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Page 54
Gain Relative Superiority
Sun Tzu continues:
Accordingly, by exposing the enemy's dispositions and remaining invisible ourselves, we can keep our forces concentrated, while the enemy's must be divided. We can form a single united body at one place, while the enemy must scatter his forces at ten places. Thus, it is ten to one when we attack him at one place, which means we are numerically superior. And if we are able to use many to strike few at the selected place, those we deal with will be in dire straits.
The spot where we intend to fight must not be made known. In this way, the enemy must take precautions at many places against the attack. The more places he must guard, the fewer his troops we shall have to face at any given point.
For if he prepares to the front his rear will be weak; and if to the rear, his front will be fragile. If he strengthens his left, his right will be vulnerable; and if his right gets strengthened, there will be few troops on his left. If he sends reinforcements everywhere, he will be weak everywhere.
Numerical weakness comes from having to prepare against possible attacks; numerical strength from compelling the enemy to make these preparations against us.

Relative Superiority Wins
The concept of relative superiority can be distilled from Sun Tzu's statement: "...we can keep our forces concentrated, while the enemy's must be divided." Another translation is worded: "...if I concentrate while he I can use my entire strength to attack a fraction of his."
In the Science of War, Colonel Henderson says, "...you must have as much as you can for yourself and as little for the enemy. The highest generalship is to compel the enemy to disperse his army, and then to concentrate superior force against each fraction in turn."
In On War, Clausewitz says, "Where absolute superiority is not attainable, you must produce a relative one at the decisive point by making skillful use of what you have."

 
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