The term 'Backgammon Impossibility' refers to a situation in which a player cannot win the game, no matter what moves they make. The crossword solutions for this term are TIE (3 letters), GODS (4 letters), LIE (3 letters), ACEYDEUCY (9 letters), and DICE (4 letters). TIE is a synonym for draw, indicating that the game is at a stalemate. GODS refers to the ancient Greek GODS who were said to have invented the game of backgammon. LIE is a synonym for deception, which can be used to describe the strategy of a backgammon player. ACEYDEUCY is a variation of the game of backgammon, and DICE is a reference to the DICE used to play the game.