I shoot pool left handed. When someone mentions it to me, though, I always respond with my standard, "well, I shoot pool left handed by I am right handed."
What many hardly notice is I use a bridge right handed.
I do not know why I shoot left handed, nor why I use a bridge right handed. It was just natural for me. I never even noticed I was shooting left handed til someone else mentioned it to me. And I didn't recognize myself that I use a bridge right handed - until 7 years after picking up my first cue, my friend Sharon Townsend pointed it out to me.
I can shoot right handed, but only on simply shots, but not because I am ambidextrous. I struggle and wiggle my cue on right-handed shots just as right handed shooters do with left handed shots.
When I started playing in my straight pool league, the discussion of being left handed comes up a lot more because we lag for the option to break or rack. This means I have to set my ball up to lag on the right side of the table. So, now the discussion of my left-handed-ness comes up a lot more. Why? Because it's more noticeable. Why? Because if they are right handed, we would get in each others way if I was lagging on the left side.
Of course occasionally I am called "lefty" which is fine by me, even though it's not "technically" accurate.
What about you?