Thanks for the chapter!
Seems like family lineage and compatibility ranks are all that goes through Joachim's head. MC should still be careful though. Considering Joachim's taunts about MC having zero compatibility means Joachim has at least good compatibility in one or more elements which will likely use to win out of desperation and refusal to lose even if looks bad as would considering losing worse. Considering how furious MC is I wonder if Joachim will be able to feed himself solid food anytime soon after the duel or will have lost all his teeth along with multiple broken bones. In any case, now know why Duke had a child with MC's mother, although not why made her a concubine. Could be wanted someone who actually looked pretty (pic of real wife and concubines made them look ugly and fat or gaunt,) and either unwilling or unable to refuse or backtalk him.
@ilikeanime I think Joachim was just being vulgar in saying he was going to open the MC up as in hitting MC so hard that his flesh will rip apart killing him despite Joachim's sword being dull due to being a practice blade.