I watched the first 3 shows. Some interesting strategy but I’ll be honest, I don’t understand why some people keep their categories and some don’t. For instance, the guy who had the most kept inheriting categories for people he challenged. He lost to someone who challenged him and that lady kept her category.
The simple answer is that each category is only dueled once. Two people face off in the category of the person that got challenged, and the winner then retains the unused category.
The long explanation is: Say your category is NFL teams. If you're chosen by the randomizer, then you are forced to challenge a neighbor in
their category. Say you challenge me, in my category of MLB teams. If you win, then you still have your own category to defend if you're challenged later. If I win, now my MLB category is spent, and I inherit your category of NFL teams. No matter which of us wins, we'd have NFL teams as our topic.
Whoever wins a duel gets the choice to go back to the floor (and then get challenged in whatever category they retain), or they can challenge another neighbor again, in that person's category. So you could keep your own category if you initially challenge someone and win, and then continue to challenge and win. As soon as you go back to the floor, now the next time you'd duel would be in your own category (because someone has to challenge you in your category). You can't be chosen by the randomizer twice, so once you return to the floor you can only duel as the challenged party (so in the category you hold).
It prevents someone from choosing some obscure topic and getting to defend it multiple times.