Improve the randomization experience

[with-heart]

Currently the experience is awkward:

Click the "Randomize Civ" button to display a random civ in the current civ box. Click the current civ box to set it as played. Click the "Randomize Civ" button again to move to the next.

I'd like for it to be more fluid and involve clicking less buttons, or at least have the buttons be part of the same experience.