[Sticky] Collection of Formulas for Dark Summoner

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Re: [Sticky] Collection of Formulas for Dark Summoner

Post by Mortium on Tue Oct 09, 2012 10:03 am

Just as my own general rule I assume 1.1m gold to level from 1-100 and 400 C monsters or 2.5m from 1-150 with 600 C monsters.

If anyone can give me an idea of how far off I am i'd be happy Smile

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Re: [Sticky] Collection of Formulas for Dark Summoner

Post by Armitaage on Tue Oct 09, 2012 10:32 am

The following figures may be a bit inaccurate, but if we assume that kyan's formula for levels gained is correct, and that the c monsters being sacrificed are 4 bp monsters from mission 4:4, then from 1-100 a rank AA monster will take 420 sacrifices and cost 1,173,700 gold and a rank AA+ monster will cost, from 1-150, 2,633,400 gold (up to 3,742,600 if we include the cost of evolution at lvl 1) and require 630 sacrifices. Using higher bp sacrifices, this cost can be reduced, but I have not run the numbers. This is, of course, assuming that you sacrifice 10 at once.

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*needs testing with certain teams to ensure quality. also, monster data doesn't update itself without me logging on to manually add monsters, yet, so some of the newest monsters might not be available for use right away. Missing max lvl stats WILL affect final stats, so make sure to pm me with screenshots of it whenever you want to add data.
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Re: [Sticky] Collection of Formulas for Dark Summoner

Post by Mortium on Tue Oct 09, 2012 10:41 am

So hey, i'm not actually far off then Smile

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Re: [Sticky] Collection of Formulas for Dark Summoner

Post by kyan on Tue Oct 09, 2012 6:20 pm

Armitaage wrote:The following figures may be a bit inaccurate, but if we assume that kyan's formula for levels gained is correct, and that the c monsters being sacrificed are 4 bp monsters from mission 4:4, then from 1-100 a rank AA monster will take 420 sacrifices and cost 1,173,700 gold and a rank AA+ monster will cost, from 1-150, 2,633,400 gold (up to 3,742,600 if we include the cost of evolution at lvl 1) and require 630 sacrifices. Using higher bp sacrifices, this cost can be reduced, but I have not run the numbers. This is, of course, assuming that you sacrifice 10 at once.

That's very close to what I came up from tracking. From 3 different leveling to 100 it cost me ~1.1mil on average and ~39 sacrifice in bulks of 10 (~as the first few levels were done one by one from skill sacrifice).

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Re: [Sticky] Collection of Formulas for Dark Summoner

Post by BlackFro on Tue Oct 09, 2012 6:26 pm

Armitaage wrote:Here is the generic formula for finding out how much gold it will cost to sacrifice N monsters when the target monster is lvl X:

Code:
Let X = Target monster's level
Let N = The number of sacrifices

(210*X*N+210*N-10*X*N*N-10*N*N)/2

since every successive sacrifice after the first sacrifice costs N-1 times 10% of the first sacrifice less than the first sacrifice. in other words, the second sacrifice costs 90% of the first, the 3rd 80% of the 1st, etc. this, therefore follows standard triangular number rules(a triangular number, for those who don't know, is a number that is the sum of all the numbers from 1 to n. examples of triangular numbers include 3, 6, 10, and 15.)

That is more complicated than the formula I use:
Using your variable references:

100*(X+1)*N*(1-((N-1)*.05))
So with 1 Monster Sacrificed it would be 100*(X+1)
With 10 Monsters Sacrificed it would be 100*(X+1)*5.5

Basically you get a 5% cost savings to total sacrifice cost for every monster beyond the 1st you add to your sacrifice batch.

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Re: [Sticky] Collection of Formulas for Dark Summoner

Post by Armitaage on Tue Oct 09, 2012 10:50 pm

@ BlackFro,
I'll make a more detailed post when I have access to a proper computer, but the savings are 10 % of the 1st sacrifice's cost. My formula is the simplified version of 0.1*(lvl+1)*100*sum of sacrifices counted from 10 down, up to the total number of sacrifices. With 8 sacrifices, for example, we count 10, 9, 8, 7, 6, 5, 4, 3 and add those numbers up, then multiply by 10 times lvl+1.

edit: now that i am home, your function certainly does return the same values. however, i prefer mine in that i do away with all the remembering about parenthesis. i reached mine by working from this:

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as the image above shows, the formula is the sum of the various sacrifices, each of which is 10% * the number of sacrifice-1 LESS than the first sacrifice. this can be rewritten as:

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which in turn can be rewritten as:

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from here, we can finally eliminate the sigma notation, because there IS a simple algebraic formula for the sum of all numbers, in increments of 1, from n to m. it is:

Code:
(m*(m+1)/2)-((n-1)*n/2)

since we know m, which will always be 10, the formula becomes:

