all you need to know about Honkai gacha
based on game version 4.0
This guide will help the captains to understand the difference between the diverse gacha supplies in Honkai Impact 3 and to know which supplies are worth to pull. Also, it will reveal some secrets behind supply drop rates. So, it is interesting for new and old players.
Based on the analysis of gacha supplies the captain should be able to choose the supply with highest chance of getting needed Valkyries and equipment. This guide will not analyze whether a specific banner is worth pulling because the meta shifts from time to time and the situation of every captains is different.
At first it is important to differentiate the supplies from the banners. Supplies can be found under Supply-tab. Different supplies have their own specific rules. The banners are the actual content in the supplies (Figure 1, A). The banners define the pool of equipment or Valkyries which of those can be get form the supplies.
Figure 1: Example of an Expansion Banner
Before going into details about different supplies in the game, it is good to know the basic rules about Honkai gacha first. In Honkai gacha crystals can be spent for one chance of pulling (single pull) or spend for 10 pulls performed at once (10x pulls) (Figure 1, C).
Also, there is at least one pity system (Figure 1, B) available in the most supplies. When no 4-star equipment or Valkyries are pulled in 9 tries, the tenth pull is guaranteed to provide a 4-star equipment or Valkyrie. The pity counter will be reset after a 4-star equipment or Valkyrie has been pulled. When a 10x pulls is performed and the 4-star pull is at 6th pull for example, the 4 surplus pulls are counted into the reset pity counter. That means only maximum of 6 additional pulls are required for the next guarantee 4-star pull. This is how the standard pity system in the game works (this name will be used in the whole guide). Some supplies have special pity counter at different values. The details of rules of different supplies can be checked directly in the details of the banner.
Normally, the pity counter won't carry over between banners within the supply, but there are some exceptions: Valkyrie Expansion supply, Focus supply and Elf supply (above v3.8) have a global pity counter system (the name is only used in this guide). The pity counter in those supplies won't reset after a banner in those supplies is over. The current count of the pity counter will be carried over into the next banner.
The game is filled with a lot of different kinds of supplies and banners. They are there to allure captains brainlessly spending the crystals and suck out the money of their credit card. Sorry, I mean to improve captain's gameplay and to increase captain's waifu count of course! To prevent brainlessly spending the crystals into useless supplies it is important to know all kinds of supplies in the game first:
(200 crystals per pull)
Dorm supply (Figure 2) is accessible for every captain from the start of the game and is permanently available. The pool contains only older Valkyries. Newer Valkyries are not in the pulling pool! A small chance also exists to pull a 4-star equipment. There are two times of 25 pulls pity counter of getting an S-rank Valkyrie. After pulling two S-rank Valkyries from this supply the pity counter will be set to 100 pulls. The minimum chance of pulling a new S-rank Valkyrie is 40 %. Additionally, there is another pity system applying only to Dorm supplies. If two already owned S-rank Valkyries are pulled, the third S-rank Valkyrie is a guaranteed new S-rank Valkyrie.
Figure 2: Dorm Supply
(200 crystals per pull)
Dorm Equipment Supply (Figure 3) is similar to normal Dorm supply. It is for pulling old 4-star equipment and permanently available. Newer equipment is not in the pool! The minimum change for getting a new 4-star equipment that the captain doesn't own is also at 40 %. After pulling three already owned pieces of 4-star equipment, the fourth 4-star equipment pulled is guaranteed to be new.
Figure 3: Dorm Equipment
(280 crystals per pull)
Valkyrie expansion (Figure 4) is the main way to get the newer Valkyries. It contains always one focused S-rank Valkyrie, one focused A-rank Valkyrie and three other A-rank Valkyries. The chance of getting focused Valkyries is increased. The pity counter for the focused S-rank Valkyrie is at 100 pulls. After 9 pulls without getting an S- or an A-rank Valkyrie the 10th pull is guaranteed with an S- or A-rank Valkyrie. If the captain doesn't get the focused S-rank Valkyrie within the available time of the supply, the left-over pity counter will be carried over into the next Valkyrie Expansion banner (global pity counter).
When a brand-new Valkyrie is introduced in the banner, it is available for 14-21 days. When the banner contains only already released Valkyries, the banner lasts for 7-14 days.
