Diablo 3 number of character combinations?

[BoomChickn]

So as we all know the skill calculators are out for diablo 3. And I was messing around seeing if I could find out how many potential character combinations. But I am not too sure of my math and I would like to see if anyone can confirm this.

For demon hunter:
Active skill setups
23 (active skills)x6(runestone variants)=138 (All possible skills and variants).

Now 138x132x126x120x114x106=3,328,246,817,280 possible active skill setups (Holy shit that's a lot)
For the multiplication, as you place each skill in, you use up 6 because you can't have the same ability bound twice with different runestones.

Passive skill setups: 13x12x11=1430 passive skill setups

So then active multiplied by passive,

3328246817280x1430=4,759,392,948,710,400 possible combinations for a demon hunter.

To put placement in words, 4 quadrillion 759 trillion 392 billion 948 million 710 thousand 400 possible setups at max level with all 5 runestones unlocked

Anyone able to confirm this?

Edit: I am sure there is a good deal of redundancy in these calculations, from reordering of skills on the action bars/character screen, but I also don't take in to account the fact there are 7 ranks to each runestone, so I think it balances out reasonably.

[Twiddly]

And yet, for every spec there will be an absolute best way to use the skills and runes :P

[Mokthol]

The number of possibilities is impressive isn't it?

This is going to be one of the most fun parts about this game, trying to find good and fun combinations.

[Lucavian]

You have calculated the number of permutations not combinations. Permutations is the number of possibilities if the order mattered (meaning Kick, Punch, Jab and Jab, Kick, Punch would be two separate setups).

Assumptions: 6 Skills each can be chosen at anytime (no order requirements) from a selection of 23, each skill can socketed with any one of 6 runes, and 3 passive skills must also be selected from a pool of 13.

23!
---------- = 100,947 combinations of active skills
6!(23-6)!

The order of the runes is also important because they are reliant upon the order of the active skill selection. That means red, blue, blue, blue, blue, blue is not the same thing as blue, blue, blue, blue, blue, red. Therefore we cannot use the permutation calculation of n^r (in this case 6^6). Instead we must
use the formula for combinations allowing repetition:
11!
--------- = 462
6!(5!)

3 Passive skills selected from 13 is a combination again:

13!
--------- = 286 passive skill combinations
3!(13-3)!

So you have 100,947 active skill combinations, 462 rune combinations, and 286 passive skill combinations for a total of:
100,947 x 462 x 286 = 13,338,329,004 unique combinations. Not Quite in the quadrillions or billions, but still several options.

[Zeta333]

please delete

[burek]

So you have 100,947 active skill combinations, 462 rune combinations, and 286 passive skill combinations for a total of:
100,947 x 462 x 286 = 13,338,329,004 unique combinations. Not Quite in the quadrillions or billions, but still several options.

not of all them make sense, for example you cant play with 6 fury spending abilities and 0 ones that generate it on a barbarian, but nevermind

how many combinations were there in diablo 2 then? you had around 30 skills and over 100 points to spend, with a maximum of 20 per skill

[Gallahadd]

sadly luca it can be scaled down from there a bit further...

take the Monk (it's the easiest example to work from)..

realistically, you're not going to run with all six Spirit builders, and nothing to spend it on, or all four Mantras, as that would be a massive waste.

so if you ONLY took the available combinations using say.. 2 spirit builders 3 spends and 1 Mantra... suddenly we see your numbers fall a bit further. its the same with the passives, no one would take for instance the passive to reduce the CD on 3 of the finishers, if they didn't HAVE those three finishers.

same thing with the barb, although for a barb I'd probably run 2/2/2 between builders, spenders and Situationals.

So while there are still ALOT of potential set ups, I don't think we're talking about millions here, I doubt it'd even be in the tens of thousands

of course I'm sure there ARE still people who will insist on running with crazy builds, but the majority of people will be using spreads like the ones I mentioned..

personally my Tank Monk will be rocking this build http://us.battle.net/d3/en/calculato...Sjb!XVU!cZYcYZ

[Lucavian]

sadly luca it can be scaled down from there a bit further...

I have no knowledge of the game itself, was just trying to help the OP with the math involved. To my defense I did say "unique combinations", I didn't say "good combinations" ;-) Still, I may have to give it a try, the old Diablo wasn't too bad.

[Underskilled]

I like the amount of skill combinations, but what I really love is how you can change them out almost any time you want.

[Verdugo]

not of all them make sense, for example you cant play with 6 fury spending abilities and 0 ones that generate it on a barbarian, but nevermind

how many combinations were there in diablo 2 then? you had around 30 skills and over 100 points to spend, with a maximum of 20 per skill

And how many of them were playable after normal.

[Laringar]

So, I'm thread necroing, but the game is actually out now, and if someone can check my math here, I'd appreciate.

Why do we use the combination with replacement for runes? Order does matter, so it should be the permutation with replacement formula, which would be n^r. (6^6, or 46,656 in this case.)

The skill and passive numbers I agree with, but I think the runes are off there. My total comes to (23! * 13! * 6^6) / (6! * 17! * 3! * 10!) = 1.347e12, or 1.3 trillion combinations. Again, not all VIABLE, but there ya go.

Incidentally, I was very glad to finally discover the Elective Mode option.