I agree with the other poster that at distances under 100yds, your biggest consideration should be meat destruction. Any bullet will easily dispatch a deer, and be accurrate enough to hit him in the eye at that range witha stright line trajectory.
The lighter and faster the bullet, the more likely it will fragment, overexpand, and destroy meat.
You want a bullet that will stay together well, with limited expansion which can be a challenge for any bullet at close range. I'd use a round nose bullet in the heaviest weight available that can pass through your deer without "blowing it up".
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