Figure 4: Valkyrie Expansion
(280 crystals per pull)
Equipment Expansion shows up when a new Valkyrie is introduced in the Valkyrie Expansion. It always contains the signature equipment of the UP S-rank Valkyrie. The chance of UP Equipment is of course increased. This supply is as long available as the Valkyrie Expansion supply. Equipment Expansion always comes along with a Valkyrie Expansion, but not every Valkyrie Expansion comes together with an Equipment Expansion. Especially when an existing Valkyrie Expansion banner comes back, its signature equipment is mostly available in the Focus Supply.
Equipment supply comes with a unique pity system. For an S-rank signature equipment there is a guaranteed pull for a single piece of the signature equipment every 50 pulls. For an A-rank Valkyrie's signature equipment the pity counter for a signature piece is at 30 pulls. That means in the worst case 200 pulls are needed for getting full equipment for an S-rank Valkyrie and 120 pulls for A-rank Valkyrie. Beside this unique pity system. It also has the standard 10 pull guarantee system. Equipment Expansion's guarantees do not carry over into the next banner.
(280 crystals per pull)
The Focus supply contains an UP set of stigmata and a UP weapon. The Focus supply banners changes once per week. There are normally two different Focus supply (A and B) banners available (Figure 5, A). One resets on Monday, the other one resets on Friday. It has a 10-pull guarantee for 4-star equipment like Equipment supply. The pity counter separately counted for A and B banners. They don't affect each other. The pity counter does carry over into the next Focus supply banner (global pity counter). So, when the guaranteed pull can't be afforded, the first pull of the next Focus supply banner will be a guaranteed 4-star pull. Additionally, the Focus supply has a “Wishing Well” (Figure 5, B). In the Wishing Well 2 copies of an UP Stigmata set together with 2000 Stigmata Resonance can be exchanged into any piece of the UP Stigmata set. The Wishing Well is useful to complete a whole set faster.
Figure 5: Focus Supply
(120 crystals per pull)
SP Supply is for pulling SP Valkyries. The SP banner contains only A-rank Valkyries with a SP Valkyrie as UP Valkyrie. Right now, there are no other supplies to get SP Valkyries beside through SP Supply. Alternatively, SP Valkyries can be unlocked via fragments farmed from the Open World or brought from the shop. The pity counter for pulling SP Valkyrie is only at 25. The standard pity system also applies. Additionally, there are bonus fragments for purchasing a certain amount of pulls. A specialty of this supply is that it can drop blank fragments which can be exchanged for A-rank Valkyrie fragments. The supply is available for mostly for 7-14 days.
(150 crystals per pull)
Elf Supply is the only way to unlock gacha Elves. This gacha cost only 150 crystals per pull and the pity counter for the UP elf is at 100 pulls. For every 10th pull the UP elf or its fragments will be dropped. There is also a global pity counter system for this supply (above v3.8).
Figure 6: Elf Supply
There are and will be more variants of supplies. Mostly they relate to special events and holidays. The imagination of the developers to bait people for pulling gacha are unlimited. Some common special supplies will be introduced in this chapter.
(280 crystals per pull)
Now there are 3 divine weapons (Xuanyuan Sword, Might of An-Utu and Twins of Eden) which can only be obtained via Divine Weapon Supply. The supply lasts for one week. It has a 50 pulls pity counter to get the UP Divine weapon (Figure 7, B). The standard pity system applies, too, but not the global pity counter system. The standard pity system doesn't reset the pity counter for the UP weapon. This means when a piece of 4-star equipment beside the divine weapon is pulled, the pity counter of UP Divine weapon will decrease normally. Additionally, there are also bonus resources for pulling a certain amount (Figure 7, A). Besides the divine weapon an extra UP weapon and UP stigmata set is also included.
Figure 7: DIVINE WEAPON – AN-UTU BANNER
(280 crystals per pull)
ADV Supply is mainly for ranking up S-rank Valkyries into SS-rank. For every 10 pulls the captain will be rewarded with a certain amount of UP S-rank Valkyrie's fragments. At 100 pulls 100 fragments (70 from reward, 30 from conversion of Valkyrie card) for a normal S-rank Valkyrie and 250 fragments (200 from reward, 50 from conversion of Valkyrie card) for an awakened S-rank Valkyrie will be gathered. This is enough to upgrade the UP Valkyrie into SS-rank, but it works only when the UP Valkyrie is already unlocked.
