This position from move 42 of TCEC Season 18 Game 80, with Black to move. Is it a win or a draw?

[FEN "8/1k5p/1P3pp1/K1P2b2/5P1P/8/8/2B5 b - - 0 1"]
  • Black to move , I forgot to say. – Stefano Jul 3 at 18:29

The key point in this endgame is that the bishops are of opposite colours. It is a trivial draw. White is a pawn up but with nothing more than barely competent play by black, white will never be able to advance his pawns. The black king can never be moved from b7 and the black bishop can take station on the diagonal between c6 and h1 making the pawn move c6 impossible. Black will also play h5 at some stage leaving him with only the g6 pawn to protect. The f6 pawn is an irrelevance.

To be able to win an opposite coloured bishop endgame one player has to have two passed pawns separated by a minimum number of files. That isn't the case here. The problem for the side with the extra pawns is that the opposing king and bishop can always blockade the colour of the bishop and the attacking bishop cannot help.

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It is rather easy to just chuck this position into a chess engine to determine the result, but let's try to manually to improve our analysis skills.

Clearly, White is up one pawn with two connected passed pawns. These pawns are threatening to check agter White moves their king to b5, and push dawn the Black king to do so. But these pawns are easily neutralized by Black's light square bishop since the pawn's checking square is protected by it, The Black king can now sit and blockade the pawns, like so.

[FEN "8/1k5p/1P3pp1/K1P2b2/5P1P/8/8/2B5 b - - 0 1"]

1... Be4

White's kingside threats are easy to counter and therefore not a threat at all. Now we can turn our eye to Black's queenside majority. Black can make a passed pawn no matter what White does, but it will never be of any use due to White's dark-squared bishop.

[FEN "8/1k5p/1P3pp1/K1P2b2/5P1P/8/8/2B5 b - - 0 1"]

1... Be4 2. Kb5 h6 3. Be3 g5 4. fxg5 hxg5 5. hxg5 fxg5 6. Bxg5 *

Neither side can advance their pawns for promotion because of the opposite colored bishops. White can try ideas such as protecting their kingside pawns with their bishop and moving their king to the queenside, but Black will always be able to force the exchange of pawns on the queenside before than.

The end effect is that the pawns are practically non-existent, leaving an opposite colored bishop endgame with only kings and them on the board, which are always are a draw, unless a FIDE player runs out of time of course.

All in all, the position is a draw.

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Is it a win or a draw?

The position from the diagram is a dead draw.

How can White win?

[Title "White wins with queenside pawns"]
[StartFlipped "0"]
[fen "8/1k5p/1P3pp1/K1P2b2/5P1P/8/8/2B5 b - - 0 1"]

1...Bg4 2. f5 {No matter how Black captures the pawn, White plays Bb2 and gets the f6 pawn} Bxf5 3. Kb5 Bg4? {I am just setting up the winning position for White, proper defense shall be demonstrated in a separate diagram} 4. c6+ Kb8 5. Bf4+ {That was the point of f5, to vacate f4 square for the bishop}  Kc8 6. b7+ Kd8 7. b8=Q+ 1-0

There are only two ideas that can make White win on the kingside:

[Title "White wins with h-pawn"]
[StartFlipped "0"]
[fen "8/1k5p/1P3pp1/K1P2b2/5P1P/8/8/2B5 b - - 0 1"]

1...Bg4 2. Bb2 Bd7 3. Bxf6 Bc6? 4. h5!+- {With Black king tied to the queenside, only bishop is left to defend, which is why Black may not take, because White king will help the f-pawn to queen, forcing Black to give up the bishop. White bishop easily stops Black's passed h-pawn} Bf3 5. h6 g5 {Sooner or later, Black will have to play this move in order to defend the h-pawn} 6. Bxg5! 1-0 

Similar idea looms in the air:

[Title "White wins with f-pawn"]
[StartFlipped "0"]
[fen "8/1k5p/1P3pp1/K1P2b2/5P1P/8/8/2B5 b - - 0 1"]

1...Bg4 2. Bb2 Bh5? 3. Bxf6 Bg4 4. Be7 Bf3 5. Kb4 Bg2 6. Kc4 Bf3 7. Kd4 Bh1 8. Ke5 Bg2 9. Kf6 Bf3? 10. Kg5 Bh5? 11. f5 {Black loses bishop if he takes the f-pawn, otherwise f-pawn promotes to Queen} 1-0

How can Black hold? What are his plans?

Black needs to:

  1. stop f-pawn from moving
  2. stop h-pawn from moving
  3. stop queenside pawns from rolling

Points 1 and 2 are easily achieved with the pawns placed on g6 and h5. Bishop then needs to be on the b1-h7 diagonal once White plays Kg5 and there will be no way for White to break through. To be ultra safe, we will keep Black's bishop as further away as possible from the White king.

Point 3 is achieved by keeping the bishop on h1-a8 diagonal.

The only question remains if White can somehow overburden Black pieces with piece maneuvers, namely with the king. Bishop is faster than the king, so Black just needs to shuffle the bishop on the relevant diagonal.

Let us put this all together:

[Title "Black holds comfortable draw"]
[StartFlipped "0"]
[fen "8/1k5p/1P3pp1/K1P2b2/5P1P/8/8/2B5 b - - 0 1"]

1...Bd7! {Now White can not perform the queenside pawn roller described earlier} 2. Bb2 h5! {No more h5 ideas} 3. Kb4 Bc6! {Flexibly posting the bishop, so he can shuffle on the required diagonals. F-pawn is irrelevant} 4. Bxf6 Bh1 5. Kc4 Bg2 6. Kd4 Bh1 7. Ke5 Bg2 8. Be7 Bh1 9. Kf6 Be4! {As long as White king attacks the g6 pawn we defend it by shuffling on the b1-h7 diagonal} 10. Ke5 Bh1 {Once White king abandons the g6 pawn, Black switches the bishop back to the h1-a8 diagonal} 11. f5 gxf5 12. Kxf5 Bf3! {Now we just shuffle on the d1-h5 diagonal} 13. Kg5 Bd1 14. Kf5 Be2 15. Ke5 Bf3! {Remember, as soon as White king moves away from the kingside pawns we switch back to h1-a8 diagonal to block the queenside pawns} 16. Kd6 Bh1 1/2-1/2 

Black can play like this forever, he will simply shuffle between the relevant diagonals as shown in this example. White has nothing in this endgame.

If you have any questions leave a comment, I will gladly reply.

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