This is going to be a brief guide to understanding probabilities within DCUO. My hope is that it will help give a bit of perspective on how drops/breakthroughs/etc are determined in DCUO and help give a starting point on discussions around drop rates/potential issues with breakthrough/etc. I’ll be going over how “random” aspects are determined, examples of item distribution in TCs/collection nodes/general loot roles, and provide some information and examples regarding breakthroughs. I’ll also give provide the last public information regarding game population size, to show what these numbers mean within our community. I added an example to help visualize how probabilities work using a normal 6 sided die. Hopefully this will help.

There are a few different systems that can be used in computer systems to get random numbers. I’m going to focus on random number tables like the image below, since they are the easiest to visualize what’s happening. Some other possibilities include using time/date (either an actual clock or play time like in Super Mario Bros), using player stats, or using some combination of sources to create a new random number (I’ll refer to this calculated random number as a “final” random number below). To use a random number table, you first need to know how many digits you need in your random number. For simplicity, I’m going to use 2 digits. If you start at the top left (column 1 row 1), you see your first number is 80. There are a few different ways you can move to get to your second 2 digit number, but for simplicity I’m going to move like reading a book, so the second 2 digit number would be 94. If you were looking for a number between 1 and 50, you would ignore these first two and end up with 25. Now if you always start in the same place, you will always end up getting the same results in the same order. In practice this could mean that every artifact breakthrough attempt would follow the same pattern. To get around this, you start in different locations called a seed point. Once you use a number at a given seed location, the next location is saved as a new seed point. Let’s say that one artifact has a seed point of column 21, row 1 and another has a seed point of column 5, row 11. For breakthrough attempts, we’ll use 2 digit numbers (00-99). At a rank 120 breakthrough you have a 40% chance of success. To represent this on the table, I will say that 00-39 will indicate a success while 40-99 would indicate a failure. For the first artifact, our number is 36 which is a success. For our second artifact, our first 8 attempts would be failures (98, 69, 93, 61, 78, 75, 48, 83) and our nineth attempt would be a success (13). Let’s say that the game “remembers” your location on the table for your next breakthrough (ranks 140), which has a 20% success rate (so we need a number between 00 and 19). The first artifact will have one failure (20) then success (18). The second artifact would have success on its first attempt (15). The reason I bring this up is that you may be able to help yourself if you get stuck in a rut, depending on the specifics of how DCUO determines random numbers for certain events. For example, if all character specific events (loot rolls, breakthrough attempts, etc) continue to pull numbers from the same point in the random number table, the second artifact listed above could have had fewer attempts needed at the artifact breakthrough screen. If player 2 (who owns artifact 2) had the seed point of column 5 row 11 and played a few instances first (using 7 sets of 2 digit numbers) before attempting the breakthrough on the artifact, they would only see one failure to breakthrough before a success on the second attempt. On the flip side, if player 2 did 8 breakthrough attempts, did something else that used two 2 digit number, then tried some more breakthroughs, they would have 3 more failures before a success. If time or stats come into play for the “final” random number to determine a loot roll or breakthrough success, you could also run some instances to help change the formula for the “final” random number. We don’t know the specifics of what items share a common point when pulling from the random number table (if DCUO uses one), let alone the specifics of that table. For example, each character could have one seed point that could be used for determining crits, loot drops, etc that also determines the seed point for an artifact when you acquire it (meaning artifact breakthroughs are independent of other in game actions that require random numbers). Another possibility is that all actions on an account share the same seed point. So, we don’t have any way of knowing what or if anything in game has an affect on our next action (or if that affect would be positive or negative).

Time Capsules, open world collection nodes, and to some extent other loot rolls are all examples of the Coupon Collector problem. In the classic coupon collector example has a certain number of items that you are trying to collect, each of which has the same chance of occurring. We know this isn’t the case for DCUO, some items are rarer than others (so the distribution is weighted). I’ll look at unweighted probabilities for time capsules first, then provide some examples with weighting. A typical time capsule has 36 collection pieces, 16 gear pieces (normal and enhanced) and 16 emblems (normal and enhanced). Each group of items (collections, gear, emblems) would be its own coupon collector problem. The probability of collecting all 36 collections (again assuming equal chance at each one) after opening 36 TCs is 36!/36^36 (3.49x10-13%). The expected number of TCs to open assuming only collections are chosen is about 150 (36 times (1/1 + 1/2 + 1/3 + 1/4 +…+1/36)).

