White can win, starting with 1.g5! hxg5 2.Kxg5 Kf7 3.h5 Ke7 4.Kg6 Kf8 5.h6! Kg8! 6.Kh5! but the much praised moves 1.Kh7 and 2.Kh8 deserve only question marks.
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This position (Horowitz-Denker, Philadelphia 1936) may be found in a new book of endgames, The Final Countdown by W Hajenius and H van Riemsdijk (Cadogan, pounds 10.99). For years, the orthodox view was that White won by a classic squeeze: 1.Kh7 Kf7 2.Kh8 Kf8 3.g5 and Black resigned, since 3...hxg5 4.hxg5 Kf7 5.Kh7 leads to the loss of the g-pawn. Hajenius and Riemsdijk, however, point out that Black can draw after 1.Kh7 with 1...h5!! when 2.gxh5 Kf7 3.h6 g6! 4.Kh8 Kf8 gets White nowhere, while 2.g5 Kh7 3.Kh8 Kg6! 4.Kg8 is stalemate.