Is trading pieces good or bad?

It depends on what else is going on. Trade when you are ahead in material, when you are cramped for space and need room, or when the piece you give up is worse than the one you get. Keep pieces on when you are behind and need chances, when you are attacking a king, or when your piece is the better one. Nothing about a trade is automatically fair just because the points match.

Should you always take back after a capture?

No, and this is a habit worth breaking early. Recapturing is usually right, but not when the recapture walks into a fork, not when there is a bigger capture available somewhere else, and not when a check comes first and wins more. Look at every recapture as a move you have chosen, not a move you owe.

What does it mean to trade pieces?

Knight for knight is three points for three points, and the scoreboard does not move. The board does.

1.Nxf6+ gxf6 is dead level on points. It also gives Black doubled pawns on f6 and f7 and opens the g-file straight at his own king.

Nothing was won there, and yet White would play it in most positions and Black would avoid it in most positions. That gap between the arithmetic and the position is what trading is actually about.

What changes when a piece comes off

Four things, and you can check them in the time it takes to play the move.

Material, obviously: is it really level, or am I giving a bishop for a knight, or a rook for a bishop, which is the exchange?

Pawns. Recaptures move pawns, and pawns do not move back. In the diagram Black’s kingside goes from three healthy pawns to a doubled pair and an open file next to his king.

Space and air. If your pieces are stepping on each other behind a wall of pawns, every trade helps you: fewer pieces need less room. The player with more space wants to keep pieces on for exactly the same reason.

Kings. Trading queens usually ends an attack. If he is the one attacking you, the queen trade is the best move on the board even at the cost of a pawn.

Who wants it

The side that is ahead. A piece up, trade everything you can and let the extra piece decide the endgame: that is simplification, and it is how most winning positions actually get converted.

The side that is worse, generally, does not. Behind in material, you need pieces on the board, because pieces make threats and threats make mistakes. Trading your last rook when you are a pawn down is often the moment the game stops being a game.

And there is the personal version. Trade off his good pieces and keep your own. If his bishop is raking your king from b2 and yours is buried behind a pawn on d4, then trading bishops is a good deal for you whatever the point values say.

Before you take, ask three things

Does he recapture, and with what? What does his recapture attack after it lands? And is there a better move than taking at all, a check or a capture somewhere else?

Most beginner trades happen automatically, by reflex, and reflex is what the counting on the piece values page is meant to replace. Two seconds a capture is enough. Half the trades you would have made on autopilot turn out to be the trades your opponent wanted.