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Normal Topic What about R and two connected pawns versus 2 Bs? (Read 2890 times)
Chevalier
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Re: What about R and two connected pawns versus 2 Bs?
Reply #3 - 05/31/08 at 11:11:05
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Bonsai: Judging from your post, it looks like the placement of both sides kings are an important factor in this endgame - particularly the defending side. For example, if the defending side's king is cut off from the connected passed pawns by the opposing rook, then obviously the attacking side's winning chances will be much higher. 

I also concluded that a knowledge of rook+pawn vs. bishop endings is essential when analysing these endgames.
  
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Re: What about R and two connected pawns versus 2 Bs?
Reply #2 - 05/30/08 at 06:47:22
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I have never seen this endgame before, neither in games nor in books, but from the top of my head, I think your conclusions sound logical. All I can add is that the position with Kd5, Rg4, c6 vs Kc8, Bh2 is a pretty famous theoretical draw named after someone whose name I can't recall right now... It only works with a c (or f) pawn, though, and the bishop must be at the right colour (that is, opposite of the pawn's promotion square).
  
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Smyslov_Fan
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Re: What about R and two connected pawns versus 2 Bs?
Reply #1 - 05/30/08 at 04:09:52
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I know from Botvinnik's book on the endgame (and sevral subsequent ones) that there are several cases in which a single bishop can stop a Rook and pawn, so adding a second B should make the resulting positions even more difficult to win. 

This is a great general question and I look forward to seeing what others will say.  I would rather have the R and pawns of course, but I don't know of a specific technique to advance the pawns without getting perpetually harrassed by the defending Bishops.I even wonder if having the pawns connected in this case may be a slight disadvantage compared to having them separated by more than three files (cf B vs 2 pawns).

Anyway, those are my first impression, but again, this is a rich topic and should be fun to work out!
  
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Bonsai
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What about R and two connected pawns versus 2 Bs?
05/29/08 at 20:15:34
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I've been recently looking at some variations of the Botvinnink semi-slav that have the potential to lead to a rook + 2 connected pawns (not particularly advanced) versus 2 bishops. At this point I realised I had absolutely no clue how this position is to be evaluated (okay, clearly the side with the rook + 2 pawns has all the winning chances, but how realistic are they?).

At first I thought this might be covered in endgame books, but it isn't and of course there's one piece too many to be in the tablebases.

Well, in the end I decided to search my database and I only found 9 games in total! However the first one was immediately quite fascinating and showed an interesting defensive idea:
Roeder,G - Schawelka,K [A00]
Bayern-chB Krumbach (4), 1973
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64.c6 Bxd5+ 65.Kxd5 Bh2 66.Rf8+ Kc7 67.Rf3 Kc8 68.Rh3 Bf4 69.Rh4 Bg3 70.Rg4 Bh2 71.Kc5 Be5 72.Rg5 Bf4 ½-½

Now, in this position 
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actually the move 65...Bh2 was a mistake and the correct way to draw was 65...Kc8. The way for white to win was (according to the tablebase): 65...Bh2 66.Rh7 Bg3 67.Rg7 Bf4 68.Rg4 Bh6 69.Ra4 Bg5 70.Ra8+ Kc7 71.Ra7+ Kc8 72.Rf7 Bd2 73.c7 Kb7 74.Kd6 Ba5 75.Rg7 Bb6 76.c8=Q Kxc8 77.Kc6 Well, a very clever maneuver by white, but it is quite hard to tell when this sort of thing works (without resorting to a tablebase anyway).

Hence maybe that this position in the 65...Bh2 variation 
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was winning maybe just came down to the fact that either white gets to play Kd6 in the line 72...Bd2 73.c7 Kb7 74.Kd6 or alternatively if black prevents that by 72...Bh4 (with the idea Bh4-g3) gets to maneuver his king to b6: 72...Bh4 73.Kc5 Bg3 74.Kb6 Kd8 75.c7+.

In the actual game however black found several only moves, including the following one to prevent the Kc5-b6 plan from succeeding:
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71.Kc5 Be5 72.Rg5 Bf4

The key point being tht 72.Kb6 could have been countered with Bc7+.
Really, after the sacrifice of one bishop it all comes down to whether white can get his king onto one of the squares where it can protect the pawn if (or after) it advances. Fascinating...

