The exchange

In chess, the exchange is not a general trade. It is the specific difference in value between a rook and a minor piece, meaning a bishop or knight. On the usual approximate scale, a rook is worth about five pawns and a minor piece about three, so the difference is roughly two pawns.

A player is up the exchange when they have gained a rook for a bishop or knight. They are down the exchange when the reverse has happened. Deliberately giving a rook for a minor piece in return for an attack, pawns, squares, or control is an exchange sacrifice.

The arithmetic is only a guide. A rook needs clear files or ranks, meaning vertical or horizontal board lines, to use its range, while a minor piece can be exceptionally strong on a square from which enemy pawns cannot drive it away or in an attack. Piece value, meaning how much a piece actually contributes, therefore also depends on activity, king safety, pawn arrangement, and coordination.