 square, when White king in e4 square, Black king must be in g4 square, that is, e5 and g5 must be suit with e4 and g4, Here is the example of White manipulation the wrong plan to make him lost.