# R+3P vs B+N+3P ending. Win or draw, and plans for both players

In a recent game I reach this position (white to play). I was playing white and eventually lost the game.

``````[fen "1R6/5pkp/4n1p1/8/3b1P2/6P1/7P/7K w - - 1 51"]

1.Kg2 h5 2.h3?! h4! 3.f5 gxf5 4.gxh4 Bf6 5.Rb4 f4 6.h5 Kh6 7.Rb5?! Bg5 8.Rf5 f6 9.Ra5 Kxh5 10.Ra8 Nd4 11.Rd8 Nf5 12.Kf3 Nh4+ 13.Kf2 Ng6 14.Kg2 Ne5 15.Rh8+ Bh6 16.Kf2 Ng6 17.Rh7 Kg5 18.Kf3 Bf8 19.Rb7 Ne5+ 20.Kg2 Bc5 21.Rb3 Be3 22.Kf1 Kh4 23.Kg2 f3+ 24.Kh2 Bf4+ 25.Kg1 Kxh3 26.Rb7 Kg3 27.Kf1 Ng4 28.Rg7 Bd2 29.Rg8 Bg5 30.Kg1 f2+ 31.Kf1 Kf3 32.Rxg5 Nh2#
``````

My question is: has white any chance to draw this game? which would be the plans for players, both white and black, to draw/win the game?

Edited: I've added the rest of the game. "Evaluations" (?! and !) are mine, maybe they're not correct.

• It looks drawish to me. Did you blunder? Dec 3, 2016 at 16:30
• not a clear blunder, afaik. If there's any blunder this is not being able to find the correct drawing plan for this position. I can add the rest of the game if it helps Dec 3, 2016 at 16:43
• Yes, seeing the rest of the game would help. To me the position also looks drawish. Black doesn't want to exchange pawns (at least not many), so if white does not do anything, the only way to win this would be by winning white's pawns starting with the one on h2. This seems virtually impossible if white's king stays around g2 or h1. Dec 3, 2016 at 23:59
• Also, it's possible that like ​ Mueller vs Yusupov , ​ white still had a draw much later. ​ ​ ​ ​
– user2668
Dec 4, 2016 at 3:09

Müller, Lamprecht, Fundamental Chess Endings:

With three against three on one wing the defender is usually able to hold on.

`````` [Title "Mueller vs Yusupov, Hamburg SKA (1991), after 66... Ba5"]
[fen "8/5p2/6p1/b1n4p/2k2P1P/4K1P1/1R6/8 w - - 0 0"]

1. f5 Bc3 2. Rg2 gxf5 3. Kf4 Kd5 4. Kxf5 Ne4 5. g4 Nd6+ 6. Kf4 Be5+ 7. Kf3 hxg4+ 8. Rxg4 Ke6 9. h5 Nf5 10. Rg1 Kf6 11. Rg8 Nh6 12. Rg1 Kf5 13. Rg2 Bf4 14. Rg1 Bg5 15. Rg2 Bf4 16. Rg1 f6 17. Rg7 Bg5 18. Kg3 Ng4 19. Rg8 Ne5 20. Rg7 Bh6 21. Rg8 Nd3 22. Kh4 Nf4 23. Rh8 Bg5+ 24. Kg3 Ne6 25. Rg8 Bh6 26. Rg6 Bf4+ 27. Kf2 Bg5 28. Rg8 Nf4 29. Rh8 Kg4 30. h6 Kh5 31. h7 Kh6 32. Kf3 Ng6 33. Ra8 Kxh7 34. Kg4 Ne7 35. Kh5 Kg7 36. Ra5 Bf4 37. Ra6 Be5 38. Rb6 Kf7 39. Ra6 Nc8 40. Rc6 Nd6 41. Ra6 Ne4 42. Kg4 Kg6 43. Rc6 Bd6 44. Ra6 f5+ 45. Kf3 Kf6 46. Ke3 Kg5 47. Kf3 Nd2+ 48. Ke2 Bf4 49. Ra4 Kg4
``````

White should just sit and wait in his fortress. However, he decided to start some misguided activity.

Dvoretsky, Dvoretsky's Endgame Manual:

If both sides have three pawns placed on the same wing, then the defender may hope for a draw (only if, of course, the pawn structure is devoid of grave flaws).

[He then analyses the endgames in Capablanca vs Lasker, St Petersburg (1914) and Timman vs Karpov, Bugojno (1980).]

Flear, Practical Endgame Play - beyond the basics:

The case where all pawns are on the same flank is interesting as the result isn't always evident. However, a general rule could be that the bishop and knight require a target in order to convert their superiority.

[He then uses Ponomariov vs Sasikiran, Biel (2004) and the aforementioned Timman vs Karpov, Bugojno (1980) as examples.]

• I'll add diagrams when I have more energy. Dec 3, 2016 at 19:33
• I just looked at the early part of the 7-piece part of ​ Mueller vs Yusupov ​ with the Lomonosov tablebases: ​ ​ ​ ​ ​ ​ Even without the 50-move rule, [both captures of g4 on move 74 draw, and from then until just before ​ 77. Rg8 , ​ it was a draw with neither side needing to find any only-move]. ​ ​ ​ The tablebase reports the position just after ​ 77. Rg8 ​ as black-mates-in-105, which might mean white draws by the 50-move-rule. ​ ​ ​ The tablebase says white's options for move 77 that hold forever (i.e., without the 50-move rule) are ​ Rb1,Rc1,Rd1,Re1,Rh1,Kg4 . ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​
– user2668
Dec 4, 2016 at 1:16
• (I did not look at positions much beyond ​ ​ ​ 77. Rg8 ​ .) ​ ​ ​ ​ ​ ​ ​ ​
– user2668
Dec 4, 2016 at 1:17
• (In the numbering that j___d added, the capture is move 8 and the probable-error is move 11.) ​ ​
– user2668
Dec 4, 2016 at 3:02
• Thanks! I'll look for such books (I currently have only Müller/Lamprecht one) to see which are the plans and ideas of such endgames Dec 5, 2016 at 8:45

Maximenko, Srokovsky, and Braslawski wrote a book on this material imbalance in the endgame called "Mastering Rook vs Minor Pieces". This imbalance only occurs in about 2% of endgames, so unless you're at least master level, knowing the theory may be a fairly low priority.