It is convenient as you don't have to swap a right-hander's mouse to the other side of the keyboard to use it.

I very rarely see a right-hander who can do the same.

Strangely I find my right to be more accurate but could be down to the extra concentration applied (particularly playing sport). You can seriously mess with a batsman in cricket if you can bowl with the right and then switch to left.

Inigo: I admit it: you are better than I am!

Man in Black: Then why are you smiling?

Inigo: Because I know something you don't know.

Man in Black: And what is that?

Inigo: I am not left handed! [switches the sword to his right hand and starts driving him back]

I find being left handed and using the mouse in my right hand very useful.

I can have a pencil writing notes in my left hand, while I control the computer via mouse in my right.

Similarity, mouse the cursor with my right and type with my left.

Yeah use the mouse with my right as well, but I've never knowingly made a conscious decision to learn to use my right, how I use things just seems natural to me.

I've had some thoughts about liking to see some studies on whether people who write left handed or are mostly left handed dominant still mostly use mouse with their right hand. And to take it further, are these people playing first person shooters with invert mouse more often than right handed people OR left handed people who use mouse with left hand?

I can mouse equally well with either hand but how often do you find a mouse on the left side of a keyboard? Keyboards themselves are arguably left-handed devices, influencing the decision to mouse with the right further. Similarly, I 10-key right-handed. Many things I do right-handed are not preferences but just learned responses to how the world works.