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I never make decisions that leaves the damage up to random. Then it might hit my science or tech.

So I never push the engines past their limits and always avoid possible danger.

"Don't shut down" and "fly blind" used to be my go-to options because they give the lower damage, but I don't fly blind anymore after my culture got messed up over it. That costs a lot of points.

(For the same reason, damaged landing gear is awful; it does damage in several places and you cannot control where...)

My highest ever was 14k-something also. This was on an old phone, can't prove it, sorry. But I like interesting results much better than high scores...
My favorite was a Cosmic Enlightenment Neolithic on a beautiful moon.

Bad scores get some pretty interesting results too! I mean, this world is horrible, but the story practically writes itself: