The introduction of the doubling cube into the game is largely responsible for the fast leap in popularity of modern backgammon. Each face of the doubling cube bears a number to record progressive doubles and redoubles, starting with 2 and going on to 4, 8, 16, 32 & 64. At any point during the game, a player who thinks he is sufficiently ahead may, when it is his turn to play and before he casts his dice, propose to double the stake by turning the cube to 2. His opponent may decline to accept the double, in which case he forfeits the game and loses 1 unit, or accept the double, in which case the game continues with the stake at 2 units. The player who accepts the double now ``owns'' the cube, which means that he has the option to re-double at any point during the rest of the game, but his opponent may not. If, at a later stage he exercises this option, his opponent is now faced with a similar choice. He may either decline the redouble and so lose 2 units, or accept and play for 4, and he now ``owns'' the cube. A player may double when he is on the bar even if his opponent has a closed board and he cannot enter. Though he does not roll the dice, for he cannot make a move, he still has the right to double. Note that gammon doubles or backgammon triples the stake of the cube!