I think that the one you get depends on which game you get. I don't recall all the details but it could be that the one you get from the distribution corresponds to the one that you get in your game.

EX:

In Ultra Sun, you can capture Groudon so from this distribution you should get Kyogre. Vice versa for the other.

That way you can possibly get Rayquaza since now you have both of them.

At least that is what I think. I could be wrong.

Aww...I get one of the Genie Trio for my birthday. Meh. Good thing I like Gen5.