Probabilities of successive failures on breakthroughs are fairly straight forward. If you have a 60% success rate, that means you have a 40% failure rate. So, you would have 40% times 40% (.4*.4) or a 16% chance of failing this breakthrough twice in a row. What these mean, is that 40% of players are expected to have at least 1 failure, and only 16% are expected to have 2 failures. You can extend this to see what the chance is for n successive failures by multiplying the failure rate by itself n times. In the case 3 successive failures, that would be .4^3 or .4*.4*.4 or 0.64 or 6.4%). Below shows the probability of up to 4 successive failures at rank 100 (60% success rate). Number of failures probability of seeing at least that many failures 1 | 40% 2 | 16% 3 | 6.4% 4 | 2.56% 5 | 1.024% 6 | 0.4096% Below is a table showing artifact ranks, their success rate, number of breakthrough attempts for 50% of artifacts at that rank to succeed (so anticipated attempts needed), and number of breakthrough attempts for 99% of artifacts at that rank to succeed. Don’t be lulled into a false sense of security on the 99% number of attempts though. Look at the next section for an idea of what 1% of players and 1% of artifacts could look like with our game population. Rank | success rate | >50% completion | >99% completion 20 | 100% | 1 | 1 40 | 95% | 1 | 2 60 | 90% | 1 | 2 80 | 80% | 1 | 3 100 | 60% | 1 | 5 120 | 40% | 2 | 14 140 | 20% | 4 | 21 160 | 10% | 7 | 44 180 | 5% | 14 | 90 200 | 3% | 23 | 152

Game population numbers haven’t been made public recently. So I’ll be using the most recent population data that I’ve found. In that article from 2014, we are told there were 18 million accounts (this is from before Xbox and Switch servers existed). That number likely includes accounts that were not active at the time (meaning anything between someone downloaded the game and played 5 minutes then never returned, to someone that had played frequently but quit). Unfortunately, there is no way to know how many active accounts (or characters) there are or any other usage numbers (how many artifacts/augments/etc are in use). I’ll make some assumptions from this number. If each account on average has 2 characters and each character has 6 artifacts, that's 36 million characters and 216 million artifacts. Based off those numbers, where I’ve previously mentioned 99% completion, there would still be 1% (360 thousand accounts/ 2.16 million artifacts) that would need more attempts to break through or open more TCs.

Here's an example to help visualize how probabilities work. Take a normal 6 sided die. How many times would you have to roll the die to get a 6? Each attempt has a 1/6 change to roll a six. One person could roll the 6 on the first attempt, another person could take 30 or more attempts. So a single person's results aren't a good gauge of the probability to roll a 6 (the equivalent to having a successful breakthrough on artifacts or augments), or the average number of attempts to roll a 6 (how many attempts would you expect to take to breakthrough without using a seal of completion). The more people that roll a die, the closer you will get to seeing the probability of rolling a 6 (1/6th of people would roll a 6 on the first attempt) and the closer you would get to seeing how many times you would need to roll the die on average to get a six (the probability of failure multiplied by itself until the result is less than 50%). So just to summarize A single roll of the die would have a 1/6 chance to roll a 6. On average you would need to roll the die 4 times before rolling a 6 (at 3 rolls 57.8% of people would not have rolled a 6, at 4 rolls 48.2% of people would not have rolled a 6) After 26 attempts 99% of people would have rolled a 6