Another example where it would not have worked is this endgame:
Maiorov,N (2516) - Onischuk,V (2469) [E62]
Rector Cup m Kharkiv UKR (7), 23.03.2007
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56.Ke3 Rb4 57.Ke4 Kf7 58.Ke3 Ke6 59.Bc3 Rh4 60.Bd4 f5 61.Ba6 Rh3+ 62.Kf2 Kf7 63.Bc4+ Kg6 64.Bb5 g4 65.Be2 Kg5 66.Bb6 Rh2+ 67.Kf1 Rh8 68.Bc5 Re8 69.Kf2 f4 70.Bb6 Rb8 71.Bd4 Rb4 72.Bc3 Ra4 73.Bd2 Ra2 74.Ke1 Ra3 75.Bb5 g3 
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76.Bc6 Kf5 77.Ke2 Ra2 78.Bf3 Ke5 79.Kd3 Ra3+ 80.Ke2 Kf5 81.Bc1 Ra2+ 82.Bd2 Kg5 83.Kd3 Ra4 84.Bc6 Ra6 85.Bb7 Rb6 86.Bf3 Rd6+ 87.Ke2 Rd4 88.Bc3 Ra4 89.Bd2 Kh4 90.Bc6 Rd4 91.Bb7 Kh3 92.Be1 Ra4 93.Kf3 Ra1 94.Bb4 Rf1+ 95.Ke2 g2 96.Bc5 Kg3 0-1

At the point where I inserted the diagram, the sacrifice Bxf4 doesn't work, because 76.Bxf4 Kxf4 77.Kf1 Rc3 78.Ba6 Kg4 79.Bb7 Kh3 80.Be4 Kh2 wins quite easily for black.

Another game where black tried to implement this defence (but failed due to a little trick based on a pin) is
Beliavsky,A (2645) - Haba,P (2515) [D17]
MK Cafe Cup-A Koszalin (8), 10.08.1998
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62.f6 Bxf6 63.Rf4 Bd1+ 64.Kh4 Kg7 65.Rxf6 Be2 66.Kg3 Bd3 67.Kf4 Bb1 68.Rd6 Bc2 69.Kg4 Be4 70.Rd4 Bc2 71.Rd7+ Kg6 72.Rd6+ Kg7 73.Kh5 1-0

Another case where the side with rook + 2 pawns avoided this idea is the following game, here the rook-side managed to avoid having the opposing king controlling the promotion square:
Nasikan,N - Zhukov,S [C34]
Kurass mem op 1st Kiev (6), 27.06.2002
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65.Kc2 Rf3 66.Bg7 Kc6 67.Be5 Kb6 68.Bd3 Ka5 69.Bd6 c4 70.Bc7+ Ka4 71.Be4 Rf2+ 72.Kb1 Kb3 73.Kc1 Rf1+ 74.Kd2 c3+ 75.Ke2 Rf6 76.Kd3 Rh6 77.Bd5+ Kb2 78.Be5 Rh5
[fen=8/8/8/3BB2r/1p6/2pK4/1k6/8]
79.Bxc3+ bxc3 80.Be4 c2 81.Ke2 c1Q 82.Kf3 Kc3 0-1

So I guess the main question is can white avoid that the sacrifice happens under the right conditions? And if not, can one avoid being forced back that far in the first place?

One of the possible defences for black against being forced too far back might be the following approach, where the two centralized bishops try to prevent white from getting his king to support the pawns:
Vaulin,A (2492) - Motylev,A (2532) [E63]
Bydgoszcz Bank Pocztowy op Bydgoszcz (10), 21.07.1999
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61.Ke3 Ke6 62.Rh4 Bg2 63.Kf2 Bd5 64.Ke3 Bg2 65.Rg4 Bf1 66.b6 Kd5 67.b7 Ba6 68.Rb4 Bxb7 69.Rxb7 Kxc5 70.Ke4 Bd6 71.Rb1 Kc6 72.Rc1+ Kb7 73.Kd5 Bc7 74.Rb1+ Ka8 75.Kc6 Bb8 76.Rb7 Ba7 77.Kc7 Be3 78.Rb8+ Ka7 79.Rb4 Ka8 80.Re4 Bf2 81.Re8+ Ka7 82.Re2 ½-½

An example, where both sides pretty much still have all options is
Atalik,S (2586) - Georgiev,V (2525) [D45]
Corus B Wijk aan Zee NED (7), 20.01.2007
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61...Bc7 62.Rd2 Ba5 63.Rb2 Kc7 64.Kf4 Kc6 65.Kg5 Bd8+ 66.Kg6 Bc7 67.Kf6 Bc4 68.Rc2 Kc5 69.e5 Bd8+ 70.Kg7 Bg5 71.e6 Kd4 72.f4 Bh4 73.f5 Bb3 74.Rh2 Bg3 75.e7 Ba4 76.Re2 Be5+ 77.f6 1-0
I guess the black bishops got a bit tangled up and got in the way of the king being ideally positioned.

Well, an interesting topic, do any of you have some more general conclusions? Or do you know of some theoretical conclusions on this topic?
  
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