Throughout the episode, I didn't quite notice anything about the prince being genius except his ability to maintain a second face and to remember names of 10 thousand soldiers. The secretary/assistant seems quite badass nyan.
They won this battle just because the prince somehow managed to secure a training period for their troops? How did he manage that? All we got was him asking the other country's ambassador. It's not like he gave her a deal or something. She just happened to agree. And what was the deal with capturing the gold mine? We got noooo details of that.
While the show seems interesting, I think they should call it Un ga Ii Ouji no Akaji Kokka Saisei Jutsu (The Lucky Prince's Guide to Raising a Nation Out of Debt).