Rook endgames
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I would try 1.b4 Kf5 2.Kf3 Rb5 (2...Rg8 looks worse) 3.Rb1 Kg6 4.Ke3 Kf5 5.Kd3 Kg4 6.Kc3 Kxh4 7.Rg1 Kh3 8.Rg6 Re8 (8...h4 9.Rxe6) 9.b5. White should win with passed pawns with an active king even in lines that require the rook to be lost.
1.b4...what about 1...Rb5??
Can white win the above position ? It seems not . I noticed that the more pawns there are on the board left the harder it is for a player to convert the one pawn advantage .