Diablo® III

Math Thread: 2.8 trillion builds?

So at BlizzCon Jay Wilson threw the number 2.8 trillion character builds around.

But did he mean per character class or in total?

And what does that mean for the number of skills available to each class?

And will all the classes even get the same number of skills to choose from?

I made some quick calculations this morning to try to get an idea of the numbers of skills we will get to play around with. If you're a wizard with numbers then please tell me if I have made any errors. Ok, here we go:

The Barbarian has got 22 active skills and 15 passive ones so far.

You get 22 skills to choose from for the first skill slot and can combine that with any of the 5 available rune stones.

22 x 5 = 110 possibilities

For the second slot you only have 21 skills left to choose from and still 5 rune stones.

21 x 5 = 105

And so on.

20 x 5 = 100
19 x 5 = 95
18 x 5 = 90
17 x 5 = 85

Ok, and for the 3 passive slots:

15 possibilities for the first one
14 possibilities for the second one
13 possibilities for the third one

Multiply all the results with each other to get the total number of builds.

110 x 105 x 100 x 95 x 90 x 85 x 15 x 14 x 13 = 2 291 551 762 500 000 or 2.29 trillion builds

2.29 trillion builds just for the Barbarian?

Lets do the same for the Demon Hunter with 23 known actives and 13 known passives:

23 x 5 = 115
22 x 5 = 110
21 x 5 = 105
20 x 5 = 100
19 x 5 = 95
18 x 5 = 90
13
12
11

115 x 110 x 105 x 100 x 95 x 90 x 13 x 12 x 11 = 1 948 781 835 000 000 or 1.95 trillion

Monk: 1.05 trillion

Witch Doctor: 1.11 trillion

Wizard: 3.42 trillion

In total: 2.29 + 1.95 + 1.05 + 1.11 + 3.42 = 9.82 trillion


So it would seem that the number 2.8 trillion will actually be per character class! Does this mean that the Monk and the Witch doctor will get a few more skills each before release, Demon Hunter and Barbarian one or so more but the Wizard might actually lose one?

At any rate we are looking at a crapload of combinations! 9.82 trillion is huge, but if everyone is to get 2.8 trillion that will make 14 trillion in total.

All of those combinations will not be viable, of course, but Jay Wilson said their goal was to make as many as possible viable and make it difficult to find synergies that are too optimal. If they succeed with that then I bet we will see some very interesting builds in the months and years following the release of the game :)
Edited by Weazle on 26/10/2011 12:14 BST
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The big problem Jay Wilson does have here is the question, what do we consider "a build".

Changing one pretty less important passive skill is another build in his theory, not in mine. So since that is pretty theoretically, there is no math for calucating the real number of different builds. But we should not let us blind by numbers here, truly different builds will be a whole lot less.
Edited by Kotzer on 26/10/2011 12:18 BST
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54 Human Warrior
570
i realy love this :)
more time to loose in this uber game
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"Simple" formula:

binomial(number_of_skills, skill_slots) * number_of_runestones^skill_slots * binomial(number_of_passive_skills, passive_skill_slots)

(note, if you consider un-runed skills as a possibility, just increase number_of_runestones by 1)

Should be 500 billion for the barbarian, the problem with your calculations is that you're also calculation with the order of the skills, so if you just swap two skills you're considering that a different build


link for calculations in wolfram alpha:
http://www.wolframalpha.com/input/?i=binomial%2822%2C6%29*5^6*binomial%2815%2C3%29

(Anyone please correct me if I'm wrong)

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And in the end there will be about 3 main builds per class.
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Its not important D2 had much more options, the only thing to consider are viable builds. Its not like every runestone has good effect, mostly its just crimson rune, and many skills arent viable in combo at all - like only signaature wizard (or any 2+ signature wizard), only spirit generator monk etc...

Most likely we will see more builds than D2 had, but not that much - Id expect ~100 viable builds per char.

Not saying thats a low number, Im fine with that, but dont expect anything higher..
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The big problem Jay Wilson does have here is the question, what do we consider "a build".

Changing one pretty less important passive skill is another build in his theory, not in mine. So since that is pretty theoretically, there is no math for calucating the real number of different builds. But we should not let us blind by numbers here, truly different builds will be a whole lot less.

Yes, pretty much this.

I guess 'combinations' would be a more accurate word than 'builds'. Still, it is a very impressive number and I will have my hands, and head, full for sure trying to come up with how I want to spec!

So...
i realy love this :)
more time to loose in this uber game

Pretty much this for me as well! :)
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I think the main difference is that in D3 blizzard really want most "builds" to be viable, whereas in D2 you basically only had a few viable specs per Character
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26/10/2011 12:29Posted by DJVibrejtr
Id expect ~100 viable builds per char.


