Is a bishop worth more than a knight?

Slightly, on average, and the average is not what you are playing. Statistical work on master games puts both at roughly three and a quarter pawns, with a real bonus for holding both bishops. In a given position the gap can be enormous in either direction, so count the pawns and look at the centre before you decide.

Why is the bishop pair worth extra?

Because one bishop is blind to half the board and two are blind to nothing. Once your opponent has a bishop and a knight against your two bishops, every square is potentially weak for him, and you can aim for exchanges that open the position and give your pair long diagonals. Larry Kaufman's 1999 study valued the pair at about half a pawn.

Should I trade my bishop for a knight?

Trade it when the knight has a permanent home in your half of the board that no pawn can attack, or when your bishop is hemmed in by your own pawns. Keep it when the position is open, when there are passed pawns on both wings, or when giving it up leaves your opponent with two bishops and you with none.

Bishop or knight: which is better?

They are both worth three, which is exactly the wrong way to think about them. Look at this position and count the material: three points against three points, and one side has a real piece.

Closed centre. White's pawns on c4, d5 and e4 all sit on light squares, so the bishop on e2 has nothing to attack. Black's knight on d4 is guarded by the c5 pawn and no white pawn can ever drive it away.

The pawns settle the argument, every time. Get the pawns right and the piece follows.

When the knight wins the argument

Locked pawn chains, like the one above. A knight jumps over the blockade and the bishop has to go round, and there is nowhere to go round to. Give the knight an outpost, a square in the enemy half that is protected by one of your pawns and can never be attacked by one of theirs, and you have a piece that will sit there for forty moves being worth more than a rook.

Knights are also the only piece that forks a king and a queen without being taken in return, so in sharp tactical positions with pieces close together they are worth watching.

When the bishop does

Open positions, and especially positions with passed pawns on both wings. A bishop crosses from a1 to h8 in one move. A knight takes six to make the same journey, and while it is travelling the pawn on the other side of the board queens.

A bishop also stops a passer from a safe distance and supports one from behind. That long range is the whole difference: in an endgame with pawns on both flanks, the bishop is usually a clean half point better, and with two bishops the gap grows. Two bishops can force mate against a lone king. Two knights, famously, cannot.

What to do when you cannot tell

Three habits that will serve you until you are strong enough to argue with them.

Put your pawns on the opposite colour to your bishop. That is the difference between a piece and a spectator, and it is the whole content of good and bad bishops.

Keep the pair unless you get something concrete for it. Larry Kaufman’s 1999 study of master games measured the bonus at around half a pawn, which is real money.

And when you take a knight with a bishop, or the other way round, ask what the pawn structure will look like after the trade rather than what the pieces are worth. That is the question, and the piece values cannot answer it for you.