Math Challenge: How many Build combinations in a Guild Wars 8 man team?

Blue! No, yel--
*Aaaaargh!*

the answer is 42 :P

actually it's 47 (Trekkie and Alias fan)

For Warrior/Ranger where
- total skills = 189
- total elites = 71

i bet that all possible combinations are something like this:


Which roughly equals to: 1,488 x10^14 possible combinations

I'm not doing it for all other professions :O

Ok, I've had a good night's sleep and 2 cups of coffee. Let's take another look at this.

Ok, how about answering a simpler question first?

How many different PvP skillbars are possible?

Let's start with the lowest numbers first. A dervish or Paragon has 69 regular skills and 15 Elites available to them. I'm deriving that from 60 profession specific skills and 9 skills that any profession can use. (Yes, 9!! Rez Signet, Empty slot #1, Empty slot #2, Empty slot #3........)

For no Elites, that's 69!/(8! x 61!) = 8,361,453,672
With 1 Elite it's (69!/(7! x 62!)) x 15 = 16,183,458,720
For a total of 24,544,912,392 possible skill bars for Dervishes and Paragon using skill from their primary profession only.

For Assassins and Ritualists, it's 84 regular skills and 25 elites. Plugging those numbers into the same formula yields 128,520,753,894 combos for those guys using only skills from their primary.

That's a grand total of 306,131,332,572 skill bars so far and I've only counted 4 professions with no secondary skills. The Core professions have Wayyyy more skills to choose from.

I need more coffee!

well you can't bring empty8 if you don't have empty7, then it would just be empty7

what about all the attribute combinations?
and you could bring different level characters too!
or you could bring less than 8 people

ze possibilities, zey are endless!

Also a simple way of getting elite skills in the equation, and empty skills
slot1*slot2*slot3 etc M being number of non elite skills possible(empty slot not included), E being number of elites

((M)*(M-1)*(M-2)*(M-3)*(M-4)*(M-5)*(M-6)*(M-7) + (M+E)*(M)*(M-1)*(M-2)*(M-3)*(M-4)*(M-5)*(M-6))
+
((M)*(M-1)*(M-2)*(M-3)*(M-4)*(M-5)*(M-6) + (M+E)*(M)*(M-1)*(M-2)*(M-3)*(M-4)*(M-5))
+
((M)*(M-1)*(M-2)*(M-3)*(M-4)*(M-5) + (M+E)*(M)*(M-1)*(M-2)*(M-3)*(M-4))
+
((M)*(M-1)*(M-2)*(M-3)*(M-4) + (M+E)*(M)*(M-1)*(M-2)*(M-3))

you get the idea
i haven't put too much thought into that so it might work. but I think it should
if you look away from the levels and attributes you can put it all into 1 (huge) formula
basically repeat the above for every class combo with different M and E values

I don't know about your formula, haven't looked at it too closely, but you're correct about the empty slots. I realized after the 3rd cup of coffee that I made a mistake with those. The correct formula is bit more complicated.

Dervish and Paragon 61/15 skills (keep the rez sig). Thats (61!/8! (61-8)!) + 61!/7! (61-7!) + 61!/6! (61-6!) + ........ Then repeat for adding back the Elite skills. Should come out slightly less than my original numbers, but still a huge amount of combos.

Ok 4 cups of coffee, 1 giant caffeine buzz and a whole lot of Geek determination and here's the results.



This is only counting builds that use skills from the primary profession only (plus a rez sig). Trying to add Primary/Secondary mixed builds caused the numbers to go up higher than my spreadsheet supports. Feel free to double check the math.

BTW, 10 of these builds are identical (8 empty slots) so you can subtract 9 from that final number.

Now aren't you glad we discarded PvE only skills and Cap Sigs!

Now factor in Attributes and weapons and all that fun stuff.

there is no end to the numbers. when you take into consideration that a "build" consists of insignias, weapons, modifiers,runes,attribute distribution, and skills, the possiblities are impossible to figure out. also you can have the same exact everything that one build has but leave out 1 or 2 things (be it attribute points,or a rune or whatever) and technically that makes it a differant build.i dont think it is possible to figure out.

thetechx, it's perfectly possible to figure it out.

Im only looking at skill bars,
I assume whatever the skill bar is,... the attributes, runes and equipment will support it. Though there will certainly be multipurpose bars, i figure that arguably balances out against the useless bars

For ballpark permutations on 1 character I figure it something down these lines. Please point out any critically flawed logic here.

slot 1 = 1160 possible choices. - picking your first skill you now have a primary class, and if you're going to use an elite, lets assume you've picked it.
slot 2 = 869 possible choices - Except for elites, which would conflict with slot 1, you can still pick any class skill here. you're allowed 2 classes..so if you're going to use a secondary class skill we assume you pick at least one of those skills now.

