Pardon my ignorance, but I'm afraid my question is more basic than these kindly meant answers are assuming.

Let me try and put it another way...
Suppose I cast with the left hand over the left shoulder as normal. What will be the
difference in the cast compared to a right hander casting over their right shoulder?
You see, I can guess that casting with the left hand over the right shoulder will produce a similar effect to a right hand cast, but I don't yet understand
what that effect is.
Once the laughter has subsided, anyone care to clarify?