Some do, but not all. Most mouse ergonomics are made to be right handed, and since learning the mouse & keyboard is a new an alien concept for both left and right handed people, they can simply learn it with their dominant hand on the keyboard.
I wonder if that would make them better at micromanaging RTS games with keyboard shortcuts vs. shooting with the mouse in FPS.
I wonder if that would make them better at micromanaging RTS games with keyboard shortcuts vs. shooting with the mouse in FPS.