If you've ever fiddled around with trying to keep your character at a certain LUC value during soul transfer, you might have thought that there is some amount of randomness involved or that the formula for determining luck is too complex to decipher or something of the sort.

There already exist a couple of other informative guides that point out a lot of good information on the LUC Stat in general though I came to realize while experimenting that both of the ones at the time of my writing of this guide are flawed in their explanation of how LUC is determined during the Soul Transfer Process. As such, I took it upon myself to do some research and testing of the edge cases to determine what I believe to be the formula used to determine LUC after Soul Transfer. I've also done a bit more digging into some of the pieces of information surrounding this around the internet and hope to clear up any misunderstandings about how the LUC stat works

As I've somehow become more attached to fiddling with the Hidden LUC stat than I have with actually playing the game, I figured It would be best to compile my findings into a guide of its own.

LUC has been observed to have an appreciable effect on basically all RNG Dependent Events in Battle such as:

1. Critical Hit Rate
   
2. Critical Gore Chance
   
3. Resonance Rate
   
4. Echo Rate
   
5. Status Recovery Chance

As such, it is generally regarded that Higher LUC is better in almost all scenarios, save for some specific Pacts and Skills that require low LUC to operate.

In addition it has also been theorized that it may also affect non-combat random elements such as Rare/Veteran Enemy Encounter Rates though this effect, if any, is much less apparent than those it has in Battle. Similarly, it is not known whether a larger LUC Value has any effect outside of the predefined LUC Tiers as the effects of LUC are difficult to precisely observe.

Before I get into any more details, I'd like to provide a bit of a reference to a lot of the various nuanced terminology I'm going to be using throughout this guide for you to reference back to when getting into the topics.

You do not have to worry about this section right away. Feel free to skim or skip over it as these will be explained in more detail as they show up in the guide.

• LUC Tier: This refers to the Word that is Displayed to you in the Status screen for LUC. (ex. Fortunate)
  
• LUC Value: This refers to the actual Numerical representation of your LUC as opposed to the one that is displayed to you with words in game.
  
  
• Base LUC: This is your Puppet's LUC Value Without Any Modifiers.
  
• Naked LUC: This is your Puppet's LUC Value Without Equipment Modifiers. This includes any other modifiers Such as from Moon Stance or Lucky Star
  
• Total LUC: This is your Puppet's LUC Value With All Modifiers Applied.

• Listed Equipment Modifier: This refers to the LUC Modifier that is Listed on your Equipment In Game. This is NOT always the actual amount of LUC that you get because it is multiplied by LUC Aptitude before being applied.
  
  
• Equipment LUC Modifier: This refers to the Modifier that your puppet's Equipment applies to your Base LUC. (See Listed Equipment Modifier for how this differs from that)
  
• Stance LUC Modifier: This refers to the Modifier that your puppet's Chosen Stance applies to your Base LUC
  
• Skill LUC Modifier: This refers to the Modifier that any Skills your puppet has add to your Base LUC (i.e. Lucky Star's +25)

• LUC Aptitude: This refers to your Puppet's Hidden LUC Aptitude Percentage that affects the Actual LUC Given by the Listed Equipment Modifier.
  
• Base LUC Aptitude: This refers to your Puppet's LUC Aptitude Without Any Modifiers. All Puppets are assumed to have a Base LUC Aptitude of 100%.

• Nature LUC Aptitude Modifier: This refers to the Modifier that Certain Natures apply to your Base LUC Aptitude.

• ST LUC: This is your Puppet's LUC Value As it appears to the Soul Transfer Algorithm. Remember to calculate this using the Stance and Nature of the New Puppet
  
• ST LUC Modifier: This refers to the amount of LUC that is added to your Total LUC during Soul Transfer. This can be easily derived from your Puppet's Lucky Number

While the Player is only informed of a character's current LUC in words as one of {Despair, Unlucky, Mediocre, Lucky, Fortunate}, It quickly becomes apparent that there is a hidden underlying numeric value for LUC backing these qualitative LUC Tiers when you look at all the equipment listing its LUC modifier as a numerical value. As far as we are aware, the LUC stat is represented internally as a number from 0~99. These Values are then divided up into 5 LUC Tiers that are then displayed to the player as LUC in the Status Screen. The LUC Tiers you will see are as follows:


This relationship between LUC Tiers and LUC Values gives us a much needed stepping stone for determining how LUC interacts with various other things in the game that modify the stat (i.e. Modifiers).

