Not that it would add much at this point, but I made this picture when I started out in the editor to help myself with this;
The top 4 chests always contain one of the 3 possible items, and only one.
The purple chest contains all 3 items at once.
I believe there are rarity tiers, because the top 4 chests seem more likely to yield gems than lives or upgrades, but I'm not sure.
EDIT: Yeah, the int values are most likely the rarity factors.