The pity counter for the UP Valkyrie is at 100 pulls and does not carry over into the next ADV supply banner. A specialty in this supply is that only 50 pulls are needed to unlock an awakened S-rank Valkyrie just with additionally given fragments. ADV supply lasts normally one week.
After the knowing of the difference between diverse supplies, which one is worth pulling, then? There are single and 10x pulls options. Which is better? Those questions are answered in this chapter. This chapter contains mathematical equations, formulas and graphs which are probably not understandable for everyone. Those people can skip all the equations and read just the summary.
The drop rates of supplies can be checked in-game. What MiHoYo doesn't explain is that the “overall drop rates”, which the game shown, consider the standard pity system already. This means that the real drop rate (without standard pity system) is lower than the shown number. So, how high is the real number?
To answer this question some math is required. For supplies for which only the standard pity system applies, the expected value can be calculated as:
The real chance of pulling a 4-star equipment is x. The chance of pulling a piece of 4-star equipment after n-tries is:
For the 10th pull which triggers the standard pity system is a guaranteed 4-star equipment. That means for the 10th pull:
With all the formula together, the following equation for expected value with consideration of the standard pity system can be set up:
The solution for x is:
That means the in-game drop rates divided by 2.54152 equals the real drop rates. This applies to every supply with only the standard pity system. For the Focus supply the real drop rates are calculated (Table 1):
Table 1: Focus Supply - In-game and Real Drop Rates
One can see that the real drop rates are much lower than the officially shown drop rates. This will have an impact on single pulls which is discussed in the next chapter.
There are some screenshots posted in the internet which shown lucky drops of 4-5 pieces of 4-star equipment within 10 pulls. Those pulls are mostly performed on the Japanese server. On the Japanese server they don't have the standard pity counter system. The in-game shown drop rates are the same. This could lead the drop of pieces of 4-star equipment very unevenly. One can get lucky and pull several pieces of 4-star equipment in a row, but there will be also situation where no pieces of 4-star equipment is pulled at all in hundreds of pulls.
Normally, with 10x pulls a lot of time can be saved during the pull of a banner. One should keep attention when pulling from a supply without global pity system. The surplus pulls won't carry over into the next banner and are wasted. It is better to perform single pulls at the end of a pull run or when only one piece of 4-star equipment or one copy of Valkyrie is needed to just get the guarantee pull and to prevent surplus. So, is there a difference in probability of getting a focus-equipment by performing single pull or 10x pulls?
When the guarantee pull is always gotten by performing single pull, then it is no drop rate difference between single and 10x pulls. The drop rate of a piece of equipment can be checked under banner's detail. The showed drop rates include the influence of the pity system as mentioned in chapter 4.1. Table 1 already showed that the drop rates without considering the standard pity system are a lot lower than official drop rates.
In short, there is no difference in probability when the performed single pulls have fulfilled the guarantee pity count.
This chapter compares all the Valkyrie supplies. An overview of all Valkyrie supplies which are introduced in chapter 3 is shown in Table 2:
Table 2: Valkyrie Supplies Comparison Table
In general, Dorm supply is not recommended for spending crystals because there are many ways to obtain Dorm supply tickets to perform free pulls. By pulling from SP supply it is only recommended to pull until the SP Valkyrie is unlocked which needs 25 pulls at maximum. Normally there will be events available at the same time to obtain 100+ SP-Valkyrie fragments for free.
By looking at the difference of drop rates between Valkyrie Expansion and ADV supply, the UP rate of the S-rank Valkyrie in the Expansion supply is higher than in ADV supply. Beside the higher drop rate, the Expansion supply also has global pity counter. ADV supply is only good when pulling for an awakened S-rank Valkyrie. It is not recommended to pull ADV supply when the captain doesn't have enough crystals for the 50 or 100 pity counters.
This chapter compares all the equipment supplies. An overview of all equipment supplies which are introduced in chapter 3 is shown in Table 3:
Table 3: Equipment Supplies Comparison Table
It is not recommended to pull from Dorm equipment. The pool of that supply contains so much stigmata and weapons that it is difficult to pull a specific weapon or stigmata set. Also, most of the equipment in the pool is obsolete. An investment in that pool rarely pays off. Divine key supply is worth to pull. It has the highest drop rate of 4-star equipment.