I'd hope for a few more viable builds, but that around 100 per class are very viable or close to optimal even.
Edited by Weazle on 26/10/2011 12:38 BST
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I hope Diablo III has kind of *Uberrun*
Like in Diablo II. Would be awesome :D
Anyone knows?
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I have to agree that all these possibilities are not good enough builds.. but.. if we take a wizard.. what kind of wizard can we build?.. melee.. ye.. what type of melee? what type of gear do we have?.. will the gear be a major part of a build? can we make a fire damage casting melee wizard? ye.. i think we got alot to go with here.. maybe not 10000000000 builds that are insane.. but i think we have enough to play with.. I myself wanna make a cold wizard.. with a twist.. :D
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As people have said already, I suspect there will be about 3-5 Optimal builds and 100's of viable ones for each class :)

This game is going to rock :)
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Im on eof those peeps that dont give a crap about optimal build,if any fun build is going to keep me alive and have me enjoying the game more than any boring optimal builds then im definetly going to use that XD

like they said in the interwiews: "you have no raids to complete,you have no massive groups of people to answer too, you have no guild to answer to. so build what you want and have fun"

Edit: math...i suck at it,but theese are the factors:

Skills
Passive skills
Possible runes
Ranks of runes
Edited by VeNoM on 26/10/2011 13:10 BST
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23 Goblin Shaman
0
Rank of runes doesn't make it a different build, it alters the potency of the altered skills. The higher ranked runes just makes the build more powerfull.

A lot of the combinations can be scrapped, since most classes will require at least one resource generating skill, so you are a bit more limited than having 6 free choices.
Of course, you don't have to choose a resource generating skill, but then the build will likely not be good and not be fun either.
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Your math is wrong, since you do not take into account that the order in which you take the skills does not matter (e.g. skill#1 in slot 1 and skill#2 in slot 2 is the same build as skill#2 in slot 1 and skill#1 in slot 2).

Assuming it is always better to rune a skill (and not let it remain rune-less), and assuming we only take the highest level runes (level 7), the formula is (where n is the amount of normal skills, and p is the amount of passive skills):
C(n,6) * 5^6 * C(p,3)
Now, given that n is 22 and p is 15, this formula amounts to 0,53 trillion.

Note: C(n,k) = n!/(k!(n-k)!)
Edited by McLovin on 26/10/2011 13:44 BST
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The big problem Jay Wilson does have here is the question, what do we consider "a build".

Changing one pretty less important passive skill is another build in his theory, not in mine. So since that is pretty theoretically, there is no math for calucating the real number of different builds. But we should not let us blind by numbers here, truly different builds will be a whole lot less.


Quoted this because i think the same way about builds in general for any game BUT even if there are 100 builds out of 40 trillion or whatever, that suits me pritty well, considering i will probably never use 100 builds for 1 class. I will just find a number of max 5 builds (maybe just a few more.....if i do separate ones for bosses) and use those depending on the situation.

I kinda see what Jay said as "don't worry u can build anything u want ....how u want.... for any situation u might find yourself in. U won't feel like a skill/ability is missing for your class"
Edited by Rebound on 26/10/2011 13:46 BST
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Your math is wrong, since you do not take into account that the order in which you take the skills does not matter
[...]
Now, given that n is 22 and p is 15, this formula amounts to 0,53 trillion.

Yeah, thats pretty much what RichoDemus wrote as well.
I guess 2.8 trillion is the grand total then and that we might get about 23 active and 15 passive skills to play with.

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I`ll try with this cloud program but i have to take steps:

I will make it easier since i don`t know that prog so well and consider each runed skill a unique skill of itself and also take in count runeless skill (whish is pointless but still...) so each skill is actually 6 skills, 5 with with each rune and then the runeless version.

22 barbarian skills x 6 = 132.

combinations of 6 from 132 skills.

http://www3.wolframalpha.com/input/?i=combinations+of+6+from+132

6.547 Billion

then add in passives:

combinations of 3 from 16 passives (16 because not having a passive is also an option and the 16 is actually zero):

http://www.wolframalpha.com/input/?i=combinations+of+3+from+15

560 different sets of 3 passives.

so 6.547 Billion x 560 =

http://www.wolframalpha.com/input/?i=6.547+billion+times+560

so the result would be 3 trillion 666 billion (really? i knew they were secretly making barbarian the devil`s advocate.) and 320 million.

With 22 skills, 3 passives and 5 rune options and not having a rune at all and not having a passive at all either is counted in.
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Nassukka, your math is flawed, you can't just multiply number of skills with the number of runes because you can't select the same skill twice with different runes in the game, you should use binomial like I and McLovin did
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Well consider this: while leveling you still are going to use "builds",and you may not always have access to the highest tier runes, meaning that the build math is far higher than jsut counting "endgame".

Builds last from Act 2 normal, so the builds are there for a very very long time, so lets not get stuck on only the endgame so keep runeranks into the math.

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