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Theory Crafting Part 1 - Highest Damage Achievable?
#1
Rainbow 
Hello all, 


Author's Note and Update log (if applicable)
Before continuing, I would like to apologise in advance if something like this has already been made.

-> Current investigation focused on Beast deck.
-> Exclusive of craft apparatus bonus damage. [if someone know's how craft apparatus damage adds on to the damage calculation please feel free to drop me a message or post a reply].
-> As always, all help will be thanked and accredited to.
-> Also for grammar nazis out there correction of sentence syntax and grammar is welcomed Tongue . Vocabulary too if it bothers you that march. <- that was on purpose heheh ^^.
-> Will include highest damage achievable for different types of deck like species/ attribute/ rainbow and even Single Card.
-> Spreadsheet + other stuff including beautification of thread will be added in the future. (Within next 2 week hopefully. Help from others is welcome in creation of sheet Smile)

Introduction of Investigation (Don't care? Skip below for Math and Findings)
For some of you who know me or seen my previous thread you'll know that I love MATHS! Well in fact I'm going to pursue a career in maths. Previously I used to play TOS a lot but I took a long break from it, so my knowledge on TOS is tad wee off and limited. However I've always enjoyed theory crafting (not sure if its a thing but yeah) and wanted to see what's the highest possible damage achievable but a single card and from a single deck. So two different investigation will be carried out. Hope ya'll enjoy this small bit of fun. Please don't take it in such harsh criticism and if you have any ideas or opinions or noticed any flaws about my investigation please feel free to discuss positively and make this a small bit of fun mathematicians playing TOS can enjoy Smile.


WARNING MATH ALERT
Don't like the math and don't want to read through everything skip to the bottom for summary


Investigation


Basically with the arrival of the Druid of Nature and Spiritual Civilisation series hitting high damage multiplier is highly probable. To make things simple the damage calculations for TOS is as follows: 

Legend
Let D = raw damage from monsters
Let C = no. of combos
Let M= damage multiplier
Let C% = combo multiplier




Base Formula



M [ D + C%*D*(C-1) ] ->PRE CRAFT APPARATUS




Now the basic setup will have to be as follows:


Team Setup
(Leader) Tapir Druid - Sumatra 
(Member 2) Tribal Warrior Odous
(Member 3) Tribal Chief Mufasa
(Member 4) Pluma the Sky-high Outlaw

(Member 5) Basti the Solar Diety (Second Highest Burst) /  Mother Nature Cybele (Increase team damage)/ DBK VR (Converter for Mufasa)

(Ally) Tapir Druid - Sumatra 


References to the cards for visual stimulus:
(Leader & Ally) http://towerofsaviors.wikia.com/wiki/Tapir_Druid_-_Sumatra

(Member 2) http://towerofsaviors.wikia.com/wiki/Tribal_Warrior_Odous

(Member 3) http://towerofsaviors.wikia.com/wiki/Tribal_Chief_Mufasa
(Member 4) http://towerofsaviors.wikia.com/wiki/Pluma_the_Sky-high_Outlaw


(Member 5)
http://towerofsaviors.wikia.com/wiki/Basti_the_Solar_Deity
http://towerofsaviors.wikia.com/wiki/Mother_Nature_Cybele,_Divine_Tree
http://towerofsaviors.wikia.com/wiki/Leader_of_Forests_-_Bull_Demon_King




Now the multiplier from the leader skill alone is 4.5 x 4.5 totalling up to 20.25. The active skills for Member 2 (M2) and Member 4 (M4) provides a 3x bonus damage and shares with adjacent beast. Thus sandwiching Member 3 (M3) with M2 and M4 the damage multiplier for M3 will increase by 9x. This leads to 20.25x3x3 increasing it to 182.25. Here's the interesting part, Mufasa's skill savage allows it increase its' damage by 10x thus the 182.25 multiplier will increase by 10 folds. This leaves the multiplier (for M3 specifically) at 1822.5. 


So now we have a 1822.5 multiplier for M2 whilst having a 182.25 for the rest of the deck. Both the leader and ally's skill increases the damage of the deck by 2 fold each IF NO HEARTRUNE STONES are made. This is a vital and important condition else the multiplier decreases to 1.5x each. Cybele's skill (M5), if you decide to add her into your deck, will multiplier the decks damage by 2.5x. This along with the leader and ally skill will sum up to 10x (2x2x2.5). The result of this will increase M2's damage to 18225x whilst the rest of the deck receives a 1822.5x damage multiplier.


If you still remember the damage equation from before, which is PRE CRAFT APPARATUS, the equation goes like this:


M [ D + C%*D*(C-1) ]



So if you sub in your damage for M2 you'll get something like this at max level = 18225 x [ (1066+70) + 0.25 x (1066+70) x (5-1) ].
Here, I'll take combo as 5 as its an average and it'll be easier to calculate. Of course, I do acknowledge some summoners out there are god-like spinners and we be like 5!? 5 is average? Welp, the more combos the better so if you are one of those professional spinners then ya'll should be aiming for 9 combos cuz thats gonna make the damage even more interesting. 


