UPDATE 12/26/2018 - Using some new, plastic dice yesterday made me realize that bouncy dice seem to like to leap over the railings on the side stairs, so I took user bainite's new side stairs that include arches and merged them into my combined dice tower. I will leave both files uploaded, however unless you specifically don't want the arches for some reason you should definitely print the one that includes arches. The file name is "Dice_tower_with_stair_arches.stl". I will upload a photo when my print finishes (30 hour total print time at .2mm layer height).
I combined most of bainite's V2 tower (1st floor, 2nd floor, left stairs, right stairs, and top floor taken from here: https://www.thingiverse.com/thing:1271858/files ) with one of Hsus' extra floors (3rd_randomizer_floor_V2 taken from here: https://www.thingiverse.com/thing:2953592/files ) into a single file for faster printing and no need of magnets to hold it together. I also smoothed out a couple stair fronts that incorrectly had stone texture on them, increased the security of the connection between the randomizer nubs and the interior wall of the 3rd floor, angled the underside of the window outcroppings so they could print without supports, and angled the underside of the central divider in the top floor so it could print without supports. It is approximately 200mm tall, so this isn't for everyone! Print time on my Prusa mk3 with mostly default settings at .2mm layer height and 8% infill is ~30 hours.
Test print successful! I'm very happy with how this has turned out, as well as how much time and filament it saves over printing each piece individually for the original design (saves nearly 10 hours of printing on my printer). Also no need to worry about magnets, so as long as you have the print space in your printer and the storage space in your house, I highly suggest printing my remix of the incredibly well-designed dice tower originally by bainite & with an added floor section by Hsus.
The tower is very sturdy and you do NOT need to do a high infill percentage - 8% is fine.