8 
[title "R vs B+B"]
[fen "8/4rpkp/6p1/8/8/4BBP1/5PKP/8 w - - 0 1"]

The engine says that this endgame is winning for white(+2.5). Is there a technique that could be used to win this for white. I understand that the ideal position for black to draw this game would be to have 0 pawns on the board which would then with the best play be a draw. If there was a passed pawn in this for white the escorting of the pawn to the final rank would be achieved with the bishop maneuvers. However, in this case, the pawns are on the same side of the board. Are the engines missing some sort of fortress position or is there a winning technique?

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  • 16
    In general, if you don't understand how white wins in a position where the engine indicates a clear win for white it's a good idea to try and defend it as black to see how the computer (playing as white) crushes you. In this endgame it will use the king and the two bishops to restrict the movement of black's rook, and eventually black will be caught in zugzwang, losing pawns. After that, it will go downhill pretty quickly.
    – Scounged
    Jan 2, 2020 at 4:37
  • FWIW, KBBP vs KRP is drawn as long as no side has a passed pawn according to 7-man table base.
    – jf328
    Jan 2, 2020 at 7:27
  • 2
    Title seems to suggest that B+B wins against R, but shown game is B+B+3 pawns vs R+3 pawns, and the accompanying text seems to suggest that B+B against R is drawn with best play. I'm a bit confused, which is it?
    – Michael
    Jan 2, 2020 at 18:26
  • Yes, I think the title should be changed to reflect the presence of the pawns.
    – Bladewood
    Jan 2, 2020 at 20:29
  • Sorry about the misunderstanding 2 Bishops against a Rook is drawn, but 2 Bishops + 3 pawns vs Rook + 3 pawns was the question.
    – SubhanKhan
    Jan 2, 2020 at 22:31

4 Answers 4

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5

The key is to create weaknesses in Black's position, while also not exchanging off too much material. For example, if you exchanged down and got a K+B+B+h-pawn vs K+R, Black could sacrifice his rook for your dark-squared bishop, resulting in the wrong bishop drawn endgame.

My strategy would be to fix Black's pawns on a certain colour complex, ideally keeping all the pawns on the board. Then with all the pawns fixed, there will be at least one weak pawn for you to attack. In this situation, the bishop on the colour of the pawn will exert pressure, while the other bishop will control key squares around the pawn. For example, if Black's pawns were fixed on f6-g5-h6, your dark-squared bishop would put pressure on the f6-pawn, and then you could plant your light-squared bishop on g6 (covering f7, h7, and f5).

Then, you'd advance your king to help both bishops in their tasks (i.e., attacking the weak pawn(s) and controlling other important squares). Your king and other bishop (the one not on the colour of the weak pawn) could try to box out Black's rook, preventing it from defending the pawn.

Squeezing your opponent in such endgames requires patience. You want to make progress, but at the same time don't want to compromise by making exchanges. A difficult part in trying to win this endgame is dealing with Black's rook checking your king from the side. You can use one bishop to block, but then the rook could go back to defending the weak pawn.

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4
  • What if the pawns were fixed on f5-g6-h5 instead? Or, on a position like in Evargalo answer, on f6-g7-h6? It seems much harder to attack the weak pawn.
    – justhalf
    Jan 3, 2020 at 8:45
  • @justhalf in that case you could put your king on g5 without having to deal with checks along the 5th rank. Then, if you could maneuver your light-squared bishop to e8 and dark-squared bishop on to the long diagonal, you'd have an ideal setup.
    – Inertial Ignorance
    Jan 3, 2020 at 9:54
  • How to kick black king out of f6 or h6, preventing white king to be at g5?
    – justhalf
    Jan 3, 2020 at 11:20
  • If the king's on f6, put your dark-squared bishop on the long diagonal, checking it. If the king's on h6, put the bishop on f8.
    – Inertial Ignorance
    Jan 3, 2020 at 19:18
8

As a complement to previous answers, notice that although this endgame should be a theoretical win for the bishops, it is not as straightforward a technical task as one might think.

Even at the highest level, in a World Championship Match, Black has been able to save his skin. The stakes were very high, since this rapid game was played during the tiebreak when the players were still tied.