Code:
(10*(10+1)/2)-((n-1)*n)/2)

since they both share a common denominator, we get:

Code:
(110-(n-1)*n)/2

the above is the generic formula for the sum of all numbers from n to 10. in our case, though, n is NOT the number of sacrifices, we have to figure it out what it is. in the event that we have 10 sacrifices, the cheapest sacrifice costs 10% of the original amount, so we'll be counting from 1. in the event of 9 sacrifices, we'll be counting from 20%, or 2. in the event of 8 sacrifices, we're counting from 30%, or 3. using this last as a basis, we can determine that we have to subtract the sum of all numbers from 1 to 10-n from the sum of all numbers from 1 to 10. we can therefore modify the generic formula to:

Code:
(110-((10-n)+1)*(10-n)))/2

removing the parenthesis from (10-n)+1 we get 10-n+1 = 11-n making the new formula:

Code:
(110-(11-n)*(10-n))/2

solving the quadratic equation using the FOIL method, we get

Code:
(110-n*n+21*n-110)/2

which we can rewrite as

Code:
(21*n-n*n)/2

with this, we have converted the sigma notation into a proper formula, making the formula for the cost:

Code:
10*(lvl+1)*(21*sac-sac*sac)/2

solving the quadratic equation again we get

Code:
10*(21*lvl*sac+21*sac-lvl*sac*sac-sac*sac)/2

moving the 10 inside the parenthesis, we finally arrive at the formula that i gave, namely

Code:
(210*lvl*sac+210*sac-10*lvl*sac*sac-10*sac*sac)/2

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*needs testing with certain teams to ensure quality. also, monster data doesn't update itself without me logging on to manually add monsters, yet, so some of the newest monsters might not be available for use right away. Missing max lvl stats WILL affect final stats, so make sure to pm me with screenshots of it whenever you want to add data.
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Re: [Sticky] Collection of Formulas for Dark Summoner

Post by krisirk on Thu Oct 11, 2012 9:19 pm

I added to the first post some formulas and information on resetting your skill points via removing allies.

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EP Calculator

Post by Ologolos on Tue Dec 04, 2012 4:34 pm

so i've been working on a "calculator" tool (just a spreadsheet) to try and figure out how many EP it would take to progress thru a certain number of levels, given some of your default stats.

I asked a few people this same question about the current event, and didn't get many good concrete answers, so I thought I would take a stab at making something for anyone else who might be wondering the same thing.

I posted it to Google Docs to see if anyone would like to review and comment on it... I'm definitely no math genius, and there are always variables that can't be accounted for, but the link is here:

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I'm also brand new to google docs, so if i did something that doesn't let you add numbers to the sheet, let me know. Thanks in advance for your input!
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Re: [Sticky] Collection of Formulas for Dark Summoner

Post by kyan on Tue Dec 04, 2012 5:54 pm

Are you talking about events or missions? Most people don't spend ep for the missions unless its also tie to an event. Missions is the thing you do with energy points when there is no event or its a bp event.

If you're talking events. The big variable is the my ep and my ep100 that is awarded. They are random and I haven't track how many are handed out on average but its a fair amount.

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Re: [Sticky] Collection of Formulas for Dark Summoner

Post by Armitaage on Tue Dec 04, 2012 5:59 pm

lol, no kyan, the big variable is the willingness of players to actually track how much energy floors take to get through, with progs and without them. i'm pretty sure that this is intended to give you an estimate of how many full refills of your energy it will take to get to a given floor, lol.

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*needs testing with certain teams to ensure quality. also, monster data doesn't update itself without me logging on to manually add monsters, yet, so some of the newest monsters might not be available for use right away. Missing max lvl stats WILL affect final stats, so make sure to pm me with screenshots of it whenever you want to add data.
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Re: [Sticky] Collection of Formulas for Dark Summoner

Post by Ologolos on Tue Dec 04, 2012 6:35 pm

correct, Armitaage, it is intended to calculate number of energy refills (via a normal energy potion or a myEnergy potion) it takes to progress through an event floor. The term "mission" in the spreadsheet is synonymous with "floor", but could apply to a regular mission as well, if you wanted to use it for that. The event missions and the regular missions seem to have the same criteria: amount of energy it take to progress one interval, the % of that interval, etc.
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Re: [Sticky] Collection of Formulas for Dark Summoner

Post by Ologolos on Tue Dec 04, 2012 6:41 pm

also (to clarify), it tries to account for the "natural" refill of your energy, so the end result -- number of energy potions -- is the amount of potions above and beyond the normal refill rate to get to the input goal. This also does not take into account a "natural refill" obtained by leveling up.

