The rating system only takes into account the predefined match length and who won and who lost, not the final score. Conclusively, the doubling cube only has a relevancy in multiple-point matches. That's part of the reason multi-point matches are so much more fun. At the start of a game, the doubling cube is equally available to both players. But, as soon as one side has doubled, only the other side can redouble.
Ownership passes from player to player after each double.
Sooner or later you will experience situations where the game will not let you perform what seems like a perfectly legitimate move. This is the workings of the often overlooked rule stating The player has to use both dice if possible. If the player can only use one die, she has to use the highest one, if possible. Note that the rule does not state that the player has to move as many pips as possible, but rather use both dice , if possible. Thus, the game will not allow you to perform a move should you by this action cause the other die to become unusable.