I haven't read into them much, (so maybe I shouldn't be repeating it here;) but there are studies about how even when women are the higher earners in relationships, they end up taking on a greater share of household management and maintenance work. (The rhetorical context is usually around why young women aren't as interested in dating.... But again, that's something I'm throwing out there w/o due diligence)
But the idea of having physical cards that you split up and assign does sound really helpful. I might look into that. I would say in my experience breaking out household chores even amongst roommates, some tasks that seem even aren't remotely so once you get into it (I have been the advantaged and disadvantaged party in different apartments) and some are simply different such that some are trivial for one person and not so for another person. But that's a part of dealing the cards, even when splitting evenly. (now I'm wondering if I can see where people are getting into arguments.... ^_^')