A modifier is anything that adds to or subtracts from your Base LUC Value. As far as I am aware there are only 3 things that act as modifiers for the LUC stat:

This said, The game does not treat all modifiers in the same way. While they all end up being added together into one big Total LUC Value and then displayed to you in a LUC Tier, modifiers have different things that apply to them in the game and some of the systems omit certain modifiers from their calculations.

I've included a brief description of what differentiates each type of modifier in the table above. I will cover each in more detail when the relevant system comes up in the Guide.

The Keen of you may have noticed that while the LUC stat is shown to you in stats (albeit obscured), for some reason it is completely absent from the in game aptitudes section. While it would be great if this simply meant that there are no LUC Aptitudes, this is NOT the case.

While it has gone mostly unknown for quite a while and caused no end to annoyances to figuring out LUC in the process, LUC Aptitude is a very real thing. The primary issue we run into with LUC Aptitudes is that, just like any other Stat aptitudes, they Modify the Actual Stats that Equipment gives as opposed to the stats that it lists. So for instance, If I had an Aptitude for a Stat of 110% and equipped a piece of equipment that lists itself as giving 10 to that stat, I would actually be getting 11 from that stat instead! The same thing happens in reverse so 90% aptitude in a stat would have 10 stat equipment giving only 9 of that stat.

When it comes to LUC Aptitude, it works the exact same way as every other aptitude in the game, though the only difference is that The Aptitude Percentage is not displayed to the player. As a result, the community has largely known that it probably exists, but no-one knew how to go about figuring out how to determine it. Well, no-one until now that is...

With Much help from the community to form my initial hypothesis and then close to 100 Near Identical Puppets & Soul Transfers to test it Later, I've finally gathered enough data to say with fairly high confidence exactly how each and every Nature Modifies your Base LUC Aptitude of 100%. So without further Ado, I present to you the Table of Nature LUC Aptitude Modifiers


You can use this table of Nature LUC Aptitude Modifiers along with your Total Listed Equipment Modifiers in the following equation to get your Actual Equipment LUC Modifer as was mentioned in the LUC Modifers section:

While we can't directly see a puppet's underlying LUC Value, we can deduce what it actually is by Equipping LUC modifying equipment until the puppet's LUC Tier just barely changes over to the next/previous LUC Tier. (i.e. when changing LUC by 1 changes the Tier)

This process is, frankly, A Royal Pain. This is primarily due to how equipment tends to only offer bonuses in increments of 5 or 10 by default and how LUC Aptitude Factors in as well.

The key to overcoming the equipment issue is taking advantage of the higher quality variants of this same equipment as the LUC stat will often only increase by a few points making this process much easier.

When it comes to LUC Aptitude, if you have a nature that modifies your LUC Aptitude you now have to deal with manually calculating your Actual Equipment LUC Modifier by multiplying the Listed Equipment LUC Modifier by your LUC Aptitude (As opposed to just having a Base LUC Aptitude of 100% meaning that those two modifiers end up being the same).

Additionally, if you want to find your puppet's Base LUC Value as opposed to your Naked LUC, You Also have to remove the Stance LUC Modifier (if you have Moon Stance) and the Skill LUC Modifier (if you have Lucky Star) from your final result.

To condense all of these annoying considerations down, here's a formulaic representation of what all this means:
Here's a real example of determining a puppet's Base LUC Value: (LEM = Listed Equipment Modifier)

• [+00 LEM] Lets say I have a puppet whose LUC Tier is Mediocre
  
• [+00 LEM] Thus I know that my Total LUC Value is 40~59 (Mediocre Tier's Range)
  
• [+10 LEM] I equip a Blessed Bell(LUC +10) and the puppet is still Mediocre
  
• [+10 LEM] My Total LUC Value must now be 50~59 (Min+10 ~ Max)
  
• [+15 LEM] I equip a Brazen Loincloth(LUC +5) and the puppet is still Mediocre
  
• [+15 LEM] My Total LUC Value must now be 55~59 (Min+15 ~ Max)
  
