WARNING: The following contains spoilers for Episode 4 of The Genius Prince’s Guide to Raising a Nation Out of Debt, "It Takes Two to Tango," now streaming on Funimation.
Prince Wein Salema Arbalest and Princess Lowellmina "Lowa" of Earthworld are old friends from their days as students at the academy. It's also horrifyingly uncanny how similarly their brains work. Originally introduced in Episode 3 of The Genius Prince's Guide, Lowa demonstrated her ambition from a young age and proved there's no bridge she won't cross to achieve her goals. Wein admired this quality in her when they were students, but only as long as she didn't rope him into her schemes. Years later, he still feels the same way.
With multiple nations conspiring to rebel against Lowa's empire, the timing is bad for her brothers to be fighting over the throne, and she is forced to step up to the challenge of preventing the rebellion on her own. To achieve this, she must become empress and get backing from another kingdom. Therefore, Lowa targets Natra and attempts to rope her old friend Wein into a convenient political marriage. Wein, however, knows better than to take Lowa's political proposal at face value as he's always known her to be a schemer.
In Episode 4 of The Genius Prince's Guide, Wein deduces Lowa has an ulterior motive that has nothing to do with the rebellion: she actually wants to be empress and is playing Wein like a chess piece. In an attempt to avert her plans, Wein contacts her suitor, Gerard Antgatal, and informs him she is at his palace, which prompts the latter to visit Natra. He counts on Gerard publicly claiming Lowa as his fiancée to back her into a corner. Lowa, however, isn't a fool and catches on to Wein's plan at the same time he's thinking it. She then schemes to leverage Gerard's gullibility to her favor in order to back Wein into her corner.
Both Wein and Lowa continue their mental chess game against each other during dinner, with Gerard being manipulated as their shared pawn. What neither individual counts on is Gerard's own drunken impulsivity screwing them both. Upon Wein admitting he took fencing lessons when he was younger, Gerard also claims he's a master swordsman and challenges Wein to a dual. Not only does Gerard want to prove his superiority in a sword fight, but he also sees it as an opportunity to win Lowa's admiration. The only thing she and Wein can think of is how badly Gerard can easily screw up their individual plans with his tomfoolery.
Wein wants to end the duel in a draw so he can avoid humiliating himself and keep manipulating Gerard. Unfortunately, Gerard's own drunkenness facilitates Wein's victory and he falls to his own death. With Gerard unwittingly dying on Natra palace grounds, both Wein and Lowa become aware of how this will look to Gerard's father, Grenache, who is a notorious tyrant. Both Lowa and Wein are forced to revise their plans as they'll both now be forced to go to war with Grenache since the latter believes they plotted his son's assassination.
With no other choice but to work together to minimize their own losses, Lowa and Wein plan their next moves carefully. The Genius Prince's Guide's hilarious irony of both monarchs coming together is that it resulted in a win for Lowa. Not only does she have Wein exactly where she wants him, but it took Wein's own miscalculation to facilitate his own checkmate.
Had Wein not sent that letter to Gerard about Lowa being at his palace, he wouldn't have gone to Natra in the first place. Without Gerard there, his jealousy wouldn't have been aroused and he wouldn't have challenged Wein to a drunken dual that resulted in his own death. In the end, Wein would've been much better off accepting Lowa's political marriage proposal.
