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Is the following position a win for White or a draw? My Stockfish 14.1 NNUE goes over 2.5 for White, but still does not find a clear win.

[Title "Draw or white win?"]
[fen "8/4b1k1/7p/8/8/1P6/6PP/5B1K w - - 0 1"]
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    When 8-piece tablebases are released, we will have an answer.
    – Lucenaposition
    Commented Aug 5 at 2:16
  • If the pawns were on h3 and/or g4 it would be a draw, as the black king enters via h4, but here white plays g3 and Bh3, cutting off the black king, and then improves their king position. Black can play Bg1 and Bf2 at some point, enforcing h3 and g4, but this takes too much time and meanwhile the b-pawn runs.
    – Nils Lindemann
    Commented Aug 7 at 2:42

2 Answers 2

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Is the following position a win for White or a draw?

It is almost certainly a draw. In opposite coloured bishop endings like this white needs to be able to generate at least two passed pawns at least 3 files apart where one of the pawns is not an a or h pawn with the same colour queening square as the bishop.

That sounds complicated but what it means here is that as white you can only win if you can exchange h pawns. If you exchange your g pawn for black's h pawn then your remaining h pawn is not sufficient for the win because black can always station the king on h8 and exchange the bishop for the b pawn as soon as it moves onto the same colour square.

There is no way that I can see that white can force this. Here is an example position of what white must achieve involving black making no moves or just shuffling back and forth:

[fen "8/4b1k1/7p/7K/6PP/1P1B4/8/8 w - - 0 1"]

The logic behind this position is that:

  1. White must play h4 before playing g4, otherwise white can never get the king to either f5 or h5
  2. Therefore white has to get the king to h5 first to protect the h4 pawn from the bishop before playing g4

In this position white can play g5 and force the exchange of h pawns and can then go on to win.

However if black is allowed a few moves also then black can set up this position:

[fen "8/8/5k1p/7K/6PP/1P1B4/3b4/8 w - - 0 1"]

and white cannot force the exchange of h pawns.

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    Why would White's king go staright for the kingside rather than trying to push the "b" pawn as much as possible?
    – David
    Commented Aug 4 at 22:55
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    Even though another reply has analyzed this position at length with an engine and suggests that White wins, I still think there is value in a human assessment of the position, and explication of the principles. So +1 from me.
    – Laska
    Commented Aug 5 at 4:47
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    An explanation why/where Stockfish is wrong would be interesting
    – JollyJoker
    Commented Aug 5 at 8:51
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    In the second diagram, what does Black to move play? It seems that White can answer with either b4 or g5, which looks like progress to me.
    – Keba
    Commented Aug 5 at 11:18
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    @Keba: From the position in the (last) diagram, I can see no defense for Black. But maybe Brian knows something I don't.
    – Kevin
    Commented Aug 5 at 21:04
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It is a win for white. I ran this through Stockfish 16.1 and managed to reach the end of the game through having the engine actually play the move line it anylyzed as the best one.

If it is White to Move

Black is Checkmated after 56 moves
Here is what happens if it is whites move at the start:

[FEN "8/4b1k1/7p/8/8/1P6/6PP/5B1K w - - 0 1"]

1. Bb5 Kf6 2. Kg1 Kg5 3. Bd7 Bc5+ 4. Kf1 Kf6 5. g3 Kf7 6. Bc8 Kf6 7. Kg2 Kg5 8. Kf3 Bb4 9. Ke4 Bd2 10. Kd5 Ba5 11. Kc5 Bc7 12. Kd5 Ba5 13. Be6 Be1 14. Bd7 Bb4 15. Be6 Bc3 16. h3 Kf6 17. g4 Ke7 18. Bf5 Be1 19. Kc5 Bf2+ 20. Kc6 Be1 21. Kd5 Bd2 22. Kc4 Be3 23. b4 Kd6 24. Bg6 Bf2 25. Kd3 Kc6 26. Be8+ Kd5 27. Ke2 Bd4 28. Kf3 Be5 29. b5 Bc7 30. Bd7 Kd4 31. Bc6 Ke5 32. Kg3 Bd8 33. Bg2 Kf6 34. Bb7 Ke5 35. Bc6 h5 36. Kf3 h4 37. Be8 Ke6 38. Ke4 Bf6 39. b6 Be7 40. b7 Bd6 41. g5 Bh2 42. Bc6 Bc7 43. Bb5 Bb8 44. Bd3 Ba7 45. Bc4+ Ke7 46. Kf5 Kd6 47. g6 Kc5 48. g7 Bb8 49. g8=Q Bg3 50. Bd3 Kd4 51. Qc4+ Ke3 52. Be4 Kf2 53. Qd3 Bh2 54. Bf3 Kg3 55. Qe2 Kxh3 56. Qg2# 1-0

If it is Black to Move

Black is Checkmated after 48 moves
Here is what happens if it is blacks move at the start:

[FEN "8/4b1k1/7p/8/8/1P6/6PP/5B1K b - - 0 1"]

1... Kf6 2. g3 Ke5 3. Kg2 Ke4 4. Kf2 Bb4 5. Bb5 Bc5+ 6. Ke2 Bb4 7. Bc6+ Kf5 8. Kf3 Be1 9. Bd7+ Kg5 10. Ke3 Ba5 11. Kd3 Kf6 12. g4 Ke7 13. Bc8 Bb4 14. Kc4 Be1 15. Bf5 Kd6 16. b4 Bd2 17. Bg6 Be3 18. h3 Bb6 19. Kb5 Bf2 20. Ka6 Kc7 21. Bf5 Bd4 22. b5 Bf2 23. Be4 Bc5 24. h4 Be7 25. g5 hxg5 26. b6+ Kb8 27. h5 Bf8 28. Kb5 g4 29. Kc6 Bh6 30. Kd7 g3 31. b7 Bc1 32. Ke6 Be3 33. Kf6 Kc7 34. Kg6 Bd4 35. h6 Be5 36. h7 Bd4 37. Kf7 Be5 38. Bg2 Bd4 39. Kg8 Kd6 40. h8=Q Bxh8 41. b8=Q+ Kc5 42. Kxh8 Kc4 43. Qb2 Kd3 44. Kg7 Kc4 45. Kf6 Kd3 46. Ke5 Ke3 47. Bf1 g2 48. Qe2#

Either way, white wins.

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    Does this kind of analysis prove mathematically that it's a win for White? Or is it just very likely?
    – Laska
    Commented Aug 5 at 4:48
  • Well I mean stockfish isn't perfect...but it's the best thing or person playing chess...so yes just very very very likely. @Laska
    – Starship
    Commented Aug 5 at 5:37
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    Note that, every time a piece has an opportunity to capture anything, you should be able to look up the resulting position in the tablebase (because it would drop from 8 to 7 pieces). Lichess will display this information automatically (if the opening explorer and tablebase is open). Spot-checking several of the captures and potential captures in both endgames, I wasn't able to find any point where Black can exchange down into a tablebase draw. Stockfish is known to have some issues with fortress positions, but if this is a fortress, it is a very complicated one and I don't see how.
    – Kevin
    Commented Aug 5 at 16:46

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