Dog takes toy and finishes game = dog wins.
You take toy and finish game = you win.
Dogs are pretty concrete in their thinking, they think the above is so.
I have one who needs to be kept in his place, and one who had a very bad start to life. It took her a whole year to get the confidence to play tug with me.
Have no clue on underbites, I don't know a heck of a lot about poodles specifically.