
Carolinus, companion of SONS |

"I go at the same time as my master and bestest buddy in the whole world, Sir Orrin! Sure I gots smarts, but he's got real experience. I trust him, and everything works better when I go along with what he wants. ...usually."
:D
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Personally, I've done it both ways. Cohorts acting at the same time as their master regardless, and as separate characters as well. Both ways work, but for streamlining combat in order to keep things moving at a decent pace, it's usually best (at least, in online/pbp games, in my experience of course) to have everything controlled by one player go/post at the same time.
Again, in my experience. tumbler will have to have final say, of course.
As for Heroic Invocation, it may be fine for the rest of you, but Sir Orrin and Carolinus would have to respectfully decline. The bonuses it gives are minimal for us (we already have moral bonuses coming out the wazoo), and becoming fatigued at the end of it!? Well, that is a HUGE penalty for a mobile melee character such as Sir Orrin. Crippling, in fact. We (Sir Orrin and Carolinus) will not willingly accept that spell, and will attempt the Will save to resist it if it gets cast on us (assuming we're allowed to by being informed of what the spell does. I'd hope we'd be good enough to each other to explain beneficial magics in full, rather than saying "this is good. Trust me" and then inadvertently screwing one of us over).
Again, it may be great for the rest of you, but not for Sir Orrin and Carolinus. To us, it does more harm than good in most situations.
(and yes, I'm playing around with a second alias/profile for Carolinus. Possibly for non-combat interactions, but mostly for organization. And someone else in paizo-land is already using the name "Carolinus", and it does not allow duplicate names, hence the "companion of SONS" addition).