Is this position with KRP against KBP a draw? I encountered the following position with White to move.

[FEN "6R1/8/3k4/pK6/Pb6/8/8/8 w - - 45 83"]


I see no way for White to win, but am not completely sure. Is it known to be a draw? More generally, is the result for all such positions with head-to-head pawns and rook against bishop known?
This endgame is indeed a draw. You can check positions with 7 or fewer pieces in the Sygyzy tablebases to see if they are a win, a loss, or a draw. If you want the depth to mate for 6 pieces or fewer, use the Shredder database
Given the context, I suppose you would like to know why this is a draw. If White was trying to win, the best option is to take Black’s pawn. Black’s bishop is stuck defending it. If the pawn falls, Black falls with it. White can and will win the pawn.
[FEN &quot;6R1/8/3k4/pK6/Pb6/8/8/8 w - - 0 1&quot;]

1. Ra8 Kd5 2. Rxa5 Bxa5 3. Kxa5 Kc5

The clutch is doing soh leaves White with a major problem. The pawn endgame is a draw! Due to having a rook pawn, White will either be stalemated by the Black king, or Black will get in front of the pawn and be stalemated by White.

[Title &quot;White is stalemated&quot;]
[FEN &quot;8/8/8/K1k5/P7/8/8/8 w - - 0 1&quot;]

1. Ka6 Kc6 2. a5 Kc7 3. Ka7 Kc8 4. a6 Kc7 5. Ka8 Kc8 6. a7 Kc7


[Title &quot;Black is stalemated&quot;]
[FEN &quot;8/8/8/K1k5/P7/8/8/8 w - - 0 1&quot;]

1. Ka6 Kc6 2. Ka5 Kb7 3. Kb5 Ka7 4. a5 Kb7 5. a6+ Ka7 6. Ka5 Kb8 7. Kb6 Ka8 8. a7


If White does not target g the Black pawn, BBlack will merely wait it out. They will just shuffle their bishop around to keep protecting their pawn. The Black king will move around such that the pawn endgame will remain drawn. Eventually, there will be a draw via the 50-move rule or threefold repetition.
For all situations with head-to-head pawns, it seems that most will be won. Moving your position one file over move creates gives a win for White. Therefore, it seems to me that the only drawn positions are ones with rook pawns and a close enough Black king. In other words, there are very few of them.
[FEN &quot;7R/8/4k3/1pK5/1Pb5/8/8/8 w - - 0 1&quot;]

1. Rb8 Bb3 2. Rxb5 Kd7 3. Rb7+ Kc8 4. Re7 Bd1 5. b5 Bf3 6. Rf7 Be4 7. Kb6 Bg6 8. Re7 Kd8 9. Re5 Bc2 10. Kc6 Bb3 11. b6 Ba4+ 12. Kd6 Kc8 13. Re7 Kb8 14. b7 Be8 15. Kc5 Ka7 16. Rxe8 Kxb7 17. Re7+ Kc8 18. Kc6 Kb8 19. Rf7 Ka8 20. Kb6 Kb8 21. Rf8#