# A Brief Guide To The Dice Chests (Tina DLC)

I haven’t seen any posts about how these chests work, but I figured some forum users might find this information useful.

The chests I’m referring to are the red chests from DLC4 that have two little D20s on top of them. When you approach one you’ll be given the option to “Roll One” for free or Roll Two" for 5 Eridium. When you “roll,” the die will spin, then a little number will appear over the chest. The number Tells you what kind of loot you are getting (by rarity). Say you roll one. Here’s a list of the loot you’ll get with each number rolled.
1: One Eridium + A Live Grenade
2 - 14: White or Green Rarity Loot
15 - 18: Blue Rarity Loot
19: 1 Blue + 1 Purple
20: 2 Purples

Simple Enough. Here’s How the “Roll Two” Option works. The RNG basically rolls two D20s and displays the higher roll - unless you get double 1s or double 20s. There is no special result for any other doubles (a double-18 gets you the same result as an 18). If you roll two:

Double 1s: 4 Eridium + 3 Live Grenades
2 - 14: Whites or Greens
15 - 18: Blues
19: 1 Purple + 1 Blue
20 (Single): 2 Purples
Double 20: 1 Legendary + 1Blue

Now for the part of the discussion that has (Gasp) math. Paying 5 E to roll two doesn’t just get you the chance for a legendary, it also increases the probability that you’ll get a higher number on your roll. When you roll one, you have an equal 5% chance of getting any result. So in effect rolling one means a 70% chance of garbage (1 - 14), a 20% chance to get blues (15 - 18), a 5% chance to get 1 blue and 1 purple, and a 5% chance to get 2 purples.

When You roll two, this changes because you always get the higher of the two rolls, except for the double-1 and double-20 outcomes.
For these special cases, since each of the two rolls are (presumably) independent, the probability of occurrence is the probability of rolling a 1 on the first die times the probability of rolling a 1 on the second. So, 1/20 * 1/20. In effect this means there’s only a 1/400 (0.25%) chance of getting double-1s, and similarly there’s only a 1/400 chance of getting double-20s.

Now for the rest of the outcomes. The probability of a single 20 when you roll two is the probability of getting one die that’s a 20 and one die that is not a 20. The probability of getting a 20 on the first die and a non-20 on the second is 1/20 * 19/20. That’s also the probability of getting a non-20 on the first Die and a 20 on the second. Add the probabilities of these two events and you get your chance of a single-20. So the probability of getting a single-20 when you roll two is 21/2019/20 = 38/400, or 9.5%.

Similarly, the probability of getting a 19 when rolling two is twice the probability of the first die being a 19 times the probability that the second is 18 or below, PLUS the probability of rolling double 19s. That is 21/2018/20 + 1/400 = 37/400, or 9.25%.

The pattern should start to be clear at this point. Probability of an 18 rolling two = 21/2017/20 +1/400 = 35/400 , or 8.75%. Probability of 17 = 21/2016/20+1/400 = 33/400 = 8.25%. Of 16 = 21/2015/20 + 1/400 = 31/400 = 7.75%. Et Cetera.

Short Version:
Double-1s: 0.25%
2 - 14: 48.75%
15 - 18: 32%
19: 9.25%
Single-20: 9.5%
Double-20: 0.25%

“Purple” includes E-tech rarity.
Any drops from the chests must be non-uniques in the global loot pool - you won’t get a Norfleet, you won’t get E-tech relics, you won’t get any of the “____ of Terramorphous” items, etc.
I think these chests may not drop relics, but that may just be my memory failing.
I am fairly certain they don’t ever do the “eridium and cash” drops that some other red chests can produce.
Exception: When a rocket launcher drops, you will get only the one item. As best as I can tell the launcher will be the higher of the rarities corresponding to the roll - e.g. a launcher dropped when you rolled 19 will be purple, a launcher on a double-20 should be a legendary (I got a pyrophobia this way).

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double 20 is not a guaranteed legendary.

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I’m fairly certain it is. Every time I’ve gotten double-20s I’ve gotten one. Can you show a video or something of a double-20 occurring where a legendary did not drop? Admittedly it MAY also be possible for the “legendary” to be a Pearlescent instead, at least in UVHM - I do not know.

Disclaimer: I’m aware that it’s also possible for these chests to (rarely - very rarely) drop a head or skin customization instead of the usual loot. If this can occur on a double-20 - which I’ve never seen - then yes, technically you’re right.

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So… when you roll both dice and a red “20” pops up over the chest is that a double 20 roll? If it is, then I’ve had several of those and over 2 years go my first legendary from a red chest Monday.

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What you described is a single 20.

If you roll a double you’ll see both dice display 20s and then the chest will make a noise and (I think) some confetti will pop out.

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Figures… the on time I sit around to watch is when I come across a single case. As many times as I’ve been through the cases behind the dragons, I’ve never got a legendary out of them. Monday I scored a thunderball fists out of the chest in the orc camp. That’s the first in almost 2 years of playing.

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Yeah, these chests are actually pretty crap for getting legendaries. You have to pay 5 Eridium for a 1/400 chance.

I would bet that standard red chests, which cost no E, are actually more likely than that to drop a legendary or pearl - to say nothing of the Merc day loot train, Pirate DLC treasure room, or Nakayama’s loot room at end of DLC3.

What they are good for is world-drop purples, if you pay the E.

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no pic but i’ve hit 20/20 a few times, and i’ve only had one orange total of all dice chests.

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I used to hop in nvhm games with friends with a lvl 72 character and farm eridium for them. You max eridium out pretty quick and I’d blow it on the chests on the way out. Never saw a legendary in any of them, even the two you wait on the golem and mimic to battle for.

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@j_r_hicks87
I know this post was created years ago, but I find it unjust that, while many hundreds, if not thousands of people read and used the information you put together, no one thanked you for your work. So let me take the opportunity…

Thank you! This has been really helpful and has been for many others, I am quite sure. It was articulated well for those who are big into numbers like myself, (I’m a statistician for the MN Twins) and also for those who do not have a head for numbers like my wife, (who was the one who actually went looking and found this post in the first place)!

Either way and again, thank you very much for your work on this! I am sorry that the community gratitude has not been there on this work since your creation of it.

All the best to all and Happy “shlooting”!

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What Killian said. This is exactly what I was looking for. Thanks!

As for anyone’s concerns about the 5 Eridium, if you’re at the level for this DLC then you can always go quickly farm the warrior for all the Eridium you can eat. Or if farming’s not your thing and you’ve got the cash you can go win some at the slots at Moxi’s Bar in the Torgue DLC.