 [FEN ""]
 [Event "Carlsen - Karjakin World Championship Match"]
 [Site "New York, NY USA"]
 [Date "2016.11.30"]
 [EventDate "2016.11.11"]
 [Round "13.2"]
 [Result "1/2-1/2"]
 [White "Magnus Carlsen"]
 [Black "Sergey Karjakin"]
 [ECO "C50"]
 [WhiteElo "?"]
 [BlackElo "?"]
 [PlyCount "167"]

 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.O-O Nf6 5.d3 O-O 6.a4 a6 7.c3 d6
 8.Re1 Ba7 9.h3 Ne7 10.d4 Ng6 11.Nbd2 c6 12.Bf1 a5 13.dxe5 dxe5
 14.Qc2 Be6 15.Nc4 Qc7 16.b4 axb4 17.cxb4 b5 18.Ne3 bxa4
 19.Rxa4 Bxe3 20.Bxe3 Rxa4 21.Qxa4 Nxe4 22.Rc1 Bd5 23.b5 cxb5
 24.Qxe4 Qxc1 25.Qxd5 Qc7 26.Qxb5 Rb8 27.Qd5 Rd8 28.Qb3 Rb8
 29.Qa2 h6 30.Qd5 Qe7 31.Qe4 Qf6 32.g3 Rc8 33.Bd3 Qc6 34.Qf5
 Re8 35.Be4 Qe6 36.Qh5 Ne7 37.Qxe5 Qxe5 38.Nxe5 Ng6 39.Bxg6
 Rxe5 40.Bd3 f6 41.Kg2 Kh8 42.Kf3 Rd5 43.Bg6 Ra5 44.Ke4 Rb5
 45.h4 Re5+ 46.Kd4 Ra5 47.Kc4 Re5 48.Bd4 Ra5 49.Bc5 Kg8 50.Kd5
 Rb5 51.Kd6 Ra5 52.Be3 Re5 53.Bf4 Ra5 54.Bd3 Ra7 55.Ke6 Rb7
 56.Kf5 Rd7 57.Bc2 Rb7 58.Kg6 Rb2 59.Bf5 Rxf2 60.Be6+ Kh8
 61.Bd6 Re2 62.Bg4 Re8 63.Bf5 Kg8 64.Bc2 Re3 65.Bb1 Kh8 66.Kf7
 Rb3 67.Be4 Re3 68.Bf5 Rc3 69.g4 Rc6 70.Bf8 Rc7+ 71.Kg6 Kg8
 72.Bb4 Rb7 73.Bd6 Kh8 74.Bf8 Kg8 75.Ba3 Kh8 76.Be6 Rb6 77.Kf7
 Rb7+ 78.Be7 h5 79.gxh5 f5 80.Bxf5 Rxe7+ 81.Kxe7 Kg8 82.Bd3 Kh8
 83.Kf8 g5 84.hxg6 1/2-1/2

White pieces were played by a grandmaster who is considered as one of the very best endgame players in History.

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  • 1
    It's very hard to use an engine to tell whether the endgame in this example is "harder" from a technical standpoint, since the eval is about the same. But I'd reckon it's more of a challenge, since the g-pawn is a bit more difficult to attack for white than a pawn at f7 is. In any sense, the point is worth making since no computer can tell us how difficult a win is.
    – Scounged
    Jan 2, 2020 at 15:53
  • 2
    While Karjakin chose a better defense since it made getting to g7 very difficult, I just read David Navara's comments to the game in ChessBase, and Karjakin was dead lost at least three times, and I confirmed this with Stockfish (one line was +93, for example). So, the general conclusion that this should be won seems to hold.
    – PhishMaster
    Jan 3, 2020 at 14:39
7

Of course, this should be a win.

Here is how future GM Robert Cvek did it as a 2265-rated player starting at move 33. The position is not exactly the same, but it is pretty close.

He struggled for a little bit in the beginning, but then, he managed to bring his king up using the bishops to block the rook checks as Initial Ignorance mentioned, and then it was over.

