You got it KNP, yep.
3 extra rolls at 3.
Then what happens is you basically monitor your force - as you want to keep it relatively clustered into a formiddable mix.
This avoids superstacks of just one unit type, and encourages more strategic selection.
For example - today - The reason America wins in real-life, is because of all the different angles they can hit you from all at once, and because they take away all of their enemies possibilities (air, tanks, mobility, etc).
It’s to reward armies that are literally just that - complete armies, they’ve got it all, and their organized into a coordinated force.
Either side can do it. But of course, sides that are at the short end of desperate - and can only afford infantry for example, struggle to keep the pace. (and the advantage isn’t -THAT- despairing) And YES the advantage is recurring each round attack and defense.