CapnZapp
Legend
Many rpgs differentiate between doublehandedness (being able to use either hand equally well, though not simultaneously) and true ambidextrousness.This. You have to pick which hand you use for the Attack action and which you use for the bonus attack. But you don't have to pick the same every time. You can Attack-action with the left hand and take your bonus attack with the right; and then, next round, Attack-action with the right hand and take your bonus attack with the left.
You can, of course, choose to always use the same hand for the Attack action, and the penalty for doing so is negligible--there are very few circumstances where it would matter. So you can be left-handed or right-handed or ambidextrous as you please. The rules treat everyone as ambidextrous.
With such a definition, the game treats everyone as doublehanded. (Before feats, of course)