• [+16 LEM] I replace the Blessed Bell(LUC +10) with Blessed Bell[Rare](LUC +11) and the puppet becomes Lucky
  
• [+16 LEM] My Total LUC Value must now be 60 (Min of Lucky Tier)
  
• [+16 LEM] I check my Puppet's Nature to see if it modifies my LUC Aptitude and it doesn't
  
• [+16 ELM] So My Equipment LUC Modifier must be the same as my Listed Equipment Modifier
  
• Thus my Puppet's Naked LUC Value must be 44 (= 60 - 16)
  
• I check if my puppet has Moon Stance and it doesn't thus my Stance LUC Modifier must be 0
  
• I check if my puppet has Lucky Star and it doesn't thus my Skill LUC Modifier must be 0
  
• Thus my Puppet's Base LUC Value must be 44 (= 44 - 0 - 0)

While Determining A Puppet's Base LUC is often a massive pain to do, once you know the puppet's Base LUC, it is usually fairly easy to keep track of and control it using soul transfer (as we'll see later). That said, what if I told you that you can shortcut that whole process of determining your puppet's Base LUC by just creating it with a certain name?

For whatever reason, when you first create a puppet, it's Base LUC is Solely Tied to the Name you give it. Furthermore, all puppets of the same initial name will ALWAYS have the same Starting Base LUC Value

Why this is and How this is implemented is up to debate (I personally think that they just ran the Name String through a basic Hashing Function cause it's simple to code...), though this does mean that we can take advantage of this by simply looking for a Name that has a known starting Base LUC Value and naming a new puppet with this name. This will result in a puppet to which we know the exact Base LUC Value to.

Since most every list of names that I have found does not mention the exact LUC Value associated with them, I will be including a list of several names and the LUC Value associated with it for your reference in the table below


The one letter names are the ones that I started adding because they were easy to keep track of. The Religious ones were to test a theory that the system might award higher Luck to religious/occult based auspicious names. Considering that Amaterasu (Japanese Sun God), and God (Not listed but same score as Amaterasu) both scored higher than anything else I'd seen, I'm guessing this idea might be not too far from the truth (Though a lot that I tried ended up giving mixed results so I stopped bothering to check the Value for each one). I Also realized that I have a bad habit of getting the 0 and the o in the input mixed up so an example of this is on the table XD.

Basically the end goal with this section is to fill out all of the possible LUC values with a possible starting Name you can use that will result in it. This is, of course, insane and I know it. If someone wants to post some names that end up filling out some of the MANY remaining Blanks it would be much appreciated, though determining LUC is enough of a pain as it is so I'm going to pass on that for now (and probably forever tbh, don't have the time anymore to fill this kind of thing out XD).

Do note that changing the character's Name after creation has no further effect on their LUC. So, assuming you have extra Mana to spend, you can name your character a certain Name for the Base LUC Value you want and then rename them immediately in Witch Petition to the name that you actually want.

I've done many many tests and made observations on how LUC is modified within the Soul Transfer System, and believe that I've probably determined how it is that the system Calculates your New Character's LUC. In a previous version of this guide, I had a giant section with a bunch of pseudo-code in it trying to work around this issues that arise with all the Modifications Stance, and Natures have, but now that I've defined the stance and skill effects in the modifiers section, and finally solved the weirdness with Natures with the discovery of LUC Aptitude, I believe that I can simplify the whole thing down to the following:


And if you want just one all encompassing function to rule them all, here's what happens when you put all those together:



During Soul Transfer a certain amount of LUC is added to your ST LUC. This amount is based solely on the Lucky Number you chose for your character at creation. While the formula for this is listed above (ST Modifier), since formulas can be overly confusing at times, below is a table that you can reference to quickly determine what your ST Modifier is based on your Lucky Number:


Note: You may have seen a similar table to this in other guides on LUC. Unfortunately, that long standing table seems to have been misinterpreted from the findings in the JP wiki and a few quick tests with a few different lucky numbers will reveal this quite quickly. The table I provide here is new and based entirely off of the formula I used in my findings. i.e. don't use a different table and complain when things don't work out right.

You may have read the above and been really confused by what `clamp(ST LUC, 0, 99)` means... Basically, when you clamp a value, you are setting a minimum and maximum for that value.

