It is the rule in war, if our forces are ten to the enemy's one, to surround him; if five to one, to attack him; if twice as numerous, to divide our army into two.
Factors in the art of warfare are: First, calculations; second, quantities; third, logistics; fourth, the balance of power; and fifth, the possibility of victory is based on the balance of power.
Should one ask: 'how do I cope with a well-ordered enemy host about to attack me?' I reply: seize something he cherishes and he will conform to your desires.
The general who advances without coveting fame and retreats without fearing disgrace, whose only thought is to protect his country and do good service for his sovereign, is the jewel of the kingdom.
The art of using troops is this:
......When ten to the enemy's one, surround him;
......When five times his strength, attack him;
......If double his strength, divide him;
......If equally matched you may engage him;
......If weaker numerically, be capable of withdrawing;
......And if in all respects unequal, be capable of eluding him,
..........for a small force is but booty for one more powerful.
He who wishes to fight must first count the cost. When you engage in actual fighting, if victory is long in coming, then men's weapons will grow dull and their ardor will be dampened. If you lay siege to a town, you will exhaust your strength.
Therefore, to estimate the enemy situation and to calculate distances and the degree of difficulty of the terrain so as to control victory are virtues of the superior general.
One whose troops repeatedly congregate in small groups here and there, whispering together, has lost the masses. One who frequently grants rewards is in deep distress. One who frequently imposes punishments is in great difficulty. One who is at first excessively brutal and then fears the masses is the pinnacle of stupidity.