Gambit
A gambit offers material — usually a pawn, sometimes more — in the opening to buy development time, open lines or seize the centre. The defender can often return the material at the right moment and consolidate, so a gambit is best understood as an investment rather than a gift. The Queen's Gambit is the most famous example, though its pawn can usually be regained.
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Accepting the gift: Black grabs the c4-pawn, but White now owns the centre and gains free development in return.