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Bishop or Knight: Which is more valuable?

You guys do realize that the second position shown here is not possible, the B cannot get to b8 with the a and c pawn unmoving. Also unless you want to believe the R on a8 was captured by a Knight and that Knight escaped to b6 (highly unlikely) it also is extremely unlikely. Move the B to c8 with Ps trapped on b7 and d7 and you would have the classic Bad Bishop.

Bishops are worth slightly more than Knights. This has been accepted since the days of Morphy. I don't know exactly how many centi-pawns Bs are worth compared to Knights ...
I just looked up Stockfish's generic evaluation of the pieces. It's a bit difficult to read, but here's about what Stockfish does:
Pawns are worth 1.008 pawns (they gain in value as they progress toward the 8th rank)
N= 3.191
B=3.266
R=4.961
Q=9.848
Source: http://www.talkchess.com/forum/viewtopic.php?topic_view=threads&p=442995&t=41916
There are some positions where Ns are worth more than Bs, but two Bs are worth about a pawn more than two Ns.
The most important thing is to remember these values change with the position. Play the position and work out which piece is better in that given position.
That's interesting.
I always kind of suspected that a queen was actually worth more than 9 points. Like I'd take a queen over a rook+knight+pawn in 90% of situations.
Two rooks are almost always worth more than a Q in a pure endgame, but a N+P is usually equal to a R in a pure endgame. The numbers Stockfish assigned have probably changed since I wrote that. But again, the numbers are averages based on analyzing millions (literally) of positions.

almost always rate them equally at 3 points. when you have 2 bishops to the opponent's 1 you might consider that an advantage of 0.5, since his position can become tender on a color-complex & the inherent weakness of the bishops (restricted to 32 squares) is negated with a pair of them.
it depends on the specifics: if the opponent keeps the position closed & puts his pawns on the color of his absent bishop (to combat yours), his position might even be preferable.
invariably, though: if you push his knights back, keep control & slowly open up the position then raking bishops can be an overwhelming force indeed... which is why most strong players don't exchange their bishops for knights indiscriminately, but usually only when they gain a concrete advantage in return, such as increased central control, better development, a wrecked kingside pawn structure to play against or a strong knight outpost.
I think it depends on your preference, which do you feel comfortable playing, how do you usually use them? I use my bishops a lot for trades and supporting other pieces, I use my knights to do lots of control over the board.
If that is the case, then the answer would be an opinion. My opinion would be a bishop.
I think both are equal and have advantages in different terrains Bus as bishops are long ranged pecies most of the people prefer bishops

Lasker said that “in chess, lies and hypocrisy do not last ling on the chessboard”.
People can have any opinion on the value of the pieces, but the game will put the lie to incorrect evaluations.

If we look at the millions of chess games computers have played we can see that the bishop is used more often and better, so the bishop I reckon has a 3.15 value
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