According to the Borderlands 2 Wikia page related to Eridium:
So far it is unknown if there is a sure-fire way to obtain Eridium, but it is an uncommon-rare drop by certain enemies and rarely found in containers like lockers and washing machines. You can also obtain it by playing the slot machines at Moxxxi's place in Sanctuary.
Moxxxi's slot machines
According to this article the following is a list of potential payouts from playing the slot machines - in addition to randomly generated weapons and items of course;
- x3 Bandits: Live grenade (Run!)
- x3 7s: Customization skin
- x3 Cherries: Green item
- x3 Legs: Blue item
- x3 Marcus: Purple item
- x3 Borderlands logo: Orange item
- x3 Eridium Bar (1): 4 Eridium
- x3 Eridium Bars (2): 8 Eridium
- x3 Eridium Stack (3): 16 Eridium (!!!!)
- Any two with non-bell: White weapon
- Any two with bell at end: Cash
It is worth noting that playing the slot machines at Moxxxi's place will get more expensive as you progress through the game, yet some of the items you can win by playing the slots scale with your character - this means that playing the slots at a lower level will cost less while still potentially providing benefit to you at the later levels.
The Vault Hunter's Relic only drops the chances of white item drops by 5% and then splits that 5% between the green and blue drops. so say if the odds of drops are:
No drop:40%, white:30%, green:15%, blue:10%, purple:5%, orange:Only on named & bosses (and often about 1% or less there) OR 3 borderlands symbols on a slot machine (about a 1 in 5,000 chance)
The Vault Hunters Relic would only make that:
No drop:40%, white:25%, green:18%, blue:12%, purple:5%, orange:Only on named & bosses (and often about 1% or less there) OR 3 borderlands symbols on a slot machine (about a 1 in 5,000 chance)
assuming those numbers were accurate (the orange is pretty close but the others I am mearly speculating) then even if it were modded to be a 30% better chance (thus eliminating white drops all together) it would still only be about: None:40%, White:0%, Green:38%, Blue:17%, Purple:5%, Orange:special.
No modding of %'s will make the Vault Hunters Relic really worth wearing once others become an option. Better to wear a relic that works to improve your strengths (such as an elemental boost on a siren or a brand-specific relic that helps boost your best weapon) or compensate for a weakness (+shield capacity or max health if you find yourself dying too easily).
Best Answer
The exact formua is as follows (from the borderlands wiki):
However that's not the whole story; it's changed by your buffs (and not all buffs seem to stack), badass rank, skills, etc. So the easiest way to find how much damage you do with your buffs is to go punch something. Melee damage is based on your level, and then increased/decreased based on the distance between your level and the enemy's level. Unfortunately I think Target Practice might be too far away to melee. You can melee Claptrap's hand if you can get him to High Five (it shows as a conversation option, which unlocks eventually), but I'm not sure how claptrap's level scales.
Probably the safest way to test melee damage is to find a bandit exactly your level and punch him in the chest, then watch the number that comes off. Hit an unarmored, even level target for the clearest idea of your base damage. Hitting resistant parts of an enemy ("armored" parts like helmets) does reduced damage, so try to hit something unarmored like the common Psycho.