Understanding the chit pull and turn order mechanic is the key to understanding and gaining the edge in Pub Battles: Brandywine. Generally, you want to move last because that allows you more control over your combat engagements.
In Pub Battles: Brandywine, when a unit’s command is activated, it may move, even if an enemy unit has moved into contact. This means if you are defending you can move out of contact, and if you are attacking it means you can move into contact without the opponent running away or reinforcing the position. Of course, especially early in the game, a command may want to go first if it is trying to reach important ground or react to events of the previous turn. Washington reacting to the British’s flanking maneuver is a primary example.
Pub Battles: Brandywine focuses on command and one of the ways it simulates this is the HQ’s ability to affect the all-important turn order. For example, if Corwallis' chit is drawn first he may wish to wait until the command he is facing (Sullivan) has moved so he can choose exactly where he wants to attack. Let’s say he makes his roll and his chit is put back in the cup, his HQ is turned over signifying he has used his action this turn. The next draw is Knypshausen and he is fine moving first since he is just biding his time threatening Greene (forcing him to guard the Fords and not fly to Sullivan’s aid) and only fires his artillery. The next draw is Sullivan and the colonial player does not want to move first so he has Greene roll and he makes his roll. Sullivan’s chit is put back in the cup and Greene moves. Cornwallis' chit is drawn next and Cornwallis still does not want to move first so this time Howe rolls for Cornwallis, he fails the roll and Howe must move. He moves but is ever mindful of his attacks as Sullivan will move after him and can just pull back or reinforce any advantageous attacks.
Why do the rules allow a unit to just walk away from an enemy attack? Remember, the rules are simulating a command advantage. This may mean the enemy has been hoodwinked and either has been out maneuvered or perhaps had been uncertain as to the enemy’s disposition. In any event, at the end of the hour and a half they had failed to come to grips with their foe. Things had fallen out such that the units ended up in the positions shown on the map. They may never have even been close, or perhaps the unit had deployed a very effective screen of skirmishers. Even though in game terms a command may move last, what it may be simulating is that command moving first before the enemy can react! Pub Battles: Brandywine dispenses with the pages and pages of rules that would be required to show what really happened (and can never capture all nuances), and focuses on what these multitudes of happenchance result in, which is all the commanders need to know, or care about, at the time.