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Actually, having the BG pointing his gun toward the shooter is BETTER since distance is safety. Highly unlikely he could miss the hostage but much more likely to miss(or not make a fatal hit) another 10-20' away.
The transition between the two is the best opportunity for a shot if that is possible. His focus is broken, he's having to shift from hostage to shooter, and the muzzle maybe in a neutral zone. He also may extend his head more to get a better view of the other target.
In this case, always try to get an angle position rather than a initial frontal approach.
Don't engage the perp in conversation, keep your focus on your aiming point.
Hopefully, you have a single action option on your handgun as now is the time to use it.
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