It Don't Matter if You're Left or Right
I can still vividly remember my first few lessons at pole classes. My instructor showed us a move or a spin and then asked us to perform it on the other side.
The groans that echoed through the studio are still repeated today. "I'm right handed, my left hand is useless" or "I just have no strength on that side."
It's a common reply to just shrug, give it a quick go and pretend that you just can't do it and move on, repeating the move or spin on the "best" side and smiling when you nail the move.

So, what's the problem? Well, a great example, would be myself. I am right handed. I write with my right hand, I use my PC mouse in my right hand and I naturally pick up objects in that hand. Imagine my surprise one day when I found out I was performing the Gemini on the other side to all my fellow "right handed friends" in class.
I had never noticed this until we attempted double Geminis in class one day and as I stood next to my usual pole partner, we realised we weren't "compatible". I couldn't believe it! I had never realised this discrepancy until now. The next few lessons I then discovered my capability to climb on different legs at the starting point and a few spins which were easier.
After discovering my almost ambidexterity it then became apparent that it came in fairly useful. Where we were shown moves where it was easier to invert on the opposite side or start climbing on the wrong leg, I was already a step ahead there, and didn't have to struggle with the first part of the move quite as much.
It wasn't that simple though and by no means increased my status to extremely advanced, it just became a touch more helpful. Switch it to the other side and it becomes a different story!