So... for an average spin of 5 combos the total damage Mufasa does is 18225 x [ (1066+70) + 0.25 x (1066+70) x (5-1) ] =41.4 Million earth damage. Whilst other cards in your deck will total to a 20.7 Million damage. This adds up to 62.1 Million damage. 
Woots. At 9 combos it'll increase to a wooping 62.1 Million earth damage for Mufasa alone whilst the rest of the deck will total up to a 31.1 Million damage. This sums up to 93.2 Million damage. WEEEE Smile


Conclusion/ Results


In short, the maximum damage for Mufasa with 5 combos is 41.4m damage whilst for 9 combos it is 62.1m damage. Can it increase more? Definitely. Just need to include other variations for maximum output in damage and include craft apparatus into the equation. 

Stay Tune for more! I'll definitely be working on this on a regular basis especially after next week when I'm done with my exams Big Grin. I'll also update it regularly and if anyone has any pending question/suggestion/request please feel free to drop me a message or send a reply. This thread will definitely be beautified over the following days. Suggestions for beautification of thread is welcomed. 

[Image: 301353d2.jpg]
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#2
Why not just just go for Uranus - PR Odin - Ed - Douman - Robert - Ally VR Daji

you'll probably beat the damage Mufasa can do by miles with the above team if you're just looking for big numbers.

ID: 60302480

Allies available: Inanna (All Max), Dumuzi (All Max) PR Apollo (All Max), PR Virgo (All max), VR Freyja (All Max), Stolas (Ame II), Huang Fu Duo (Max lvl, Ame IV), PR Yang Jian (Max lvl, Max CD), PR Athena (All Max), Beelzebub (All Max), Samael (All Max) Jia Rou (Ame IV, set on weekends), Satan, Guan Yu, Lu bu. 
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#3
Why not use Sumatra, Peking Duck, Odous, Mufasa, Medusa, Sumatra... that gives a bigger burst, assuming you done everything correctly Smile

But, I think the OP Burst Deck is
Proto, Ed, Douman, Odin, Robert, Daji....
Or
Ed, Douman, Robert, Medea, Odin, Daji

ID: 25923781
Looking for: Any ally that is at least dual max

Main Allies: Azathoth, Killua, Yusuke, Aqua, Darkness, Hiei, Natsu, Lucy, Atlantis


CN ID: 878758321
Main Allies: Daoloth, Meso
Looking for: Daoloth, Meso


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#4
(03-17-2016, 12:05 AM)deathexe Wrote: Why not just just go for Uranus - PR Odin - Ed - Douman - Robert - Ally VR Daji

you'll probably beat the damage Mufasa can do by miles with the above team if you're just looking for big numbers.

Hey there,

That's an interesting proposition. Here's what I calculated. Correct me if I'm wrong^^

(L) Uranus - x7 
(M2) Douman - x2.5
(M3) Robert - x3 (But gaines from Douman) x2.5
(M4) Odin - x3
(M5) ED x15
(Ally) VR Daji Combo count 1.25+0.25 = 1.5 combo multiplier. Good proposition.

The damage multiplier will be 315x for Robert, 105x for Douman, 630x for Ed and 42x for the rest. Your combo count, assuming you make 10 combos with Daji's Skill, will make  the multiplier increase to 598.5x, 199.5x, 1197x and 79.8x multiplier respectively. Now including the 10 combo count but lets make it 13 for simplicity sake. The combo multiplier will add an addition +18x damage.

It gets mathy here. Lets make 1197x as 1200x and call it E for Ed's damage. Now E will be multiplier with 18 and added to the original. So its E + 18E giving you 19E. Ok. This simplifies the calculation to 19(1200) for Ed's damage giving you a multiplier of 22800 inclusive of combo. So he's raw damage multiplied by 22800 = 2167*22800 = 49.2 Million which is great. Slightly more than than Mufasa.

Also if we solely looked at the leader skill, Double Sumatra gives a constant multiplier of 20.25. Thus in order of Uranus / Daji to beat that multiplier it would take roughly:

M [ D + 1.5 x (D) x (C-1) ] 


7 [ 1 + 1.5 x (1) x (C-1)] = 20.25
[ 1 + 1.5 x (1) x (C-1)] = 20.25/7
[ 1 + 1.5 x (1) x (C-1)] = 2.89
[ 1 + 1.5C - 1.5] = 2.89
[1.5C - 0.5] = 2.89
1.5C = 2.89 + 0.5
1.5C = 3.39
C = 2.25
C = 3 Combos

So yes, you are right Smile on both accounts. At an average Uranus and Daji will do higher damage and in terms of Highest possible damage Double Sumatra Beast loses out by a couple of million. Also a very interesting proposition. I will look into dual Uranus and explore the realms of dragons and more focus on Ed with demon series Smile Thank you for your contribution!

