When to shoot twice: XCOM’s Rapid Fire probabilities broken down

You’re near the end of an especially hairy XCOM: Enemy Unknown scenario. An alien has one health, and you have an Assault specialist in firing range. Should you use the Rapid Fire ability for two shots at a 15% reduced hit chance, or take one shot? You could make the decision with your gut, or you could do the math, as University of Kent Research Associate Neil Brown has done. In a blog post today, Brown answers that question and others with numbers and glowing probability graphs.
The result: If a normal shot has a hit chance between 34% and 96%, the alien only needs one shot to kill, and ammo isn’t an issue, you should use Rapid Fire. If one shot isn’t enough and you want to do as much damage as possible, you should use Rapid Fire only when your normal hit chance is above 30%.
I won’t embarrass myself by attempting to explain Brown’s math, but you can see the equations on his website. He also (almost definitely correctly) points out that Firaxis must have done the same math when arriving at the 15% Rapid Fire accuracy penalty. That’s no surprise, of course, but a reminder that nothing in games is arbitrary. Though I tend to get lost in the surface-level war metaphor and make gut decisions, the best possible decision in any game comes down to the numbers at play—XCOM just puts them on the surface for us to poke at. And by “us,” I mean people like Neil Brown, whose mathifying I can enjoy