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I reached this position in a game. I don't think either side can force a win?

White to move.

[FEN "8/pB6/P7/4pK2/3b1p2/5P2/3k4/8 w - - 0 1"]
5
  • FWIW, Fritz 11 SE thinks this position is a effectively a draw. If we back up one ply, Black might have chances playing 1 ... Bf6 or 1 ... Bg3 instead of 1 ... Kd7. The engine evaluates both of those moves as -1.89 (after searching 30 plies deep), but the King move evaluates as -0.12. Of course, even making one of the Bishop moves, White will still need to make some kind of mistake somewhere down the line in order for Black to get a win.
    – patbarron
    Jul 10 at 6:34
  • yes it is a draw Jul 10 at 10:35
  • Just an addition: Endgames with opposite-colored bishops are frequently drawn. (In this case, both sides simply play "nothing".) Mostly you win a) with two passers on opposite wing, b) with one passer that can't be blocked by the king. Jul 11 at 8:16
  • No offense, but this question could easily be answered by hooking this up to any engine...
    – fartgeek
    Jul 11 at 14:22
  • @fartgeek i tried but im not smart enough. Jul 13 at 15:27
3

In addition to the other answer, you can see the results from Stockfish 13+ NNUE at depth = 78 (half moves, so 39 moves). All lines are evaluated at 0.0 (Position on Lichess).

This is a draw (with perfect play). There is no way to make progress. There's always enough time for the other side to hold against your attempt to make progress.

Note: diagrams below have a1 in the lower left.

[FEN "8/pB6/P7/4pK2/3b1p2/5P2/3k4/8 w - - 0 1"]

1. Bc6 Ke3 2. Bb7 Bc3 3. Be4 Bb2 4. Bd5 Ba1 5. Ke6 Kf2 6. Kf5 Bd4 7. Bb7 Kg3 8. Bd5 (1. Be4 Ke3 2. Bb7 Bc3 3. Be4 Bb2 4. Bd5 Ba1 5. Ke6 Kf2 6. Kf5 Bd4 7. Bb7 Kg3 Bd5 Bb2) (1. Ba8 Kd3 2. Be4+ Ke3 3. Bb7 Bc3 4. Be4 Bb2 5. Bd5 Ba1 6. Ke6 Kf2 7. Kf5 Bd4 8. Ke4 Ke2) (1. Ke6 Ke3 2. Bd5 Kd3 3. Be4+ Kc4 4. Kf5 Kc5 5. Bd3 Kb6 6. Ke4 Bc3 7. Kd5 Kc7 8. Bf1 Bd4)
     

Regarding bringing the Black king to b5 or a5 I would like to see the line. If the line is centered around "hoping White makes a mistake" that is fine for practical chances as long as it doesn't objectively lose, though objectively the line would still seem to be a draw. And White can't capture on e5 or f4.

For example, in the line below, once the Black king reaches b5 then White has two ways to hold with (5. Bd3+) and (5. Bb7). These are the only two moves. Black's king can reach a5 but White's king can blockade on e4.

[FEN "8/pB6/P7/4pK2/3b1p2/5P2/3k4/8 w - - 0 1"]

1. Ke6 Ke3 2. Bd5 Kd3 3. Be4+ Kc4 4. Kf5 Kb5 5. Bd3+ Kc6 6. Be4+ Kc5 7. Bd3 {Eval = 0.0 at depth 55.} (5. Bb7 Ba1 6. Ke4 Ka5 7. Kf5 Kb4 8. Be4 Bd4 9. Bd3 Kc3 10. Be2 Kb3 11. Bd1+ Kb4 12. Be2 Bc3 {Eval = 0.0 at depth 55.}) (5... Ka5 Ke4 {White can respond with 6. Ke4, Be2, Bf1, Bc4, and Ke6 with each line receiving an eval of 0.0, depth = 70.})
2

Yes it is a draw. The most basic thing about this game is that only black can push(or try) for a win. So if I see this position from black prospective only one idea come to my mind for pushing:-

Bringing black king to b5 or a5 and then pushing e4 hoping white will capture from pawn or from bishop but because of white king having squares like e4,d3,d5,f5 white can capture that pawn from king which is a draw.

2

This is an easy draw thanks to the opposite-colored Bishops, each of which defends all of its own side's pawns and cannot attack the opponent's, so neither side can make any progress. Black's extra pawn is academic.

Black to move can force the draw by just moving the King "randomly", keeping the Bishop on d4 where it already defends both the d4 and e5 pawns (with the e5-pawn in turn holding f4). White can make no progress as long as Black avoids the blunder of playing Kc5 when White's King can capture a7.

White can start with Ke4 and then shuffle the Bishop between b7 and c8, unless the Black King moves to attack c8 when White can instead play Bd5 (since the Black King can't attack both c8 and a6) and back to Bb7. Black can make no progress.

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