Sacrifices in chess are where you give your opponent some “free stuff”, but it’s not really free. In return for a sacrifice, you usually aim to get a checkmate, or to get a strong attack (that hopefully leads to checkmate), or sometimes in advanced chess, you might sacrifice some material to gain some space or time advantages.
Sometimes you sacrifice only a single pawn. In fact, there are several openings that are called “gambits” where you sacrifice a pawn very early in the game. In return, gambits give you some extra time to get your pieces out to start attacking quickly.
Attacking sacrifices against an enemy king can take many forms. Often it will be a sacrifice of a smaller piece (Knight or Bishop) in order to get your Queen next to the enemy king for checkmate. But sometimes it might be a Rook sacrifice, and sometimes even a Queen sacrifice is possible.
An exchange sacrifice is a common sacrifice, which means sacrificing a Rook (worth 5 pawns) for either a Bishop or a Knight (both worth about 3 pawns). So an exchange sacrifice is like sacrificing 2 pawns.
Most sacrifices are part of attacking. However, sometimes a sacrifice can be a useful defensive measure. Defensive exchange sacrifices are actually quite common.
Related Chess Tactics
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