A critical endgame in the French Winaver

Question

This endgame may even be critical of the entire variation. Stockfish 13 on move 34 depth 70/94 11.3 M of six men tablebases suggest a line that lead to the following endgame.

[FEN "8/2k5/1p4bP/3p4/8/4B3/1KP2P2/8 w - - 0 1"]

I tried with Houdini 6.02 and it give a fixed score of 1.49 , but on the second iteration ( after lot of depth and lot of moves) evaluation started going up. It suggest a deep win , but is really true? After all , Black may have a better defense, or may be able to reach the 50 move rule. What happens with perfect play? I suspect only Stockfish 13 running on DruDru technology on depth 70 ( or even higher!)with 7 men tablebases is able to give a definite answer.

Answer 1

The position is a draw, but not as easy as I first thought.

At first this looks like a simple fortress for Black.

Black needs to play...b5 : anyway, White can force it by bringing the wK to f4 (after c2-c3). Black has to react with ...Ke6 to prevent a trivial win on the kingside, and thus to push ...b5 to not let this pawn hanging.

Then the bB holds the h7-b1 diagonal and the bK defends against wK invasions:

• Against wKf4, we play ...Ke6. No invasion through the kingside.

• Against wKb4, we play ...Kc6. Instead, allowing wKc5 would soon lead to zugzwang: b5, d5 and h7 are three weaknesses, one too many for the bK and bB.

• And just one subtelty: against wKa5 we play ...Bd3! to prevent the only possible plan for White : invasion through the a-file and the 8th-rank:

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[FEN "8/8/2k3bP/1p1p4/1K1B4/2P2P2/8/8 w - - 0 1"]

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Now 1.Ka5!? starts the plan Ka5-a6-a7-b8-c8-d8-e8-f8-g8 ! We cannot stop the wK on c8 or e8 because of zugzwang, so we need to react now:

1...Bd3! 2.Be3 Kb7! 3.Bd4 Kc6 4.Ka6? b4! (reduces the number of pawns) 5.Ka7 bc3 4.Bc3

White will certainly win the Pd5 through zugzwang, but Black doesn't care : the resulting B+f,h vs B is a trivial draw.

[FEN "8/5k1b/7P/8/3B1K2/5P2/8/8 w - - 0 1"] 

Black just waits with, e.g., Bg8-h7-g8

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Edit : White can try to improve on this plan by placing her bishop on b4 and reaching this position (with Pf4 rather than Pf3) :

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[FEN "8/1k6/7P/Kp1p4/1B3P2/2Pb4/8/8 w - - 0 1"]

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Now:

If it is White to move, he can lose a tempo by 1.Bf8 Kc6 2.Be7 Kb7 3.Bb4, since 2...Bh7 3.Ka6 progresses

So let's consider it's Black's move. A bishop move loses immediately, so the two tries are 1...Kc6 holding b5 or 1...Ka7 preventing breakthrough down the a-file.

I believe White has chances in both cases:

1...Ka7 2.f5! is a surprising deflection that exploits the bK being so far from h7: 2...Bxf5 3.Kxb5 Kb7 4.Kc5 Be4 5.Kd6 and White wins with Kg7 and h7 - after replacing the bishop on d4 to prevent an exchange of the last pawn.

1...Kc6 2.Ka6 (there is no ...b4 now) 2...Bh7 3.Ka7 Kc7 4.Ba5 Kc6 5. Kb8 Bf5 6.Bb4

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[FEN "1K6/8/2k4P/1p1p1b2/1B3P2/2P5/8/8 w - - 0 1"]

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Now :

• 6...Kd7? 7.Kb7 allows the wK to c5 and leads to the loss of a pawn (and the game) by zugzwang: 7...Bh7 8.Kb6 Bd3 9.Kc5 Ke6 10.Kc6Z

• 6...Bh7? let the wK progress along the 8th rank: 7.Kc8 Bg6 8.Kd8 and the wK reaches g7, winning again.

In both cases White wins, yet Black still has a draw with either the passive 6...Kb6! denying any more progress for the wK, or 6...d4! 7.cd4 Kd5, aiming for counterplay. Thanks to @Scounged for checking this with Stockfish 13.

Answer 2

Here is my analysis of this endgame.

The analysis partially repeats some findings by Evargalo's answer, but as connected variations.