Ok, now I remove the remaining 8 classes as possible skill choices since we've locked in to our primary and secondary. To simplify I'm going to use an average of 86 non-elite skills per class. 172 choices -1 the non-elite we just picked.

slot 3 = 171 remaining possible choices
slot 4 = 170 possible , slot 5 = 169 possible .... slot 8 = 166 possible.

Which gives me a total of (2.31 *10^19) possible character skill bars.
Multiply 8 to make a full team. (1.85 *10^20) possible team skill bars.
Or, 185 Quintillion. (1 Quintillion = 1 Billion Billions)

??..ballpark since i'm using averages for the smaller (lol) numbers. More accuracy is certainly possible.

You still have to multiply it with 90, because u did only 1 out of 90 possible class combinations

You actually have to make 2.31E19 at the eight power instead of simply multiplying by eight. My first estimation (taking means, without taking into account one-elite only, allowing repetition of skills and such) was about 10^150 posible builds. A second try allowing only one elite and no repeated skills gave 2.7E138. And even so, only three or four are played in PvP.

O________________o




I don't think there's enough "wtf"s in this world to express my feelings.

I thought about trying to figure this out, but as I began to think about it, the shear complexity of the problem made my face turn into one of these.

You guys forget 1 thing, 1 character can't use skills of different attributes,

i.e. Sword warrior can't use Axe and Hammer skills, Pyro ele is unlikely to use spells of 3 other magic, etc etc.

If you factor that in, the equation will get really messy.
Since a War can put 1point in sword, 1 point in axe, 1 point in hammer, etc with weapon swap.

Thus in theory, a sword warrior can use axe/hammer skills, the same can be said by the other classes.

I did it! (Poured the coffee straight into the spreadsheet software this time )

The total number of PvP skill bars possible in the game is 3,682,658,694,659,070. That's 3 Quadrillion, folks! That's a lot of skillbars to test.

Attached is a spreadsheet with all the numbers. In order to attach it here, I converted it to .txt format. The columns are Tab delimited. In order to view it properly, upload it into a spreadsheet program. It's difficult to read in Notepad. Unfortunately, this destroyed the formulas that were in each spreadsheet cell and left only the resulting values. If you really want to see the formulas, contact me and I'll e-mail the spreadsheet to you. (Sorry, I couldn't attached an .xls file here. Security precaution since they can contain macro viruses)

skillcombos.txt

So, is there a prize for this? Other than the Guru Geek of the Year award that is.

I started by counting up the skills available for each profession in PvP. If my counts are wrong, please reply. +1 has been added to all professions for the Rez Sig.
Warrior 95/36
Ranger 96/35
Elementalist 100/35
Mesmer 94/34
Necromancer 98/35
Monk 97/35
Assassin 76/25
Ritualist 76/25
Dervish 61/15
Paragon 61/15


What's included and what's not:
- No PvE only skills were added. By doing this I was able to drop the Cap Sig which would have complicated matters even further since you can have more than 1 on the bar.

- No Eye of the North skills

- This is evaluating unique skillbars only. Runes, weapons, armor, attribute distribution is not considered. (No!! I'm not calculating that. Don't even ask!!!!!!! )

- There are 55 different profession combos in the game. For these purposes, a Warrior/Ele is treated the same as an Ele/Warrior. Both can run the same skillbars. A Warrior with no secondary though is a unique combo.

- Order of skills doesn't matter. A bar with Spiteful Spirit, Arcane Echo and 6 empty slots is the same as a bar with Arcane Echo, 2 empty slots, Spiteful Spirit and 4 empty slots and is only counted once.

- Duplicate bars across professions was eliminated in the final total.
For Example:
A Dervish has 10,917,708,417 different skillbars available using only Dervish skills (and a Rez Sig).
A Paragon also has 10,917,708,417 skillbars.
A D/P has 2,982,677,338,196 skillbars, but 21,835,416,834 of those are duplicates of the Dervish only and Paragon only bars. That 21 billion was subtracted from the D/P total for the final numbers.
Another Example: A warrior has 131 skillbars that use only 1 slot. A Ranger also has 131 bars. A Monk has 132. For a total of 394. Wrong. 3 of those bars are identical. (Rez Sig + 7 empty slots) For this reason 54 was subtracted from the total.

- ALL PvP bars are counted. The good bars, mediocre bars, bad bars and the truly horrible you-should-uninstall-the-game bars. (Flare, Mending, Riposte, Cyclone Axe, Hammer Bash, Deep Freeze, 2 empty slots) I don't judge 'em. I just count them.

- Oops, I lied. Not every PvP skills was counted. Dragon Arena skills, Snowball skills, Beetles and any other speciality arena skill wasn't counted.

Whew, I'm outta coffee. I'm going home.

Edit: Oops, almost forgot. Multiple that number (3,682,658,694,659,070) by 8 to get the answer to your 8-man team question.

Lock this before mah brain explodes...