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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"]
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  • If you still have it, do you mind giving the line SF played? Just curious to see what it did. Jun 19 '21 at 14:34
  • Well, I see someone keeps downvoting me on this site. How unfriendly.
    – user21820
    Jun 19 '21 at 15:38
  • I was curious so I ran Stockfish 13+ NNUE out to depth 62. It evaluates Kg1, Kf1, and Ke1 all as 0.0 . There may be a deeper win here. Further, this assumes perfect play so there may be parts of these lines that contain difficult-to-find moves for Black so White may have practical chances here. I suspect that may be the case, though I haven't identified any yet. Jun 19 '21 at 17:43
  • @SecretAgentMan: That's what I thought at first but after realizing that I can see the 7-piece endgame database on Lichess I'm sure InertialIgnorance is correct. If your SF version follows his/her given line, it is a confirmed win at the end. To turn the database on, click the Book icon. I didn't realize it myself until just now.
    – user21820
    Jun 19 '21 at 18:05
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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.

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  • Based on my comment above, are the defenses to your line hard to find or inhuman? Jun 19 '21 at 17:44
  • @SecretAgentMan I also used SF 13 to analyze these lines, but I didn't let it think to the levels of depth 62. After 1.Kg1 what move is given? Jun 19 '21 at 23:11
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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.)

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