When a new Valkyrie comes out, her signature gear will be both in the Equipment supply and in the Focus supply, although Focus supply only lasts one week. The Equipment supply lasts as long as the Valkyrie supply, mostly 14-21 days. The Focus supply has a Wishing Well and a global pity counter system. The Expansion equipment supply has its own unique pity counter system. Answering the question, which one to choose for pulling, needs a more detailed analysis which is the topic of the next chapter.
So, which one needs lower pull count for the whole S-rank signature set? This is the topic in this chapter. First the drop rate of both supplies will be separated in detail (Table 4).
Table 4: Detailed Drop Rates of Equipment and Focus Supply
It is clear to see that Focus supply has higher drop rates in UP equipment than Equipment Expansion, but it can't be concluded yet, that Focus supply is better for pulling the whole UP set because the influence of the pity counter system of equipment supply and the Wishing Well of the Focus supply are not considered.
A Chinese Uploader 鱼仙 (UID: 34075114) on bilibili has done a simulation of 108 trillion pulls each for Focus and Expansion supplies. The data is shown as cumulative distribution function (CDF) in the following graph (Figure 8):
Figure 8: Simulated Result of Focus and Expansion Supplies
The expected value of Focus supply is 108.5 pulls and Expansion supply is 111.2 pulls. This means by adequate amount of pulls the captain needs 108.5 (Focus supply) and 111.2 (Expansion supply) pulls in average to get the full set.
The median, 50% of the people, needs 100 or lower pulls from pulling Focus supply to complete a set and from Expansion supply 110 or lower pulls. Those values are close to each other, but there is a difference in the course of those curves.
Both graphs cross at 130 pulls. That means 73.56% of people have finished the whole signature set by pulling under 130 times. Before 130 pulls more people, who have pulled from the Focus supply, have finished the set than those who have pulled from Expansion supply, but there are 4.23% of people pulling from the Focus supply who can't finish the set after 200 pulls. By 200 pulls the Expansion supply will hit its unique pity system all 4 times and finish the set automatically.
When the captain has under 130 pulls of crystals (36400 crystals) it is better to pull from the Focus supply. By having more than 36400 crystals the risk of hitting the 4.23% is to too big by pulling from the Focus supply. In that case Expansion supply is safer. The statistical average number of pulls for pulling a full set is 108.5 (Focus supply) and 111.2 (Expansion supply).
Elves in the game are nice to have, but not indispensable. It has standard pity system and the global pity system (above 3.8). The impact of the elf is not higher than completing a signature set of a strong Valkyrie. When the focus of the captain is on the meta and still lacking meta relevant Valkyries and equipment, the crystals are mostly better invested in the Valkyrie and Equipment supplies first.
In the Valkyrie Supplies the Valkyrie Expansion is the main way to get new S-rank Valkyries. Even when not pulling the S-rank Valkyrie the already spend pulls are lowering the global pity system for the next banner. ADV supply is only good for ranking up already owned Valkyries into SS-rank. Because of lacking the global pity system, it is only worth pulling when the 50 (unlocks awakened Valkyries) or 100 pity count can be hit. SP supply is only worth to pull to unlock the SP Valkyrie.
Between all the equipment supplies Divine key supply has the highest chance of getting a piece of 4-star equipment. Between Focus and Expansion supply, Focus supply is better when under 130 pulls are performed. When more than 130 pulls are planned, the Expansion set is safer. The average (expected value) number of pulls for getting a full set is 108.5 (Focus supply) and 111.2 (Expansion supply).
Dorm supplies are not worth to spend crystals on. Instead the free tickets should be used for that. Elf supplies should be avoided when the captain with meta focus is still lacking strong Valkyries and equipment. The impact of those on the gameplay is stronger than the influence through the elf.
There is no statistical difference between single pull and 10x pulls when both hit the standard pity counter. Without hitting the standard pity counter, the single pull has lower drop rates than the official drop rates. Single pull is good for fulfilling the pity counter to prevent surplus pulls.
This guide covers most important information about the Honkai gacha. Hopefully it can help the captain's decision when pulling gacha. I wish all captains good luck in pulling! If you have any questions and suggestions, you can contact me on Discord (ID: Raz0r#8620).