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An expression used in gaming in general (board games, card games, etc.) meaning a second chance where luck is involved. The mulligan makes sure that bad luck won't make the game too unbalanced, and is usually only available the first turn (or at game start). How the mulligan is implemented differs from game to game, and can be a dice reroll (e.g. Titan) or a reshuffle (e.g. Magic: The Gathering).

I assume the term is adopted from golf, after reading dannye's writeup.