The PGN viewer on this site is a bit awkward in my opinion, so I also created a blog post on my chess.com user site.

The endgame is a win, as long as white prevents the black king reaching c4 (followed by b5-b4), or sacrificing the d5 pawn at the right moment. The general winning approach is to come closer with the king, and if the black king opposes, then the bishop "stings" him away. If black plays Kc6-b5-c4, then white plays (for example) Bd4 and Kd2-e3-f4-e5. If black plays Kd7-e6-f5, then white plays Bd4-g7-f8+ and Kd2-e3-d4-c5. The critical attempt is d5-d4 and K to d5, then white plays Kb2-b3-b4-a5-a6-a7 and then goes to g7 via b8, or he wins the b5 pawn by sacrificing his h7 pawn. But this route is not possible when the black king can close it by bringing the king to c4. Then it is a draw.

You can check the table base wins and draws mentioned in the analysis, for example on shredderchess.com, or on Lichess.

[Title "Analysis"]
[FEN "8/2k5/1p4bP/3p4/8/4B3/1KP2P2/8 w - - 0 1"]

1.c3 $1 {White moves the pawn to a square where it is not attacked.} ( 1.
Bd4 $2 {Let's first look at this move which, slightly surprising, throws 
away the win.} 1...Kc6 2.c3 Kb5 3.Kc1 {what else?} ( 3.Kb3 Bd3 $10 ) 3...
Kc4 4.Kd2 ( 4.Bxb6 Kxc3 {also draws as the white king is too passive.} ) 
4...b5 {The threat is b4.} 5.Ke3 Bb1 ( 5...b4 $2 6.cxb4 Kxb4 7.Kf4 {does 
not draw, the black king is too far away.} ) 6.Bg7 {Moves away from the 
danger zone d4.} ( 6.Kf4 b4 $10 ) 6...Bh7 7.Kf4 d4 $3 {The key move. The 
black king needs the square d5.} 8.Bxd4 ( 8.cxd4 b4 9.Bf8 Kxd4 10.Bxb4 Kd5
11.Kg5 Ke6 {is a table base draw. The pawns are separated by just one 
column, black blocks them on the h7-b1 diagonal. The white king can not 
reach g7.} ) 8...Kd5 $3 ( 8...b4 $2 {is wrong.} 9.cxb4 Kxd4 10.b5 Kc5 11.
Ke5 {and the white king does the job alone.} ) 9.Kg5 Ke6 $10 {This is a 
position where the black king and black bishop block the white king along 
the diagonal h7-b1.} 10.Bg7 Bb1 11.Kf4 Bh7 12.Ke3 Kd5 13.Bf8 {controls b4,
otherwise, black plays Kc4 and b4.} 13...Bb1 {Black waits.} 14.Kd2 Bh7 15.
Kc1 Bg6 16.Kb2 Kc4 17.Bb4 Bh7 18.Kc1 Kd3 19.Kd1 Bg6 20.Ke1 Bh7 21.Kf1 Bg6 
22.Kg2 Ke4 23.Kg3 Bh7 24.Kg4 Ke5 25.Kg5 Ke6 {White has not made progress. 
So, this shows the main drawing idea for black. Notice how the black king 
just has to stay one of the three squares e6, d5 and c4 to prevent that 
the white crosses the Rubicon anywhere on the board. If c3 and b5 
disappear, we get a table base draw. Let's now return to the position after 
1.c3, which, amongst other moves, wins.} ) 1...Kc6 2.Kc1 {Now black has 
three choices.} 2...b5 ( 2...Kb5 {has the same idea as in the 1.Bd4? 
line: Go to c4 and play b5-b4. But here c3 will be protected when the 
black king reaches c4. Or the white king will be placed more active on e3.
} 3.Kd2 Bh7 4.Bd4 Bb1 5.Ke3 Kc4 6.Kf4 $5 ( 6.Bxb6 Kxc3 7.Kf4 {actually 
also wins, because the black king is too far away, but let's execute 
black's idea, to show that it doesn't work.} ) 6...b5 7.Ke5 Bh7 8.f4 Bb1 9.
f5 Bxf5 10.Kxf5 b4 11.cxb4 Kxd4 12.h7 $18 {This is why the idea doesn't 
work.} ) ( 2...d4 {Stockfish's main line after long pondering. It has the 
