To Alex, the duel was just a mere side quest; the real benefit of it all was the popularity he would get out of it.
Alex himself was a 'Royal Prince' and the new 'Saint' of the god of wisdom church, but the church was in a dire state at the moment and didn't have the money to do publicity stunts at all.
To spread the faith of the god of wisdom, Alex needed something that would catch the attention of many.
If it was usual, he would need to organize various kinds of campaigns to deceive people into becoming believers of the god of wisdom by either giving them food or clothes for free or by giving them something valuable.
But those kinds of methods are very bad for a church, and those kinds of believers are usually not loyal enough and won't contribute much to the faith of the god of wisdom itself.
Alex needed some other way, and the duel came right on time.
He used the test and trap of his enemy to his advantage and made the duel into a publicity stunt for the Church of Wisdom!
