Originally posted by bikingviking
It is said that in 9 of 10 situations the Bishop is better. (Perhaps exaggerated). It can swiftly move to many squares. BUT! It can only control squares of one color. Some textbooks rate the bishop as 3.5 pawns and the knight as 3 pawns.
2 bishops or 2 knights togheter cooperate well (the knights can protect each other).
Some textbooks say theat ...[text shortened]... thinking process. Also could that information easily qualify as "mainly an accademic knowledge".
K+B v K+N is a dead draw, checkmate is not possible. With K+R v K+N checkmate, or at least helpmate, for the side with the knight is possible:
Checkmate is not possible for the side with the bishop in K + B v K + R:
here black is forced to interpose with the rook and after white takes he's got a draw, but there is no win with K + B v K.
If black has a pawn either piece can checkmate, again this is a help mate, there's no way of forcing this:
So is the knight better? It can beat a rook but a bishop can't. In general bishops are better in open positions when they can control diagonals, knights are better in closed positions when the bishop's are hemmed in by pawns, but the knights are still mobile.
Here are a couple of endings to illustrate this. In the first one black's knight wins because the white bishop has little scope:
Game 1060430
[FEN "8/p2n1p2/1p3k1p/2p5/2PpPKPP/1P6/P3B3/8 w - - 1 37"]
38. g5 hxg5 39. hxg5 Kf6e6 {If white tries 39. Bg4+ and swaps pieces he can find himself stuck as his king has to stay in touch with the d pawn} 40. Be2d3 {The bishop is wasted as a blockader here, it may as well be a pawn} Nd7e5 41. Bd3e2 Ne5g6 {Driving white's king back} 42. Kf4f3 Ke6e5 43. Be2d3 Ng6f4 44. Bd3f1 Nf4e6 {Now white is losing a pawn} 45. Kf3g4 Ke5xe4 46. Bf1g2 {White can't stop the pawn without giving up his bishop so he tries to make a passed pawn of his own} Ke4e3 47. Bg2d5 d3 48. Bd5xe6 fxe6 49. g6 d2 50. g7 d1=Q {Black promotes with check, but even with white's king on g5 promoting wouldn't help black as his king and pawn are in a line} 51. Kg4g5 Qd1g1 52. Kg5f6 e5 {White resigned in another ten moves. I can give up my queen to stop the pawn as I have another passed pawn.}
In this one the bishop wins because it can protect a passed pawn from a distance. It's a good demonstration of how the short range of the knight can make it a liability:
Game 1388116
[FEN "8/p2Pk3/1p4p1/7p/2P1p3/6PB/n2K1P1P/8 w - - 0 43"]
44. Kd2e3 Na2c3 {Black wants to keep his pawn} 45. Ke3d4 Nc3d1 {He wants to keep his knight even more} 46. Kd4d5 {If I take the pawn he can fork my king and bishop and I'll lose the passed pawn as well} a5 {This is a passed pawn and passed pawns should be pushed, but the timing's out, it's better to keep in on a7 as then his central pawn is more of a threat because I take longer over eliminating the b pawn} 47. Kd5c6 Ke7d8 48. Kc6xb6 Nd1xf2 49. c5 {The bishop has done it's job, the pawns are now more important} Nf2xh3 {Pushing his own pawn would make more sense} 50. c6 Nh3g5 {This is the problem, the knight is just can't get across the board fast enough.} 51. c7 Kd8xd7 52. Kb6b7 Kd7d6 53. c8=Q {Black played on for another 15 moves and resigned when I'd taken his two passed pawns} 1-0
Pawns on the edge of the board can be a real asset in an ending, don't think the are
necessarily worse than the ones in the centre of the board. The assessment of how good or bad any of these things are depends on all the pieces on the board. It's the whole position that matters, not just whether you've got a knight or a bishop.