Card box for game box interior (for Above & Below)

This is my first attempt at making a box of any kind! It holds four decks of cards that come with the boardgame Above and Below.

It took me three tries to get this prototype “right” but I’d love some help from someone who has worked on similar projects. The fit of the pieces together is very loose; I’m gluing this one together. I think I’ve seen the term “kerf” around and maybe that’s what I didn’t account for. Does anyone have some advice on how to do this so that the pieces fit together a little more snug right from the beginning?

Thanks, everyone!