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The player who last accepted a double is said to own the cube. Only that player may make the next double of the game. Prior to the first double, neither player owns the cube (see centered cube) and either player may double.
A guideline for cube handling in pure race positions. If you add 10% to your pip count, you should double if the result is not more than two pips greater than the opponent's count, and you should redouble if the result is not more than one pip greater. Your opponent should accept the double if your count plus 10% is no more than two pips less than his count.