Here's an image of the new Time Capsule tooltip from the Flashpoint Time Capsule. Posted by Iconic Simulation here. Just to note, these rarities aren't listed on the older Time Capsules, so there is no guarantee that they would apply to those older ones. A few things to note about rates shown. They are listed as the chance of getting that rarity or something more rare. So the chance of getting that specific rarity is actually the rate listed minus the next rarest rate listed. So that results in the following: Common/Uncommon - 28.9% Rare - 42% Epic - 26.2% Legendary - max of 2.9% (see Exotic) Exotic - exact rate is unknown, greater than 0% but less than 1%. At first glance, the rate for common/Uncommon looks "low". These should be what you get most often, but rate for these two categories is lower than Rare. We'll look at this in more detail later. As for Exotic, I'll use three different probabilities (1%, 0.5%, 0.1%). The actual chance at an exotic could be even smaller than 0.1%, but you'll start to see how hard it becomes to get this with those examples. It looks like Exotic items would be the rarest collection piece and possibly the Ultra Rare item that either dropped or didn't when you opened a capsule, regardless of your loot choices. Some examples of the Ultra Rare are the Zeus Orbital from the Amazon Time Capsule, the Neon Chroma box (black or white) from the Dark Multiverse Time Capsule, or the Harlequin Chroma from Oracle's Time Capsule. I'll break down the chances for Exotic here but do a more detailed breakdown of the other rarities in a post for the three loot choices (Gear, Emblems, and Collections). For a breakdown of your chance at an Exotic, Exotic chance | >50% of players obtain | >99% of players obtain 1% chance | ~70 | ~460 0.5% chance | ~140 | ~920 0.1% chance | ~690 | ~4600 What these numbers mean, is that with a 1% success rate half of the players that open 70 Time Capsules would have the Exotic item by that point, and 99% of the players willing to open 460 Time Capsules would have received the Exotic item by that point. This looks like a really low number for half of people to obtain the item, so you can be sure that Exotic has a smaller chance.

Here are images of the Gear rarity from the Flashpoint Time capsule. It was posted by Dragonnes here. So there are 4 Common, 6 Uncommon, 3 Rare, and 3 Epic pieces. Looking back at the rarities from the Time Capsule tool tip, we only have a listed chance for Common and Uncommon combined, so we actually have 10 items in that category. Also, with no chance of rolling a Legendary or Exotic gear piece, we need to do something with that 2.9% or our chances of getting a certain piece would be off. There are a few options for this: Instead of an Epic gear piece having a chance of 26.2%, it could have a chance of 29.1% (since the tool tip does say Epic or better and there isn't better in gear). New percentages for everything could be created based just on the total of the total of Common/Uncommon, Rare, and Epic. The percentage chance for Legendary or better could be added to Common/Uncommon. For option 1, our percentages would be Common/Uncommon - 28.9% Rare - 42% Epic - 29.1% For option 2, our percentages would be Common/Uncommon - 29.8% Rare - 43.2% Epic - 27% For option 3, our percentages would be Common/Uncommon - 31.8% Rare - 42% Epic - 26.2% These might not look too different, but it can slightly change the distribution that you get. I'll use option 1, since I feel it's most likely with the wording in the tool tip, but be aware that this is only one possible way they could have handled the chance at gear. The chances listed above are for getting anything in that rarity. It might be useful to know how likely it is to get a specific piece in each rarity. That would be the chance of getting that rarity divided by the number of pieces in that rarity. Common/Uncommon - 2.89% (28.9% / 10) Rare - 14% (42% / 3) Epic - 9.7% (29.1% / 3) So, for example, if you are just missing the Enhanced Head style, you know it has a 9.7% chance of dropping. This is roughly the same chance as the rank 160 breakthrough. Half of people would get it by the 7th Time Capsule, 99% would get it by the 46th (this being 9.7% pushed the 99% success rate out a few more compared to the rank 160 breakthrough).

