The drop chance is about 10%. And it is somewhat around there.
I've got lots of cold pizza slices and birthday cakes to constant keep refilling my energy bar nonstop to run the missions.
And yeah, I've had to sacrifice XP gain and the likes for the mission. 😰 But based on how much I can make each day and the value of each card (and expected future value), I find that's a good trade off for me. If you can make vastly more Starbits from just your normal missions, it would probably be better to just buy what you need from the market.

!PIZZA