Nothingness: You should read the rules again. If a player doubles, the other player must accept or concede the current game. If the opponent concedes, then the doubling player immediately wins the current game and receives a number of points equal to the current value of the game before the double. For example, if no player has previously accepted a double in the current game, it is worth 1. After one double is accepted the game is worth 2, after 2 doubles it is worth 4, and so on. If the opponent accepts, then play continues normally at the increased stakes. So it normally makes no sense to double when you are hopelessly behind, because you are just doubling the amount your opponent will win (and giving him the opportunity to redouble). A player who wins an undoubled game wins 1 point, unless the win is a gammon (2 points) or a backgammon (3 points). If the game has been doubled and accepted once, then a single game is worth 2 points, a gammon 4, and a backgammon 6.
Until the cube has been turned (i.e., until a double has been offered and accepted) either player can offer a double before rolling the dice on his turn. Once a double has been accepted, then only the player accepting the double can offer another double. In this way "possession" of the doubling cube passes back and forth between the players, changing hands after each accepted double in the current game.
One other doubling rule is the "Crawford Rule." The Crawford Rule states that, when one player reaches a score that is only one point away from winning the current match, his opponent may not double in the next game. After that game (called the "Crawford game", which BrainKing erroneously calls the "Crawford Round", the trailing player may double normally.
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