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Re: [Sticky] Collection of Formulas for Dark Summoner

Post by kyan on Tue Dec 04, 2012 7:41 pm

Err... The energy it takes per floor is pretty standard. Its been the same for several events of this type. The only thing that changes frequently is the first 200 floors and that's pretty easy to track if you want to. It doesn't change that often. From 200-2000 its 55 per floor with a 4x prog. 11 energy per tap. From 2000+ its 60 per floor with 4x prog. 12 per tap. Its easy to estimate if you want to.

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Re: [Sticky] Collection of Formulas for Dark Summoner

Post by kyan on Tue Dec 04, 2012 7:43 pm

Ologolos wrote:also (to clarify), it tries to account for the "natural" refill of your energy, so the end result -- number of energy potions -- is the amount of potions above and beyond the normal refill rate to get to the input goal. This also does not take into account a "natural refill" obtained by leveling up.

You can calculate in the level up if you want to. The amount of xp it needs to level is a linear increase. The amount of xp awarded per tap/interval is also standard. For the current event is energy+1. Its been like that for "floor" type of events since the beginning.

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Re: [Sticky] Collection of Formulas for Dark Summoner

Post by Ologolos on Wed Dec 05, 2012 10:16 am

Thanks Kyan,
yeah, I'm nowhere near getting to floor 200, nor do i have a progression monster, which is why i wanted to make a tool that could estimate EP. Seems like if you have anywhere close to enough EP (or time) to get to floor 2000, you probably don't care how much it takes, lol. I wouldn't know.

Maybe I'll try adding in something for the level up factor sometime... I guess I'll need to account for starting level, starting exp, exp per mission, the exp equation for a level up, exp increase per mission (like ep expenditure), and "natural" exp growth (i think you get a certain amount of EP per hour, or something like that, via achievements). Let me know if there's something I forgot.

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Re: [Sticky] Collection of Formulas for Dark Summoner

Post by Deathblob on Sun Dec 16, 2012 10:14 am

Anyone figured out the new formula for gold lost in battle yet?

Today I lost 9.76% on defense: 1784.0 / (1784+2127+14538-175)
Then 12.75% on attack: 2127.0 / (2127+14538)

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Re: [Sticky] Collection of Formulas for Dark Summoner

Post by YoungOak on Mon Sep 23, 2013 8:33 pm

blah wrote:
krisirk wrote:
I think we have more questions than we started with.
Yup, the two hardest formulas in Dark Summoner to figure out are:

1. Sacrificing and its formula.
2. Combat system and damage dealt per hit given attack/defense stats.
2.5 Damage dealt by special skills(not really that hard after #2).

As a point, I would like to mention that with sacrificing, I have not had a monster level up less than 2 levels when sacrificing with 10 sized batches. Even at level 60-70(haven't tried with AA/+), I seem to gain at least 2 levels, even with 1 bp and 2 bp sac. fodder. Also, I find it difficult to gain exp beyond 1.5 times from level 1 with 1 monster sacrificed, even though 3 wisdoms did essentially level a 65 to 70.
Hey, I found something like damage calculation formula on this site: 
[You must be registered and logged in to see this link.], but it's written in Japanese. Anyone can translate it? There seem to be many other formulae there.

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Re: [Sticky] Collection of Formulas for Dark Summoner

Post by ryesteve on Mon Sep 23, 2013 9:27 pm

Google translate had a hell of a time with it, but I did see some spots that mentioned random numbers, which is a conclusion I came to myself, which means designing a battle simulator is a lost cause.

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Re: [Sticky] Collection of Formulas for Dark Summoner

Post by Armitaage on Mon Sep 23, 2013 9:45 pm

Perhaps not, if we can figure out the general formula of damage and how it applies random numbers, particularly with regard to hit and dodge values. PHP(the scripting language) has a function for generating pseudorandom numbers so, as long as we know the general formula(and where to insert the pseudorandom number in it), we can design something that would give us an idea of relative strengths of forms. And it's not just PHP that has such a function, all programming or scripting languages do(but not markup languages).

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*needs testing with certain teams to ensure quality. also, monster data doesn't update itself without me logging on to manually add monsters, yet, so some of the newest monsters might not be available for use right away. Missing max lvl stats WILL affect final stats, so make sure to pm me with screenshots of it whenever you want to add data.
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Re: [Sticky] Collection of Formulas for Dark Summoner

Post by ryesteve on Mon Sep 23, 2013 9:49 pm

Yeah, I get that, deriving a random number is no big deal; the problem is knowing whether or not you've accurately replicated their formulas. If there are random components, you've got nothing to verify against.

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Re: [Sticky] Collection of Formulas for Dark Summoner

Post by Armitaage on Mon Sep 23, 2013 10:22 pm

Honestly, I didn't have to even glance at that post to know dark summoner heavily utilizes pseudorandom numbers. That said, let's give a properly translated version of the link the benefit of the doubt. I have no idea what the Japanese post's sources were, at the beginning he does say he will not share them. It is entirely possible that he's managed to get a peek at the real code.

