What would happen if an ambidextrous pitcher faced a switch-hitting batter?

Like, suppose an ambidextrous pitcher was pitching on the mound and he has to face a switch-hitter. How would that scenario play out? Like, who would make the decisions as to which side the pitcher should throw from and which side the batter should hit from? In case you're wondering what ambidextrous means,... show more Like, suppose an ambidextrous pitcher was pitching on the mound and he has to face a switch-hitter. How would that scenario play out? Like, who would make the decisions as to which side the pitcher should throw from and which side the batter should hit from?

In case you're wondering what ambidextrous means, it's defined as an ability to use both the right and left hands equally well.
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