 [FEN ""]
 [Event "CZE-ch U20"]
 [Site "Usti nad Labem"]
 [Date "1996.??.??"]
 [Round "6"]
 [White "Cvek, Robert"]
 [Black "Neuman, Petr"]
 [Result "1-0"]
 [ECO "E62"]
 [WhiteElo "2265"]
 [BlackElo "2215"]
 [PlyCount "173"]
 [EventDate "1996.??.??"]
 [EventType "tourn"]
 [EventRounds "9"]
 [EventCountry "CZE"]
 [EventCategory "3"]


 1. Nf3 Nf6 2. d4 g6 3. g3 Bg7 4. Bg2 O-O 5. O-O d6 6. c4 c6 7. Nc3 Qa5 8. a3 Be6 9. Nd2 Qa6 10. d5 cxd5 11. cxd5 Bd7 12. Nb3 Rc8 13. e4 b5 14. Be3 Qb7 15. Bd4 a5 16. e5 dxe5 17. Bxe5 b4 18. axb4 axb4 19. d6 Rxa1 20. Bxb7 Rxd1 21. Nxd1 Re8 22. dxe7 Bb5 23. Bd6 Bxf1 24. Kxf1 Nfd7 25. Ne3 Bxb2 26. Nd5 Bf6 27. Nc5 Kg7 28. Nxd7 Nxd7 29. Bxb4 Nb6 30. Nxb6 Bxe7 31. Bc6 Rb8 32. Bxe7 Rxb6 33. Bf3 f6 34. Bc5 Rb5 35. Be3 Rb2 36. Bd5 Rb5 37. Bc6 Rb2 38. Kg2 Ra2 39. Bd5 Ra5 40. Bf3 Ra2 41. g4 h6 42. h4 Ra5 43. Kg3 Rb5 44. Be2 Ra5 45. Kf3 Rd5 46. Ke4 Ra5 47. Bd4 g5 48. Kf3 Ra3+ 49. Kg2 Kg6 50. Be3 Kg7 51. Bc4 Rc3 52. Bd5 Rd3 53. Be4 Ra3 54. Bf5 Rb3 55. Bc5 Rc3 56. Bd6 Rc6 57. Bg3 Rc4 58. f3 Ra4 59. Be4 Ra2+ 60. Kh3 Re2 61. Bd6 Rb2 62. Kg3 Rb6 63. Bc7 Rb3 64. Kh3 Ra3 65. Bg3 Rb3 66. Kg2 Rb2+ 67. Kf1 Ra2 68. Bd3 Rb2 69. Be2 Rb4 70. h5 Rb3 71. Kf2 Ra3 72. Bc4 Rc3 73. Bd5 Rd3 74. Be4 Ra3 75. Ke2 Rb3 76. Bd3 Ra3 77. Ke3 Rb3 78. Kd4 Ra3 79. Be4 Ra5 80. Bd6 Rb5 81. Bc5 Ra5 82. Kd5 Rb5 83. Kc6 Ra5 84. Bd6 Ra6+ 85. Kd7 Ra7+ 86. Ke8 Ra5 87. Bf8+ 1-0
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-4

I would say the engine is just an engine not perfection. White is up one 'point' for material. Maybe two if you count the two bishops versus rook as another one. Not sure why the engine would say 2.5.

And I see no way to force a win.

With zero pawns black sacs the rook for a bishop == 1/2 1/2

No way for white to force a passed pawn.

Black puts the king on N1 or g8. Black can keep the white king from being a threat. The bishops can not do anything by themselves.

I will defer to @Phishmaster if he has a plan but I do not see any and was fairly good at end games back when I played tournaments.

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  • 6
    A tip for learning why the computer evaluates this as winning for white is to see why your defensive plans for black fails. The main point is that white will use the bishops to restrict the movements of black's rook, and use the king to push it away from the 7th rank. Then white uses the king + lsb to attack f7, forcing an f6 push. After this, use the two bishops to restrict the black rook's movements, and use the fact that once black's rook allows white's dsb to attack f6 it's basically game over.
    – Scounged
    Jan 2, 2020 at 4:33
  • I tried it against an engine and I was squeezed entirely as black, so it is indeed winning, but does, of course, require a lot of patience and technique.
    – SubhanKhan
    Jan 2, 2020 at 6:25
  • 3
    You realize that the engine's score is not solely based on material?
    – Quintec
    Jan 3, 2020 at 1:18
  • 1
    We wouldn't need an engine if it were just counting piece values.
    – Apollys supports Monica
    Jan 3, 2020 at 2:08
  • Yet there is no obvious positional advantage nor way to win.
    – yobamamama
    Jan 3, 2020 at 3:06

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