So in this case, the ST LUC value is `clamped` within the range of 0~99 meaning that:
if your ST LUC is <0, the game treats it as having exactly 0, and
if your ST LUC is >99 the game treats it as having exactly 99.

This differs from what happens at the end which is...

Soul Transfer can mostly be thought of as just adding a fixed amount of LUC (the ST Modifier) to your character and then using the modulo operator "%" to put it somewhere inside the range of 0~99. If you come from a programming background, you'll probably be familiar with this operator (specifically python...) but if not I'll give a brief explanation of what it is and what it does. When you were in school and first learning how to divide numbers, you might remember that when doing long division, you would end up with some part of the number you were dividing that was "left over" afterwards and was known as the "remainder". The modulo operator is used to get the remainder of the division of two numbers.

So for instance, lets say I wanted to divide 3 by 2 (3/2). If I divided it, I would see that 2 goes into 3 once with a remainder of 1. If we were dividing, I would then add a zero to the end of that and move over a place value, then find out that 2 goes into 10, 5 times so I end up with 1.5. However, when taking the remainder with the modulo operator, we don't care about how many times the number goes into the other number, we just care about what part of the number doesn't go into the number. This means that if I did (3 % 2) instead, the answer would be 1 since that is the remainder of dividing 3 by 2.

To bring it back to what this means for our algorithm here, we are doing modulo 100 on our final result ((...) % 100). This means that the New Base LUC that you get out at the end Must be between 0~99. This is because if the number ended up being 100 or greater, then 100 will go into 100 once with a remainder of 0, which means that it loops back around to 0, and if the number ended up being less than 0 (which gets complicated), that would wrap back around the other way to be 99.

If that is too much for you to wrap your head around, you can think about it like this:
Add or subtract 100 from the final number until you have a number that is between 0~99

Now that I've covered exactly how the Soul Transfer System Calculates your New Base LUC, this gives us the ability to precisely manipulate our character's LUC Value to become anything we want.

In a previous version of this guide, I had this crazy set of 4 different algorithms for doing this in certain scenarios since I didn't really have just one all-encompassing formula at the time. Now that I have a more robust formula, we can actually just figure out what equipment we would need to equip for a certain New Base LUC after Soul Transfer by solving for it in the formula (though we will have to ignore the clamp function for now to do that...).

So if we wanted to figure out how much of a Listed Equipment Modifier to LUC we need to equip in order to get a certain New Base LUC Value after Soul Transfer, the formula would be as follows:


(Note: Modulo is not a reversible operation so with this formula, we can only ever talk about Listed Equipment Modifiers in the range of 0~99. Though because of the clamping, this is a non-issue as you will see in the pitfalls section...)

So all we have to do is follow the right formula and it will spit out exactly how much LUC in equipment I need to equip to get the New Base LUC Number I want right? Sweet!

...Except there are a few more pitfalls you want to try to avoid here:

Remember that there was one part of the Soul Transfer Algorithm that we ignored when making the Listed Equipment Modifier Formula? Right, the clamp function.... The reason why we ignored that part was that it A) deals with just limiting the LUC Values to the range of 0~99 and B) isn't really something that I know how to rearrange parts out of in an algorithm (if you even can...).

Since we did ignore clamping when rearranging our algorithm, you could get some bad information about what kind of Listed Equipment Modifiers for LUC you need if you are not careful. The main consideration we need to make is:
Is your ST LUC in the range of 0~99?
If it isn't in that range, then it will be clamped to either 0 or 99

If this happens to you, there is usually a really easy fix:
Just remove/add 100 from your how much you equip as a Listed Equipment Modifier

This will give you the negative/positive equivalent of your Equipment Modifiers. This works because, If the clamping part didn't exist, either of these two values would give you the exact same results (in fact you could add or subtract 100 as many times as you wanted and get the same result because of the modulo operation). Though since the clamping part does exist, you will need to use the value that doesn't cause your ST LUC Value to get Clamped.


