I'm fairly certain there will be 3 different cards, all looking the same except for different Pokemon inside the eggs (with different moves ofc). Just by looking at the card it will just display the egg sprite, as cards can give eggs.
Nothing in Pokemon is truly "random", it's only "random enough" at best
Distribution will probably be based off of (m)any of the following: OT/ID combination, download time, account name/ID (if thats how you'd get it), and/or IP.
Card hex theory