"They have equal value which worths 3pts." ++ No. N = 3.05 P < B = 3.33 P, See Table 6
You should study the basic checkmates KBB vs. K, KBN vs. K, KNN vs. KP.
Then you will understand why B > N.
Roughly B = N + tempo.
After 1 e4 e5 2 Nf3 Nc6 3 Bb5 a6, white has a choice between keeping the bishop but losing the tempo with 4 Ba4, or losing the bishop but gaining the tempo 4 Bxc6.
Closed positions favor knights and open positions tend to favor bishops. Mathematically place one of every piece on one of the central squares, then count how many spaces it can go.
Thanks tygxc.
Apart from the computer evaluation, a knight's endgame can be more pleasurable for its devious combinations. Capablanca clearly agreed. But bishops can be surprising as well, especially against rooks, as pawn promotion supports, and to create discovered checks/attacks and complex multi-pin situations. Overall I prefer the bishop pair, but a lone knight over a lone bishop. It all depends on pawn structure too, and the resulting mobility it affords.
I have written this in another forum thread, but I'm reposting it -
Both can be said as equally powerful peices. Knight (
) can move in a L shape and most importantly can jump over pieces which other pieces apparently can't. Considering this advantage, we can say that knight is an essential piece. Bishop (
) on the other hand is more useful in checkmates and open positions as it allows us to move it diagonally forward or backwards. Considering this benefit, we can say it is a powerful peice. Even the strongest peice (Queen 
) has the quality of a bishop (and Rook 
but excluding it as it's not related to this topic). So seeing these things, we can say both are major and prime pieces in chess. That is -
As I have learnt the values of chess peices, it was written that both knight () and Bishop () are given 3 points each. Two bishops can give a checkmate, two knights can't.
I prefer bishops in an open position and endgames, but in closed positions knights can move much more freely, even penetrate pawn blockades. There is a time and a place for both.
@5
"a lone knight over a lone bishop"
++ No. A bishop dominates a knight in an endgame.
They have equal value which worths 3pts. Equal power of strategy So, I.m asking your opinion which one do you prefer? In my case, I prefer a knight because its flexibility. A Knight can jump other pieces, can go all squares and more suitable to fork attack. Someone would prefer bishop because a bishop goes further and faster than a knight/