It is important to Remember that Moon Stance and Lucky Star are both modifiers which affect the LUC Value that you see on your character at all times. The formulas I provided on Soul Transfer will let you know how much equipment to equip to get a certain New Base LUC (i.e. your LUC with NO modifiers). This means that if you take Lucky Star (the Skill Modifier) or Moon Stance (the Stance Modifier), these will modify the luck that you see on your character after Soul Transfer as they are supposed to, giving you your Naked LUC (i.e. your LUC with nothing equipped).

In case you like a formulaic representation of this, here is the formula for Naked LUC:

Do note that this has nothing to do with the Soul Transfer Formula, This is just a fancy name for the modifiers mentioned doing what they are supposed to do - modifying your LUC Value. Basically you need to refer back to the "Determining Your Puppet's LUC" section again to refresh on how to determine your Base LUC

As an aside, If you plan to try messing with the Soul Transfer formulas to take a given Naked LUC instead, you will need to consider that the range for your Naked LUC is effectively clamped between:

• 0~99 if you don't have any non-equipment modifiers
  
• -30~69 if you only have Moon Stance
  
• 25~124 if you only have Lucky Star
  
• -5~94 if you have both Moon Stance and Lucky Star

So don't come complaining to me when you can't get a Fortunate Moon Stance Character without Lucky Star, cause its just plain not possible without equips.

Also Note I said Lucky Star which is a skill NOT Lucky Nature which is a nature and was shown in the "Introducing: LUC Aptitude" section.

Easy, You can't

Basically, If you are contemplating on soul transferring to a Lucky Nature Character, Just Don't. There is really no conceivable reason you would want a character with this nature if you can control what LUC you get anyways.

If you really want to Soul Transfer to a character with the Lucky Nature just for the lols, Just recognize that you will only be able to target New Base LUC Values in increments of 3 because of the +200% LUC Aptitude that it applies.

If you already have a character with the Lucky Nature, it will suck trying to find your exact LUC Value because you will always overshoot. The silver lining is that you can act as if you don't have it when you inevitably decide to Soul transfer to a character with another Nature (Since Soul Transfer only cares about what Nature the New Character will have).

Just to put my harsh stance on this nature in perspective, let's list the known Benefits of this nature shall we:

• Makes Equipment that Increases LUC 3 times as good (i.e. a 300% LUC aptitude)

Now the Detriments:

• Decreases all aptitudes other than HP, SP, and LUC by 50%
  
• It Makes Equipment that Decreases LUC 3 times as bad (i.e. the 300% LUC aptitude's downside)
  
• Makes it nearly impossible to Determine your LUC Value with Equipment
  
• If you pick it up during Soul Transfer, It makes it impossible to get certain exact LUC Values

While it is possible that there is some hidden effect of this Lucky Nature on random LUC calculations, this nature seems to do far more harm than good.

So the take away is Lucky Nature Fundamentally limits your options when it comes to manipulating your LUC Values and there's not much you can do about that other than just not taking the Nature.

While I've been throwing around a bunch of formulas here and there and showing how they work, I haven't actually shown very many actual verified examples of how I figured out half of this stuff.

In a previous version of this guide, I had pasted a GIANT section here of a bunch of tests I had run and how I had calculated the values. While this was likely quite informative to understanding how I came to my conclusion at the time, I've determined that it was likely just a lot of TMI that was just clogging up the guide. As such, I've compiled those findings along with my insane number of tests that I did for determining the exact LUC Aptitude for every Puppet Nature into a Google Sheets Spreadsheet that I'll put a link to right here: https://docs.google.com/spreadsheets/d/1q6p9GQNQLWPKXq5SIBNROd9vXXi39MRwT9iJKZNej_Q/edit?usp=sharing

So you took one glimpse at the mass of formulas and decided that you don't give two flips about how the system works and that you just want to be able to have Maxed out LUC without any real hassle. Well I can't really blame you.

As such I'm going to give you a near surefire way to keep yourself at near Maximum LUC.

No seriously, its fast, easy and gives you an Initial Base LUC Value of 98. what more could you ask for? That's the Letters "G" "o" and "d". The case matters, and I know from firsthand experience just how similar the number "0" looks to the lowercase letter "o" in this game so don't make that mistake either (lots of people have...). If you'd prefer something more Japanese, you can also go with "Amaterasu" (the Japanese Sun God) which also gives a LUC Value of 98 (No-one has ever gotten a 0 or 99 for Initial Base LUC Before, so they are probably not possible to get initially...).

