@DQM Ohhh nice! This is a problem me and my brother always have when trying to figure out these puzzles ourselves, a lot of Conan relies on Japanese<->english wordplay.
So have you figured out the cards then? If it was a similar situation, I was thinking poker hands, but the card sets differ in size and one of them even has six cards, so that didn't seem right. Although I noticed that none of the cards go above 6, so that might be significant.
Also, I notice Wakita is trying to solve the mystery and doesn't seem to be observing Conan solving the mystery. Though he might be doing that in the third chapter, so no idea if that contributes to evidence of Wakita being Rum or not.