“It will be best to let half the army get across, and then deliver your attack.”

Attack when the opponent is neither gathered nor fully across; the half-state is the weak moment.
Chapter 9’s river rules turn offensive: if you wish to fight despite the enemy’s precautions, let half his army get across, and then deliver your attack. The half-state is Sun Tzu’s named moment of maximum vulnerability — committed enough that retreat is costly, divided enough that force is halved. The verse is the ancestor of every modern tactic that times a strike to the middle of an opponent’s transition.
An enterprise vendor announces a platform migration, giving customers eighteen months. A challenger counts the months and waits: at month nine, the installed base is half-committed — locked out of the old platform’s roadmap, not yet stable on the new one — and at its most persuadable. The challenger’s campaign lands in that window and takes the accounts that were neither staying nor gone, but stranded.
Striking the half-crossed requires certainty about which half they are in — attack too early and the enemy simply stays on his bank; too late and the crossing completes. The verse assumes observation, and Chapter 9 spends its length teaching exactly that. Also note the asymmetry: this rule is for the attacker by choice; the defender’s version is to never be caught mid-river, which is why the previous verse said get far away.