same idea as 7...d4 in the 1.Bd4? line, but here the black king can not 
reach c4 and black can not exchange the b-pawn against the c-pawn.} 3.Bxd4
$1 ( 3.cxd4 $2 Kd5 4.Kb2 Kc4 {does not win, because the white king is 
bound to b2.} ) 3...b5 4.Kb2 $1 Kd5 5.Kb3 {White has prevented Kc4} 5...
Bh7 6.Kb4 Kc6 ( 6...Bd3 7.h7 Bxh7 8.Kxb5 {is a table base win. The pawns 
are separated by two columns. The black king and bishop can not work 
together harmonically on one diagonal, like g8-a2 or a8-h1, to prevent the
simultaneous advance of both pawns.} ) 7.Ka5 Bd3 8.Be3 {Zugzwang} ( 8.Ka6 
$2 b4+ $10 ) 8...Bh7 9.Ka6 Bd3 10.Ka7 Kc7 11.Bf4+ $18 {The white king will
reach g7, or win b5, leading to above table base win. Let's go back to the 
position after 2...b5.} ) 3.Bd4 {Prevents d4 ideas for the moment and 
frees the way for the white king.} 3...Kd7 4.Kd2 Ke6 5.Ke3 Kf5 6.Bg7 Ke6 
7.Kd4 Kd6 8.Bf8+ {Forcing the king away from the opposition.} 8...Ke6 ( 
8...Kc6 9.Ke5 {and the white king goes undisturbed to g7.} ) 9.Kc5 Bd3 10.
Bg7 {Zugzwang} 10...Bh7 11.Kxb5 {We saw a comparable position where black 
drew with the d-pawn on b5. Here the white king is active and by attacking
the d-pawn, which binds the black bishop, white will slowly push back the 
black king.} 11...Kd6 12.Bf8+ Ke5 ( 12...Kc7 13.Kc5 Be4 14.h7 {leads to 
the already mentioned table base win.} ) 13.Kc6 Ke6 14.Kc7 Kf7 15.Bg7 Ke7 
16.Bd4 Be4 17.Bc5+ {Again forcing the white king to leave the opposition.}
17...Ke6 ( 17...Ke8 18.Kd6 {leads to the main line at a later moment.} ) 
18.Kd8 Bg6 {Preventing Ke8.} 19.Be7 {Zugzwang} 19...Kf7 ( 19...Ke5 20.Kd7 
d4 21.cxd4+ Kxd4 22.Ke6 $18 {The black king is too far away.} ) 20.Kd7 Be4
21.f4 {Otherwise, Bf3 is disturbing.} 21...Bh7 22.Kd6 Be4 23.Bg5 Bh1 24.Ke5
{Now, the black bishop would like to protect both d5 and the diagonal b1-h7
by going to e4, but this runs into c4. But the black king alone can not 
handle the f- and h-pawns.} 24...Bf3 25.f5 Bg2 26.Bf6 {The threat is h7.} 
26...Kg8 27.Bg7 Kf7 28.f6 {Threatening h7 again.} 28...Kg8 29.Ke6 Bh3+ 30.
Ke7 $18 {f7+ can not be prevented.}

Answer 3

According to Stockfish 14.1 NNUE White Wins with C3, though it IS very complicated and it IS necessary to go to depth =. 79 or higher to get it.

Answer 4

Based on the answer of Evargalo, who demonstrates nicely a critical attack line to storm the fortress. Following the bishop on b4 line at "1...Kc6 2.Ka6 (there is no ...b4 now) 2...Bh7 3.Ka7 Kc7 4.Ba5" Black can deviate, counterattacking and modifying to a smaller fortress, with a line like Kd6 5. Kb6 Ke6 6. Kxb5 Kf5 7. Bc7 Kg6 8. Kc6 Bg8 9. Kd6 Kxh6 10. f5 Kg5 11. Ke5 Bh7 12. Bd8+ Kg4 13. f6 Bg8 14. Kd6 Kf5 15. Ke7 Kg6 drawing.

Answer 5

According to Stockfish 14.1 NNUE depth =90 the position is evaluated at 4.25, that appears to be a win, yet it may be necessary FinalGen to get a definitive answer.

Answer 6

After long analysis, it seems that Black defense could be broken. But more than 50 moves without pawn moves or captures are necessary at a certain point. With still 8 pieces on the board , and therefore a draw under both FIDE and ICCF rules , though it is not a technical draw.