"Backgammon Gambit" is an orchestral piece on the Season 4 soundtrack.
Sawyer informs Locke about Kate's plan to set up a meeting between Ben and Miles. Locke decides to talk to Miles', but finds the boathouse where he is being held empty. Meanwhile, Kate, along with a bound Miles, break into Locke's house and then into Ben's cell.
Sawyer comes to Locke's house to challenge him at a game of Backgammon. A "gambit" is another word for a ploy used to gain an advantage. In this case, Sawyer informs Locke of Kate's plan in order to get Locke out of his house to investigate, while Kate uses this diversion to carry out her plan.