Here's an image of the Emblem rarity from the Flashpoint Time capsule. It was posted by Dragonnes here. So we have 6 Common, 2 Uncommon, 6 Rare, and 2 Epic. Looking back at the rarities from the Time Capsule tool tip, we only have a listed chance for Common and Uncommon combined, so we actually have 8 items in that category. As above, I'll be using option 1 for how I handle Emblems lacking Legendary and Exotic items. The chance for getting a specific Emblem is: Common/Uncommon - 3.6% (28.9% / 8) Rare - 7% (42% / 6) Epic - 14.5% (29.1% / 2)

And finally, here are the rarities for the collections for the Flashpoint Time Capsule. The color for the 12th collection in each set isn't confirmed, but these would be the rarest in the set so I feel fairly confident in the rarity I've assigned below. It's a Horrible Life (rewards Future Flash's Cowl). Lighning Rod Electric Chair Time-lost Father's Letter Wally West's Missing Cell Phone "CCCCOLD" Vanity License Plate Pied Piper's Cyborg Rat Troupe Trixter's "BOOM" De-wheeled Skateboard $100 Wayne Casino Gambling Chip Bag of Tawny Tiger Chow Warlord's Missing Eye Highball Hal Jordan's Box of Regrets Cosmic Motorcycle's Speed Force Tank Green Arrow Industries Power-Dampening Prison Neck Clamp Penthesilea's and Orm's Delights (rewards Lasso of Truth waist). Amazonian Royal Wedding Garb Wreath from Hippolyta's Funeral Pyre Bottle of Tainted Atlantean Wine Amazonian Reeducation Seminar Pamphlet Lois Lane's Last London Broadcast Tara Markov's Honorary Amazonian Equipment Sunken Vatican Stained Glass Dove Chunk of Markovian Bridge Thomas Curry's Dropped Crutch Memorial to Drowned Europe Jimmy Olsen's Secret Communicator Camera Recording of Abin Sur's Press Conference Memory-Vest (rewards Madness Chroma) Busted Herne-Ramsgate Cauldron Abra Kadabra's Pink-to-Orange Roses Mindwarp and Raven's Shattered Soul-Self Statues Remains of Subject 2 Deadman's Costume Makeup Dr. Frankenstein's Reconstructed Journals Damaged Stasis Tube Mazursky's Plasma Project M Notes Shrieve Jr.'s Hunting Knife Bride's 4-Gun Back Holster Map to Romanian Monster Sanctuary So there are 9 Uncommon, 9 Rare, 13 Epic, 4 Legendary, and 1 Exotic in the collections. The chance for getting a specific Collection is: Uncommon - 3.2% (28.9% / 9) Rare - 4.7% (42% / 9) Epic - 2% (26.2% / 13) Legendary - 0.7% (2.8% / 4) Exotic - 0.1% (there's only one Exotic collection) For Exotic I chose to use the 0.1% rate from earlier, which made the overall Legendary rate 2.8%. If the Exotic chance is 1%, the overall Legendary rate would be 1.9% with a chance of ~.5% per collection piece.I won't be redoing the Coupon Collector problem from earlier with different rarities for items. The number of Time Capsules you would need to open becomes highly dependent on the order you receive items. Though it's a safe bet that the Exotic item would typically be the last thing you get, so could use the average (50% ) or 99% success numbers for the Exotic item as the number needed to complete the Time Capsule in general.

So you're saying that when I tried to break through my alt's Transformation Card to level 140, which has a 20% success rate (80% failure rate), that it was just the worst rng that I broke 11 seals of preservation before the 12th attempt worked? The probability that I would fail 11 times is .8^11, or a whopping 0.086% (rounded up); is that right? I got DCUOed.

I wouldn't call it the worst rng, there's still several thousand people or several million artifacts that would take even more attempts without using a seal of completion. But it was pretty terrible rng. At some point you need to cut your losses. You ended up spending more on preservation than the cost of a seal of completion. I usually plan for needing somewhere between the 50% and 99% attempt numbers. For rank 140 that means between 4 and 21 attempts. If I remember correctly, 10 seals of preservation cost the same as a seal of completion. So you can look at it as guaranteeing the breakthrough for one price, or nearly guaranteeing the breakthrough for double that price (since there's still a chance that you wouldn't have broken through after 21 attempts). I usually use a seal of preservation or two, just to see if I'm lucky, but generally I end up using completion there.