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Hi all! I've seen quite a few discussions here, in my alliance and the region chats about what is the most preferable way to farm Axi relics, so I decided to look into that. The objective of this post is to ascertain which of the common locations for Axi relic farming is the fastest: Marduk, Hieracon and Xini. To do this, I will calculate the expected time for getting both a) any Axi relic and b) an Axi relic in particular.

## A primer on statistics

Here I'm going to be talking about random variables, expected values and so on. If you're familiar with these or just want to get to the results, feel free to skip this section!

Before we start, I want to take a moment to explain how this is all calculated. As you know, most of the loot you get in Warframe is random, that is, you don't know what you're going to get beforehand. For instance, the Jackal in Venus can drop Rhino's chassis, neuroptics or system blueprints, with a chance of 38.72%, 38.72% and 22.56% respectively. This is what we call a random process and the drop you get is what we call a random variable; you don't know what it is, but you know which chance you have to get each part.

Random variables are not exclusive to Warframe, of course. There are lots of real-world examples you can use. For instance, a coin toss is a random process with a 50% chance of head and a 50% chance of tails. Or rolling a 6-sided dice is a random process where each side has a 1/6 = 16.67% chance to be rolled.

Opposite random processes are deterministic processes, which are these in which you know exactly what will happen. This is pretty obvious stuff: if you have a coin on a table and it's heads, if you turn it around, you know that you're going to get tails. But the reason I wanted to clarify this is that depending on what you measure, a process can be both deterministic and random. For instance, every time that you get to rotation B on Xini, Eris, getting an Axi relic is a deterministic process; you know that you're going to get one no matter what. However, you don't know which Axi relic you will be getting: which exact relic you'll get is a random variable. This is going to be critical later when we discuss Xini. 🙂

Thankfully, DE publishes the drop tables online, so we know which chance we have to get any drops in the game. But this is only one part of the puzzle, because even if we know the chance of getting a relic after completing a mission/round/excavator, we also need to know how much time we needed to get there. Of course, it's not the same to get an Axi after 20 minutes than after 2 hours, is it?

My objective here is to calculate, in average, how much time it takes you to get an Axi relic; this is called the expected time. Here comes an important "but": if you have a 50% chance to get a relic after 5 minutes, then sometimes you'll get a relic after 5 minutes, but sometimes you'll need 10, or 15, or 20… or maybe an hour if you're very unlucky. The expected time only means that, in average, it'll take you that long. But be aware that the more you play, the closer you'll be getting to the expected time. Luck tends to even out on the long run; there is even a mathematical law for this, called the law of large numbers. In general, it's wisest to go for the option that yields the shortest expected time, even if it doesn't guarantee you your relic. Sometimes you'll get unlucky, but sometimes you'll also get very lucky and get your relic in an extremely short time. And when you play Warframe for hundreds or thousands of hours, bad luck and good luck get even really quickly and the total time spent is almost always very close to the expected time.

But how do we calculate the expected time? It's actually very simple:

Expected time to get a relic = (Time needed for one roll of the drop tables) * 100 / (Chance to get a relic as a percentage).

So for instance, in a game mode where we got a drop every 5 minutes and we got an Axi relic 50% of the time , the expected time would be 5 minutes * 100 / 50 = 10 minutes.

## How often do we get a chance of an Axi?

While we know exactly the chance to get each relic in rotation of each game mode, in order to calculate the expected time, we need to know how long it takes before we get a drop:

– Marduk: 4:10. The shortest time I've managed to complete a solo run of Marduk is 4:10 from the moment I click on the mission to the moment I'm on the "mission results" screen after extracting. I did this with a speed Volt and a fairly fast computer. While some people may get fastest times on their Marduk runs, I believe that 4:10 is a fair average time for our calculations.

– Xini: 8:15. This is actually fairly easy to calculate and not very contentious, as interception rounds usually take more or less the same time as long as the people in the team know to capture their points quickly. 4 rounds of Xini will typically take 16:30, counting the time you need to clear out the area after you've won the round and then the extract/battle screen. Since by round 4 you've got 2 chances of Axi (rotations B and C), for our calculations it's fine to say that you get one every 2 rounds, or every 8:15. It would be more accurate to say that you get one after 12:22 and another one after 4:08, but I promise this won't change the end result.

– Hieracon: 5:00. Now this is a bit of a ballpark figure, but I believe it's a very fair representation. I've been doing runs of 36 excavators in Hieracon in 41 or 42 minutes with randoms, so this amounts to 70 seconds, or 1:10, for every excavator. However, to account for the risk of destroyed excavators and so on, I'm giving it an extra five seconds and estimating it as 1:15. You only get a chance of Axi relics in rotation C, which is every 4 excavators, so then it's approximately once every 5 minutes.

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Note that I don't count the time to get in and out of the mission in Xini and Hieracon because as you can do lots of rounds in just one mission, the effect is much smaller here. For instance, if it took 30 seconds and you pulled out in Xini after 20 rounds, then you'd have had 10 Axi relics by then – a loss of only 3 seconds per relic; in Marduk you'd always lose that amount of time for every single relic you got.

