Your opponent’s bishop takes your knight on c6 and you have ten seconds to decide whether to be pleased. Three points for three points, so it is level, and you play on. That decision, and almost every other trade you will ever make, is settled by five numbers: pawn 1, knight 3, bishop 3, rook 5, queen 9.
Nothing in the FIDE Laws mentions them. They are a rule of thumb, built from what happens in millions of games, and Larry Kaufman’s statistical work on master results sharpened them a little: knight and bishop about 3.25 each, rook 5, queen 9.75, with an extra half a pawn for holding both bishops. Round them off and you are back to 1, 3, 3, 5, 9.
The king sits outside the scale. It is never traded, never captured, and if you lose it you have lost everything, so no number fits.
The exchange, and why it gets its own word
A rook for a bishop or a knight is not an even swap. It is five points for three, and the two-point difference comes up so often that players named it.
7
2
d
g Winning the exchange is the other side of the same coin, and it is a perfectly good way to win a game slowly. What you must not do is treat it as small. Two points is a pawn and a bit, and in an endgame a rook against a knight with pawns on both wings is usually decisive.
The other trades worth knowing by heart: three pawns for a minor piece is roughly fair and often good if the piece was doing nothing, a queen for two rooks is nine against ten and favours the rooks once they have open files, and a queen for three minor pieces favours the pieces in the middlegame and the queen once the board empties.
When the numbers lie
They lie all the time, and here is the standard case.
7
2
g Count material and it is dead level, nine points each. Count useful moves and White is much better. A piece is worth what it does, and a bishop that cannot leave its own back rank is worth less than the pawn in front of it. That is the difference between a good and a bad bishop, and it is why strong players will hand over the exchange to get a knight onto a square like d5.
Three more places the count misleads you. A passed pawn on the seventh rank is worth far more than one, because it is one move from being a queen. A knight shut in the corner on h1 has two squares to its name and is doing less for you than a healthy pawn until it gets out. And a piece that is hanging is worth nothing at all, because it is about to belong to your opponent.
So use the numbers as a first check, then look at the board. Before every capture, add up what goes off on both sides, and before every move, ask what your opponent is attacking. That second question is the one that actually saves points: how to stop blundering turns it into a routine.