R+P VS B+P endgame

The positions come from  a game I play with Chess.com bot,I am black.

Why these moves are blunders? And what's the key point to play R+P vs B+P endgame?

Thank you in advance!

Hi, give me a line

Thank you

I don't now the theory of R+P vs B+P

I think I need to read Doversky's endgame manual to learn it ,but I haven't seen that part yet( Chapter 11)

https://www.chess.com/game/computer/89194883

here's the game

please give your comment

thank you

After giving up the b3 pawn, there was no forced win for Black.

Your plan of walking the king all the way round to the h5 pawn is fine, but white could well counter it by attacking the g7 pawn with his king.

Bc6 is marked as a mistake because if Black plays precisely, he can bring his king to h6/f6 (something that was not possible with the bishop controlling the a2-b8 diagonal).

At the first glance, the correct plan seems to be sacking the rook for the bishop and the pawn at the moment when you can maintain the opposition in the resulting endgame. In any case, approaching the pawn with the king seems like an obvious first step.

As for the specific line, this doesn't look easy to achieve because the bishop can control g8 and the white king wouldn't let you go past him.

I don't think there's any "theory", the way to go is probably just play around with the tablebase and try to understand why it works.

I think this is a very difficult endgame. The best moves you can see with the help of tablebases.

https://syzygy-tables.info/?fen=5k2/6p1/8/6KP/8/1B6/7r/8_b_-_-_0_1

A similar position I found in my database. The 2500 Elo "blunderd" this endgame, too.

Thanks for your all

Thank you for the position you offer , I appreciate it very much