user2785: My coach showed me a famous game Fisher vs. Taimanov (1971) where Fisher expertly used the bishop's advantage over a knight in an endgame.
[fen ""]
[White "Robert James Fischer"]
[Black "Mark Taimanov"]

1. e4 c5 2. Nf3 Nc6 3. d4 cxd4 4. Nxd4 Qc7 5. Nc3 e6 6. g3 a6
7. Bg2 Nf6 8. O-O Nxd4 9. Qxd4 Bc5 10. Bf4 d6 11. Qd2 h6
12. Rad1 e5 13. Be3 Bg4 14. Bxc5 dxc5 15. f3 Be6 16. f4 Rd8
17. Nd5 Bxd5 18. exd5 e4 19. Rfe1 Rxd5 20. Rxe4+ Kd8 21. Qe2
Rxd1+ 22. Qxd1+ Qd7 23. Qxd7+ Kxd7 24. Re5 b6 25. Bf1 a5
26. Bc4 Rf8 27. Kg2 Kd6 28. Kf3 Nd7 29. Re3 Nb8 30. Rd3+ Kc7
31. c3 Nc6 32. Re3 Kd6 33. a4 Ne7 34. h3 Nc6 35. h4 h5
36. Rd3+ Kc7 37. Rd5 f5 38. Rd2 Rf6 39. Re2 Kd7 40. Re3 g6
41. Bb5 Rd6 42. Ke2 Kd8 43. Rd3 Kc7 44. Rxd6 Kxd6 45. Kd3 Ne7
46. Be8 Kd5 47. Bf7+ Kd6 48. Kc4 Kc6 49. Be8+ Kb7 50. Kb5 Nc8
51. Bc6+ Kc7 52. Bd5 Ne7 53. Bf7 Kb7 54. Bb3 Ka7 55. Bd1 Kb7
56. Bf3+ Kc7 57. Ka6 Ng8 58. Bd5 Ne7 59. Bc4 Nc6 60. Bf7 Ne7
61. Be8 Kd8 62. Bxg6 Nxg6 63. Kxb6 Kd7 64. Kxc5 Ne7 65. b4
axb4 66. cxb4 Nc8 67. a5 Nd6 68. b5 Ne4+ 69. Kb6 Kc8 70. Kc6
Kb8 71. b6 1-0

I want to consider the position at move 45 (with black to move), but move white's bishop to a dark square.  Let's say this position:
[fen "5B2/8/1pnk2p1/p1p2p1p/P4P1P/2PK2P1/1P6/8 b - - 0 1"]

All I've done is move white's bishop from b5 (a light square) to f8 (a dark square).  This seems substantially harder for white to win, and perhaps it's unwinnable for white.
Question: If we move white's bishop to a dark square in the Fisher-Taimanov (1971) bishop vs. knight endgame, can white still win?
I think white cannot win, and if that's correct, then there's an interesting nuance in the position: Fisher didn't simply win because "the bishop is better than a knight", but because he organized his pawns to suit.

user18809: I would say no.
Black's king is doing a very good job at protecting the queenside, with no possible threats on the kingside. Also, the e4 square could be a great source of counterplay for Black. In short, I wouldn't say that White even has an edge in that position. I'd prefer being Black if I could choose. 
Finally, the statement "the bishop is better than the knight" is just meaningless. Even if such an advantage exists, other existing factors in the position will make too big of a difference to apply the general principle. By the way, knights are OFTEN better than "good bishops" at defeating "bad bishops"

user12873: The thing is, with the light-squared bishop White could attack two weaknesses. His bishop could attack Black's g6-pawn while the king could attack the b6-pawn. If the bishop is dark-squared, White has no piece that can get to Black's g6-pawn. He can only attack the one weakness on b6.
Granted, White can attack the b6-pawn with more firepower, but since Black only has to focus on defending that one pawn it isn't too hard to draw. So White probably can't win with the bishop on a dark square.

