How do the dice loot chests work?

Question

In the 'Tiny Tina's Assault on Dragon Keep' DLC, dice chests have been introduced:

I reckon the result of the dice roll decides the rarity of the loot the chest contains. How does it work? Which numbers dictate which loot rarity (or chance of getting rarer loot) a chest contains?

Answer 1

If you open the chest normally, 1d20 will be rolled. The chest will give the following based on the result of this roll:

• 1: 1 Eridium, live grenade
• 2-3: White (common) items
• 4-14: Green (uncommon) items
• 15-18: Blue (rare) items
• 19: One blue and one purple (epic) item (a rocket launcher will be purple rarity)
• 20: Purple or E-tech items

If you spend 5 Eridium, 2d20 will be rolled and the higher of the two dice will be taken as the result for determining loot quality (i.e. rolling with advantage in D&D 5e). In addition to the above, the following special cases apply:

• 1 on both dice: 4 Eridium, three live grenades
• 20 on both dice: Orange (legendary) item; possibly a pearlescent item if in UVHM

Source: Borderlands Wiki

Answer 2

The higher the roll, the better chance at a rarer item. There are no set breakpoints for which roll give which rarity tier, just higher chances. By spending 5 Iridium, you can roll both dice with only the higher die counting.