The answer is "the perfect one" to get you the gig.
OK, so we get together and we have a fabulous session and you have that perfect headshot.
And you show up for the acting or modeling call ... you hand it in, they look intently at your headshot ... look up at you and then they ask the dreaded question "Do you have anything else ?" ( Meaning another pose, or expression or outfit or background)
Terror! Ah ... that's my "perfect headshot" it's ... freaking perfect!
If you don't have a variety of other shots to offer they will whip out their "point and shoot" or phone and take a shot of you ... with your hair and makeup ... "not perfect". That picture gets stapled to your headshot and resume and ... "Next !"
You can't know what they are looking for - but you can come prepared. So in addition to your perfect headshot you can have images of you smiling, serious, formal, casual, "waist up" and "full length", fierce, sweet, urban chic and "flannel".
The comp card can also be the answer - it's a quick look at all your looks.
Remember - the purpose of your headshot is so that they will remember you. Versatile, epic, handsome / beautiful / stunning / approachable / awesome you.