2785: <p>My coach showed me a famous game <a href="http://www.chessgames.com/perl/chessgame?gid=1044361" rel="nofollow noreferrer">Fisher vs. Taimanov (1971)</a> where Fisher expertly used the bishop's advantage over a knight in an endgame.</p>

<pre><code>[fen ""]
[White "Robert James Fischer"]
[Black "Mark Taimanov"]

1. e4 c5 2. Nf3 Nc6 3. d4 cxd4 4. Nxd4 Qc7 5. Nc3 e6 6. g3 a6
7. Bg2 Nf6 8. O-O Nxd4 9. Qxd4 Bc5 10. Bf4 d6 11. Qd2 h6
12. Rad1 e5 13. Be3 Bg4 14. Bxc5 dxc5 15. f3 Be6 16. f4 Rd8
17. Nd5 Bxd5 18. exd5 e4 19. Rfe1 Rxd5 20. Rxe4+ Kd8 21. Qe2
Rxd1+ 22. Qxd1+ Qd7 23. Qxd7+ Kxd7 24. Re5 b6 25. Bf1 a5
26. Bc4 Rf8 27. Kg2 Kd6 28. Kf3 Nd7 29. Re3 Nb8 30. Rd3+ Kc7
31. c3 Nc6 32. Re3 Kd6 33. a4 Ne7 34. h3 Nc6 35. h4 h5
36. Rd3+ Kc7 37. Rd5 f5 38. Rd2 Rf6 39. Re2 Kd7 40. Re3 g6
41. Bb5 Rd6 42. Ke2 Kd8 43. Rd3 Kc7 44. Rxd6 Kxd6 45. Kd3 Ne7
46. Be8 Kd5 47. Bf7+ Kd6 48. Kc4 Kc6 49. Be8+ Kb7 50. Kb5 Nc8
51. Bc6+ Kc7 52. Bd5 Ne7 53. Bf7 Kb7 54. Bb3 Ka7 55. Bd1 Kb7
56. Bf3+ Kc7 57. Ka6 Ng8 58. Bd5 Ne7 59. Bc4 Nc6 60. Bf7 Ne7
61. Be8 Kd8 62. Bxg6 Nxg6 63. Kxb6 Kd7 64. Kxc5 Ne7 65. b4
axb4 66. cxb4 Nc8 67. a5 Nd6 68. b5 Ne4+ 69. Kb6 Kc8 70. Kc6
Kb8 71. b6 1-0
</code></pre>

<p>I want to consider the position at move 45 (with black to move), but move white's bishop to a dark square.  Let's say this position:</p>

<pre><code>[fen "5B2/8/1pnk2p1/p1p2p1p/P4P1P/2PK2P1/1P6/8 b - - 0 1"]
</code></pre>

<p>All I've done is move white's bishop from b5 (a light square) to f8 (a dark square).  This seems substantially harder for white to win, and perhaps it's unwinnable for white.</p>

<p><strong>Question</strong>: If we move white's bishop to a dark square in the Fisher-Taimanov (1971) bishop vs. knight endgame, can white still win?</p>

<p>I think white cannot win, and if that's correct, then there's an interesting nuance in the position: Fisher didn't simply win because "the bishop is better than a knight", but because he organized his pawns to suit.</p>
 18809: <p>I would say no.</p>

<p>Black's king is doing a very good job at protecting the queenside, with no possible threats on the kingside. Also, the e4 square could be a great source of counterplay for Black. In short, I wouldn't say that White even has an edge in that position. I'd prefer being Black if I could choose. </p>

<p>Finally, the statement "the bishop is better than the knight" is just meaningless. Even if such an advantage exists, other existing factors in the position will make too big of a difference to apply the general principle. By the way, knights are OFTEN better than "good bishops" at defeating "bad bishops"</p>
 12873: <p>The thing is, with the light-squared bishop White could attack two weaknesses. His bishop could attack Black's g6-pawn while the king could attack the b6-pawn. If the bishop is dark-squared, White has no piece that can get to Black's g6-pawn. He can only attack the one weakness on b6.</p>

<p>Granted, White can attack the b6-pawn with more firepower, but since Black only has to focus on defending that one pawn it isn't too hard to draw. So White probably can't win with the bishop on a dark square.</p>
