user9192: I reached this endgame, which Stockfish 10+ evaluates as +3.9, but failed to convert it to a win. I feel that it may be a draw after all. Is that the case?
[Title "White to move"]
[FEN "8/8/8/4k1p1/1R3p1P/5P1B/r4K2/8 w - - 8 57"]


user12873: It should be winning:
1.Kg1 Ra1+ (1...gxh4 runs into 2.Re4+, winning the f4-pawn) 2.Bf1 gxh4 3.Rb5+ Kd4 (3...Kf6 4.Rh5, and after Rxh4 it will be easily winning with just the f-pawns on the board) 4.Kf2 Ra2+ 5.Be2. And now White's rook will snag one of Black's pawns.

user11144: Lines are no answers, at least if the long run counts ;-)
First of all, it is necessary to know which piece-only endgames are drawn and which are won. RB/R is draw (even if a hell to defend, I'm talking from personal experience on the receiving and dishing end). So, first priority: Don't let the Pf3 drop. Luckily, the wB wears a large "Hands Off" sign. Second, your coordination is lousy. Black has good chances to play his king to e3 (your R will probably make a detour to h4, grabbing the P) and entangle your B and K into defending. Thus, next priority is improving your K and B position, without dropping the P. After that, stuff becomes merely technical (took me ten seconds to calculate in my head how to push the bK off the defense of the Pf4: a typical position after your pieces became active would be Ke4 Re6 Bg4 - Kg3 Rf8, now 1.Rg6 Re8+ 2.Be6+ or 1...~ 2.Bf5), especially as White can always offer a rook trade. After the Pf4 drops, just queen the Pf3. Black has at most a few lame stalemate traps.
That said, now that you understand what are the long-term aims, you can put the position into Syzygy (after the h pawn drops) and play out a few concrete lines. For example, to get out of the rut, the computer temporarily plays the R to a3 to defend the Pf3, then (wK is on h3) the bishop from the lousy g2 via f1-d3 to e4, already forcing Black into defense mode. (Note that as Black I will play "better" than the computer in the sense that I choose the most annoying instead of the objectively best line.)

9192: <p>I reached this endgame, which Stockfish 10+ evaluates as <code>+3.9</code>, but failed to convert it to a win. I feel that it may be a draw after all. Is that the case?</p>
<pre><code>[Title &quot;White to move&quot;]
[FEN &quot;8/8/8/4k1p1/1R3p1P/5P1B/r4K2/8 w - - 8 57&quot;]
</code></pre>
 12873: <p>It should be winning:</p>
<p>1.Kg1 Ra1+ (1...gxh4 runs into 2.Re4+, winning the f4-pawn) 2.Bf1 gxh4 3.Rb5+ Kd4 (3...Kf6 4.Rh5, and after Rxh4 it will be easily winning with just the f-pawns on the board) 4.Kf2 Ra2+ 5.Be2. And now White's rook will snag one of Black's pawns.</p>
 11144: <p>Lines are no answers, at least if the long run counts ;-)</p>
<p>First of all, it is necessary to know which piece-only endgames are drawn and which are won. RB/R is draw (even if a hell to defend, I'm talking from personal experience on the receiving and dishing end). So, first priority: Don't let the Pf3 drop. Luckily, the wB wears a large &quot;Hands Off&quot; sign. Second, your coordination is lousy. Black has good chances to play his king to e3 (your R will probably make a detour to h4, grabbing the P) and entangle your B and K into defending. Thus, next priority is improving your K and B position, without dropping the P. After that, stuff becomes merely technical (took me ten seconds to calculate in my head how to push the bK off the defense of the Pf4: a typical position after your pieces became active would be Ke4 Re6 Bg4 - Kg3 Rf8, now 1.Rg6 Re8+ 2.Be6+ or 1...~ 2.Bf5), especially as White can always offer a rook trade. After the Pf4 drops, just queen the Pf3. Black has at most a few lame stalemate traps.</p>
<p>That said, <em>now</em> that you understand what are the long-term aims, you can put the position into Syzygy (after the h pawn drops) and play out a few concrete lines. For example, to get out of the rut, the computer temporarily plays the R to a3 to defend the Pf3, then (wK is on h3) the bishop from the lousy g2 via f1-d3 to e4, already forcing Black into defense mode. (Note that as Black I will play &quot;better&quot; than the computer in the sense that I choose the most annoying instead of the objectively best line.)</p>
