After giving Blackheart the required amount of Doubloons, he fires 12 cannons at your enemies fort. Is there a certain pattern to his cannons firing at a certain fort or is it completely random? I want to know if there is a way to tell because you can siege a specific fort with Blackheart before he starts firing to increase the chances of destroying it.
The Cannons on Blackheart's Bay always follow the same pattern: Gate, Gate Turrets, Inner Turret, Healing Fountain, and then the Keep itself. (Connecting walls are never explicitly targeted, but they may be destroyed due to splash damage)
The cannon barrage will always target the outermost set of keeps, and will go Middle -> Top -> Bottom.
The long and skinny of all this means that if you have a single lane pushed far ahead of the other two, you're not going to get Blackheart's help with that lane until the other two even out, so to maximize Blackheart's help, you want to siege all 3 lanes evenly.
Edit: Upon further experimentation, the base forts target the healing fountains before the inner turret, but are otherwise the same.