## What is the expected time to get an Axi relic?

With that out of the way, let's now look at the expected time to get a relic in each map:

Marduk

According to the official drop tables, you have a 5.88% chance of getting each Axi relic and there are 9 relics, so in total that's a 52.92% chance of getting any Axi relic after a Marduk run. We estimated that it would take 4:10 minutes, or 250 seconds, to complete a Marduk run from the navigation screen to the mission results screen.

• Any Axi relic: 250 seconds * 100 / 52.92 = 472 seconds = 7:52 minutes.
• A particular Axi relic: 250 seconds * 100 / 5.88 = 4251 seconds = approx. 1 hour and 10 minutes.

Also, since there's a 47.04 % chance of getting a Neo relic, you'd expect to get a Neo relic every 8:51 minutes.

Xini

Xini has a 100% chance of dropping any Axi relic in rotations B and C, and a 14.29% chance of dropping most specific Axi relics. The exceptions are Axi P2, which has a 28.58% chance to appear on rotation B, and Axi A6, which cannot appear on rotation B (0% chance). Also note that you cannot get any V9s and S5s here.

• Any Axi relic: 495 seconds * 100 / 100 = 495 seconds = 8:15 minutes.
• A particular Axi relic (except A6 or P2): 495 * 100 / 14.29 = 3465 seconds = 57:45 minutes
• Axi P2: 1/2(495 * 100 / 28.58) (rot B) + 1/2(495 * 100 / 14.29) (rot C) = 2599 seconds = 43:19 minutes
• Axi A6: 990 * 100 / 14.29 (only rot C) = 1 hour, 55 minutes and 30 seconds

Additionally, it has a 70% chance of dropping a Neo relic in rotation A, so the expected time for each Neo would be 11:43 minutes.

Hieracon

Hieracon has a 11.06% chance of dropping each specific Axi relic on rotation C, which adds up to 77.42% for any Axi relic. Note that, unlike Marduk, it doesn't drop V9s and S5s. So the expected times would be:

• Any Axi relic: 300 seconds * 100 / 77.42 = 387 seconds = 6:27 minutes
• A particular Axi relic: 300 seconds * 100 / 11.06 = 2712 seconds = 45:12 minutes.

Also, it has a 46.69% chance of dropping a Neo relic in rotation B (none in rotation A), so the expected time for each Neo would be 10:42 minutes.

From the above calculations, it seems clear that Hieracon yields the shortest expected times for Axi relics, so with this data in hand, this would be my top recommendation for relic farming. However, you'll also notice that the differences between maps are not massive, so most of the time you'll be fine with any of the maps. For instance, in average, Xini will be 28% slower than Hieracon for Axi farming… which is not a massive difference anyway.

Note, however, that you should never try farming Axi A6s in Xini because they don't drop in rotation B, so the expected time to get these goes out of the roof. And always check the drop tables to ensure that the relic you want is dropped there; at the time, Marduk drops some Axis that Xini and Hieracon don't.

There's a common argument that Xini is better for farming relics because there you get guaranteed drops, but this is not as clever as it sounds. While you're guaranteed to get drops there, on average you'll be getting better results in Hieracon, so for long farming sessions you'd need to be very unlucky to get fewer relics – most of the time, you'll be getting more in the same time. And moreover, most of the time you're going to be farming a specific relic, not any relic in particular, so the argument falls flat here. If you're going for, let's say, Axi D1, then any other drop is going to be garbage to you. Xini just guarantees that you're going to get one particular kind of garbage. Personally I'd only consider Xini if I really needed to get 2 or 4 Axi relics in little time and I didn't care which ones they were, which is not very usual anyway. Or if I needed P2, since Xini is currently the fastest for these.

As for Marduk, looking at the results, it's hard to justify the position held by some that it's the fastest way to farm Axis. Unless I'm missing something here, it lags behind Hieracon significantly. However, it does have the advantage of not requiring any randoms who may hinder you by taking a long time to extract. In my experience, people in Xini and Hieracon know what they're doing more often than not, but you'll almost always pick up stragglers in Marduk, so please do this one solo if you prefer it. A good thing about Marduk, however, is that you'll get more Neos than in Hieracon and Xini, so it's a good option if you're interested in both.

Lastly, there's Hieracon. Randoms seem to be pretty good most of the time here, so you can jump in with your Frost or Limbo and easily open a lot of excavators. Of course, a good defensive frame and some coordination will help a lot here – playing with friends or clanmates is a good idea here.

## TL,DR

• Hieracon is fastest, but not by a massive difference.
• If you dislike Hieracon, Xini and Marduk are viable alternatives too.
• Stay off Xini if you're farming A6 for Atlas Prime Neuroptics!
• Always check the drop tables to ensure that the relic you want is dropped in your chosen mission.

Thanks a lot for reading! (I hope. :P)