It's called 'Flip' Where you both try and flip each other right/left
Politically? Sorry, couldn’t resist. It’s election season.
I’m 6’3 250 pounds, would take a girl with some skills to flip me over
I'd be put off by the "game", as described. It seems to be something that leads to intimate touching or positioning. Seems like "wrestling" , or a strategy that leads to the statement "Oops! Didn't mean to cop a feel!" I definitely would not be comfortable with that.
I agree with @Tawny2018. As much as I enjoy wrestling with friends, that's not what a cuddle session with a client is about. There is too much of a chance of there being "accidental" inappropriate touching, making the session awkward and unprofessional.
When I want sex, thats what I want. When I want a cuddle, I want cuddles, not wrestling. Cuddling is for recharging my batteries not games.