Ps. This is taking into consideration that Uranus Crits. 50% chance at most.
PPs. I will update this with your suggestion and accredit you for it ^^
[Image: 301353d2.jpg]
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#5
Don't forget to include Daji's actives boost damage too, since her active boost is the main reason why I didn't want to consider dual Uranus instead.
ID: 60302480

Allies available: Inanna (All Max), Dumuzi (All Max) PR Apollo (All Max), PR Virgo (All max), VR Freyja (All Max), Stolas (Ame II), Huang Fu Duo (Max lvl, Ame IV), PR Yang Jian (Max lvl, Max CD), PR Athena (All Max), Beelzebub (All Max), Samael (All Max) Jia Rou (Ame IV, set on weekends), Satan, Guan Yu, Lu bu. 
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#6
Uranus - PR Odin - Ed - Horned King - Robert - Ally OVR Daji would be slightly higher actually.

You didn't count in Daji's per rune bonus? IIRC it's like 2.5x for dissolving the entire board or something.

Also you're not counting rune damage/amelioration bonuses? Though it's true that's fairly annoying to calculate...
ID: 40 944 239  
Allies (All/Dbl Max): Darkness, Aqua, Kurama
Other Frequently Used Leaders (All/Dbl Max): Lucy, Mellow, VR Greek (FELDW), Hiei, Azathoth, Daoloth, PR Haza, etc.
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#7
Hehe sorry guys if I wasn't clear just noticed my phrasing of words were poor.

"Your combo count, assuming you make 10 combos with Daji's Skill, will make  the multiplier increase to 598.5x, 199.5x, 1197x and 79.8x multiplier respectively"


This was inclusive of Daji's active skill when the board is cleared. It adds 1.9x max. But yeah... Including amelioration is annoying but... I WILL DO MY BEST TO INCLUDE THEM! Big Grin after my exams... T.T


Source: http://towerofsaviors.wikia.com/wiki/Benevolent_Xian_Vixen_-_Su_Daji
[Image: 301353d2.jpg]
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#8
I think most of us here have experience with the 500 millions damage challenge. Here is some way to do it
Ed + PR Odin + Horned King + Robert + Flygja + VR Daji

Ed's base ATK=2103
PR Odin gives 3x
Horned King gives 2.5x (3 attributes)
Robert gives 3x
Flygja gives 2.5x (Take note that Flygja buff is at card icon so you won't exceed the 4 buffs limit)
VR Daji which is 2.5x with full board dissolve. (Take note that we are using refined form)

With 5 set of dark runes prepared and 10 combos in total, total damage is
2103*5*15*3*2.5*3*2.5*2.5*5*(1+9*1.75) = 1,857,581,543

Now we add in crafts, presume we can custom make a craft with all 3 effects are
increase dark atk against light enemy by X %, with X = 46/50/100 for 1/2/3* (According to statistic collected by Chinese side, these are the highest no. they found right now, maybe higher)

Using a 3* crafts and score 35000 points, you get
2 + 25000/10000*0.5 = 3.25 (damage boost cap for craft score)

Against light enemy, you get 1.5x attribute bonus
In total, you get
1,857,581,543*1.46*1.5*2*3.25*1.5 which is about 40 billions. I believe that is crazy enough...
Available Cards:
[Image: ho8FMRF.png]
ID: 43061313
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#9
(03-17-2016, 01:09 AM)ikiewe Wrote: Hehe sorry guys if I wasn't clear just noticed my phrasing of words were poor.

"Your combo count, assuming you make 10 combos with Daji's Skill, will make  the multiplier increase to 598.5x, 199.5x, 1197x and 79.8x multiplier respectively"


This was inclusive of Daji's active skill when the board is cleared. It adds 1.9x max. But yeah... Including amelioration is annoying but... I WILL DO MY BEST TO INCLUDE THEM! Big Grin after my exams... T.T


Source: http://towerofsaviors.wikia.com/wiki/Benevolent_Xian_Vixen_-_Su_Daji
OVR Daji has a higher max multiplier actually
ID: 40 944 239  
Allies (All/Dbl Max): Darkness, Aqua, Kurama
Other Frequently Used Leaders (All/Dbl Max): Lucy, Mellow, VR Greek (FELDW), Hiei, Azathoth, Daoloth, PR Haza, etc.
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#10
I'm pretty sure that you cannot use Pluma's+Odous's active at the same time unless they changed that recently, similarly to how you can't use Mufasa's with Basti's at the same time.
Leaders I'm MISSING
Black: WaterXi, Rakhshasa,  Maya, Atlantis,Pompeii. 
VR: Seth, Daji, DBK, W. CN God. 
PR: Yunyang, Ninurta, dark babilonian. 
Rares: Satan, Guan Yu, Cao Cao, Amaterasu, Sakura, Azathot, XHD, LDB+waifu,SHJ, Mai, iori, Turing.
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