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The only possible traction advantage an LSD could have is if the front axle had zero traction in a turn and the traction between the two rear tires was uneven. The xDrive would then behave like a standard open differential RWD car, while the LSD would behave like a RWD car with LSD.
The odds of such a scenario occurring are 0%, considering it is physically impossible to turn (or to continue turning if it happens mid-corner) if there is zero traction in the front wheels.
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