Can you find white's winning plan without consulting the tablebase? This the toughest R+P vs R ending I have seen.
8/k7/8/8/8/7P/2r5/1R5K w – – 0 1
The idea is actually quite simple. But it is difficult for amateurs to understand the move sequence. This is a very good exercise to learn R & P endgame.
I had to work out a few variation to understand why they don't work before I could find the first move. I considered Rg1, h4 and Rb5. After that I could understand the main idea of this puzzle.
1.Rb4! Ka62.h4 Rc1+3.Kg2 Rc84.Kh2 Ka55.Rb3 Ka46.Rh3 Kb57.h5 Rh88.h6 Kc59.Kg3 Kd610.Kf4 Ke711.Kg5 Rg8+12.Kh5 Rh813.Rc3 Ke614.Rc7 Ra815.h7 Kf616.Kh6 Rd817.Rb7 Ra818.Rb3 Kf519.Rf3+ Ke420.Rf7 Ke521.Kg7 Ke622.Rf8 Ra7+23.Kg6 Ra224.h8=Q Rg2+25.Kh7 Rh2+26.Kg8 Rxh8+27.Kxh8 Kd5It's a winning position for white.
Consiser 1.Rb3 side by side with 1.Rb4. Then you can explain why 1.Rb4 works. I don't want go through the entire line you give, Alena, but I think black can force white into a Q vs R ending with best play.