You’ll need to prepare wood for the sides and ends that is 40mm wide and 8mm thick, for the lids that is 8mm thick, and some 3mm thick mdf for the base.
Carve the parts flat first, producing the two sides, two ends, two lids (you’ll want to replace the initials with something else I expect), and one base.
Now cut the parts to fit the playing cards: my sides were 225mm long with one base groove end stopped 2mm in from one end (the two separate side workpieces are mirror images of each other). My ends were 107mm long.
Now mill the ends of the each end. One end gets three fingers left each end, while the other gets two.
The end with the three fingers, is cut narrower now removing the two outside fingers and making space for the lids to slide in.
A little filing and sanding should get all the parts to fit well. If you have a shoulder plane, that makes fitting the lids even easier.
Glue the box up and clamp it, ensuring that both lids can still slide in easily.
Why not line the box with baise or similar, highlight the lid designs, and either lacquer or varnish it.
Now just learn how to fool your audience!