Suddenly it was obvious to me in my analysis I had missed what Fischer had found with the greatest of ease at the board.
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[Event "rated untimed match"]
[Site "?"]
[Date "????.??.??"]
[Round "?"]
[White "Unknown"]
[Black "Unknown038"]
[Result "0-1"]
[Annotator "David Hayes"]
[BlackElo "0"]
[FEN "8/8/7p/p4kp1/6P1/P4K1P/8/8 b - - 0 1"]
[SetUp "1"]
[TimeControl "0"]
[WhiteElo "0"]
1... Ke5 2. h4 Kd4 ( { Black can try: } 2... gxh4 3. Kg2 Kf4 ( 3... Kd4 4. Kh3 Kc4 5. Kxh4 Kb3 6. Kh5 Kxa3 7. Kxh6 Kb2 8. g5 a4 9. g6 a3 10. g7 a2 11. g8=Q a1=Q 12. Qg7+ Ka2 13. Qxa1+ Kxa1 { Draw. } ) 4. Kh3 Kg5 5. a4 Kf4 6. Kxh4 Kf3 7. Kh5 Kg3 8. Kxh6 Kxg4 9. Kg6 Kf4 10. Kf6 Ke4 11. Ke6 Kd4 12. Kd6 Kc4 13. Kc6 Kb4 14. Kd5 Kxa4 15. Kc4 Ka3 16. Kc3 Ka2 17. Kc2 { The black king will
never be able to leave the a-file. Draw. } ) 3. h5 a4 { Kd3 and even Ke5 are
also good for the win. } 4. Kf2 Kc3 5. Ke3 Kb3 6. Kd3 Kxa3 7. Kc3 Ka2 8. Kc2 a3 9. Kc1 Kb3 10. Kb1 Kc3 11. Ka2 Kd3 12. Kxa3 Ke4 13. Kb3 Kf4 14. Kc3 Kxg4 15. Kd3 Kxh5 { Black wins with a large material advantage. } 0-1