endgame study: corrected! I hope

white to play.


Delicate.



Actually the trade of rooks here loses for white, as the b pawn is too strong.  White's first move is crucial.


1. Re7+  Kd3, 2. Ra7  a4, 3. h4  Kc3, 4. Kg3  Kb3, 5. h5  Re8, 6. f4  a3, 7. f5  a2, 8. Kf4  Kb2, 9. f6  a1, 10. Ra1  Ka1, 11. Kg5  b4, 12.  f7  Rf8, 13. Kg6  b3, 14. h6 b2 -+.  
(Stockfish says 1. h4! yet without that waste of a move white still is losing.)

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In this similar study to the last position we have  improvements for white at the start position: what's the result?!?
1. Re8+   Kd3, 2.  Ra8  a4,  3. h4  Kc3,  4. h5  Kb3,  5. f4  a3, 6.  f5!   Re1!. 7. Kf4  a2, 8. h6  a1, 9. Ra1  Ra1, 10. Kg5 b4, 11.f7  Ra8, 12. Kg6  Ka2, 13. Kg7  b3, 14. f8  Rf8 -+.   This surprised me greatly.
..........
Stockfish says 1. h4!  (I was wasting a move.)  This position draws, using Stockfish's tip.