Though in all seriousness, if you don't want to be a Fortunate Character (or have trouble with spelling), you can name your character anything you want given that it has a starting LUC Value that you are happy with keeping since this Lazy Man's Guide will make it so that the value will never change again after Soul Transfer.

(Also remember that renaming your character afterwards in the Witch Petition is completely fine, it is only this initial name that matters for LUC)

If you really want to change it up, you can go with any one of the following:
{42, 44, 46, 48, 50}
This is for 2 reasons:

1. To make Soul Transferring Hassle free later
   
2. To take advantage of the Leveling advantages of the 666 Pact later (Even Lucky Numbers only)

It kills your aptitudes, makes figuring out your Base LUC value neigh impossible, and makes Soul Transfer a pain. Its only "benefit" is that it multiplies all positive... and negative LUC modifiers by 3... I.e. worthless.

If you want to make things even easier, try to stick to only the ±0% Natures if you don't want to deal with the slow creeping changes that LUC Aptitudes will cause. There is an argument that if you want to minmax, the -5% Natures are probably the best, but I'm not going to be bothering with them in this part cause I'm Lazy... The rest of the Lazy Man's Guide assumes that you stuck with the ±0% LUC Aptitude Natures, Okay?

If YES:
Equip:

• Rusted Lance [Legendary] (You can get it from the Campanula B3: X18,Y21 Event [Should give -39 LUC])

Then Soul Transfer. You will end up with 98 Base LUC or the same as what you started with.
(though, do realize that your final Naked LUC with only Moon Stance will be 68 (or at absolute maximum, 69))

If NO:
Equip:

• Rusted Lance [Legendary] (You can get it from the Campanula B3: X18,Y21 Event [Should give -39 LUC])
  
• Choose 1 [Normal Rarity only]: {Baffling Blade, Wild Ape Sword, Rusted Lance, Stubborn Mallet, Hate Bell, Carrion Katar} (i.e. any weapon that gives -30 LUC)

Then Soul Transfer. You will end up with 98 Base LUC or the same as what you started with.

Side Note: If you find that the Rusted Lance [Legendary] from the Campanula Event isn't -39 LUC, You can either reload and try again, or look for some other equipment later on that will give you the required LUC

Since you end up with the same LUC as what you started when you Soul Transfer, you can do the exact same thing every Soul Transfer and you will keep the exact same LUC. This means that you will no longer have to worry about your LUC as long as you remember to follow these 4(5?) Simple steps. Of course if you Stray from these steps, you will probably have to either suck it up and read the rest of the guide getting into the nitty gritty details of LUC manipulation, or simply try again with a new character. Your Choice ¯\_(ツ)_/¯

At this point you should know more than you ever cared to know about how LUC works in this game (Assuming you actually read the whole guide XD). If there is anything you think I missed or am mistaken on, please feel free to post in the comments section about it. If you can include the Relevant information on how to replicate the issue it would be much appreciated.

This is the first guide I've written on Steam as I've never really seen an unknown mechanic in a game that had so much depth and partial information on it available as this one did. I tend to get engrossed in solving puzzles like this one and particularly love getting into the details about how the inner workings of games operate so this just kinda ended up calling to me to try to solve.

I'd like give thanks to the many people who have done work on this topic before me including the writers of 2 other guides:
https://psteamcommunity.yuanyoumao.com/sharedfiles/filedetails/?id=1517202577
https://psteamcommunity.yuanyoumao.com/sharedfiles/filedetails/?id=1915802242
As well as the members who contributed to trying to solve this problem over on the JP Wiki[wikiwiki.jp] (マジで助かったよ^_^;）

In addition, thank you to everyone in the comments for providing invaluable feedback in making this a better guide. In particular:

• @HAVYN for pointing out a typo in an intermediate step of the validation formulas
  
• @Irisu for first bringing my attention to the existence of Hidden LUC Aptitude modifiers on Puppet Natures.
  
• @Muffins Just for mentioning how LUC also affects Status Recovery Chance in Combat.
  
• @Small World For Helping out tremendously with ascertaining the existence of Puppet Nature Affinities.

Anyways, I think that should just about do it. Thanks for reading!