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*needs testing with certain teams to ensure quality. also, monster data doesn't update itself without me logging on to manually add monsters, yet, so some of the newest monsters might not be available for use right away. Missing max lvl stats WILL affect final stats, so make sure to pm me with screenshots of it whenever you want to add data.
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Re: [Sticky] Collection of Formulas for Dark Summoner

Post by lennon_68 on Tue Sep 24, 2013 12:16 pm

Hmm, I took a quick peak and it looks like the important nugget there (if I'm reading it right... I very may well not be!) is his example:

Damage = (12069 - 5000) + α ∈ [50, 200 +7069 × 10%]
               = 7069 + α ∈ [50, 906]


I'm not entirely certain I deciphered what's going on right though...  My take is:
- 12069 was his card's attack after all bonuses were applied (which we know how to do). 
- 5000 was the defending card's defense (after bonuses) divided by 2?
- 7069 was his card's attack after bonuses minus the defending card's defense divided by 2?
- This thing α ∈ [m, M] just means a random number between m and M


If that's all correct than the damage formula becomes pretty darn easy to calculate actually.  Is that how everyone else read it or am I oversimplifying somewhere?  I'm really not sure about the 5000 or 7069 as it wasn't clear to me at all what he was saying.


Edit, I just read the next example about how much attack is required to ensure you can kill Enmiria in one hit and I'm pretty sure I've got it right.  Armitaage you on this one?  I might be able to put something together eventually but I'd have to re-do all the stuff you've programmed calculating the combos


That makes it:
(ATK-DEF/2) + α ∈ [50, 200 + ((ATK-DEF)/10) ]           (oh, and if ((ATK-DEF)/10) ends up less than zero it just becomes zero)

Which means a battle damage simulator would be somewhat accurate when ATK and DEF are close but pretty unreliable as the difference between the two becomes greater.  Also I suppose this is maybe missing the tiny detail of misses and critical hits lol.  I'm sure those formulas include random numbers as well, guessing at 3 random numbers wouldn't give very reliable results.


Last edited by lennon_68 on Tue Sep 24, 2013 3:07 pm; edited 1 time in total

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Re: [Sticky] Collection of Formulas for Dark Summoner

Post by Armitaage on Tue Sep 24, 2013 2:22 pm

Misses and critical hit chance are somewhat easy, I just lack details on the relationship between the hit and dodge values that monsters have. Once I know that, the chance a hit will land is basically rolling a random number between 0 and 100 and if it falls between a range of the computed number using hit and dodge values and 100(or 0, I'm not sure how ATeam does it), then the hit lands,  otherwise it misses. Crit rate would work similarly, except that it's pretty straight forward, as there is no critical avoidance value to compare to. The only other thing I need to know is how critical damage formula differs from the regular damage formula.

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*needs testing with certain teams to ensure quality. also, monster data doesn't update itself without me logging on to manually add monsters, yet, so some of the newest monsters might not be available for use right away. Missing max lvl stats WILL affect final stats, so make sure to pm me with screenshots of it whenever you want to add data.
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Re: [Sticky] Collection of Formulas for Dark Summoner

Post by lennon_68 on Tue Sep 24, 2013 3:06 pm

I looked at it a little longer and see that the critical hit damage formula is in there too.  The translation was really fragmented at that point but I think the jist was that it's not a multiplication of the normal damage formula but just an attack without defense and a different calculation for the random amount to be added.

His example was a monster with 10k attack and he said a critical hit would be 10100 - 11200.  Looking at the untranslated text I think it's supposed to be:
ATK + α ∈ [100, 200 + (ATK/10) ]

Actually looking at that it's almost the same as the normal damage calculation with no defense.  Looks like the only difference is that the random number's low value is 100 instead of 50.

Looks like there's formulas in there for celestial lightning, etc. as well but I couldn't make those out at all lol

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Additional Formula & Figures

Post by Nesfuratu on Sun Nov 17, 2013 4:47 am

Hey just wanted to add the formula regarding evolving AAA's. Also I created some charts showing the evolve levels for each card assuming both the base card and the sacrifice card are the same level. If they aren't use the below formula and always use the higher level card as the base card to save gold.


  • Evolver = The level of monster to be evolved

  • Sacrifice = The level of monster being sacrificed


Rank AAA Cost = 4,380,000 - (base * 19800) - (Sacrifice * 1800)

Below are the charts to help you calculate some basic leveling and evolve costs.


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Again the above chart stats assume both cards are the same level. If yours are not use the formula(s) listed above.

Hopefully I got that in order. Hard to see with such a small reply editing box lol. As always this and more guides on the DS guide website. Link in my signature. If anyone has questions about this or something else feel free to PM me or contact me on KiK for a much faster response.

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Re: [Sticky] Collection of Formulas for Dark Summoner

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