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Kuba
04-04-2013, 08:38 AM
Hi all,

I was wondering how many different builds are possible to have in-game. So I did little math to find out. I hope my calculations are correct, if you find any mistake, please write it, so I can correct it.

1) Classes

Right now there are four basic classes, each class has three advanced classes, total 16 different classes. Without any limits on six character teams, we are picking six characters(letter "k") from sixteen classes(letter "n"), we can repeat whatever class we want and order of characters doesn't matter. Formula is ((n + k - 1)!)/(k!(n - 1)!). Total number of combination is 54264 different builds. Since our team is limited, total number will be lower.

2) Limits

Currently limits are: exactly 6 character max 2 Varls max 3 Archers max 3 Raiders
Based on these limitations following builds are possible: (Varls are V, Archers A, Raiders R)
R R R A A A V R R A A A V R R R A A V V R A A A V V R R A A V V R R R A

3) Calculation

For every possibility from above I calculated number of builds using same formula and then summed all to get final number of builds.


R R R A A A - 1 * 20 * 20 = 400
V R R A A A - 8 * 10 * 20 = 1600
V R R R A A - 8 * 20 * 10 = 1600
V V R A A A - 36 * 4 * 20 = 2880
V V R R A A - 36 * 10 * 10 = 3600
V V R R R A - 36 * 20 * 4 = 2880

Total number = 400 + 1600 + 1600 + 2880 + 3600 + 2880 = 12960

4) Considering ranks

In my first calculation I haven't consider levels of characters. Base classes have only single rank, advanced classes have three, so new calculation are following:


R R R A A A - 1 * 220 * 220 = 48400
V R R A A A - 20 * 55 * 220 = 242000
V R R R A A - 20 * 220 * 55 = 242000
V V R A A A - 210 * 10 * 220 = 462000
V V R R A A - 210 * 55 * 55 = 635250
V V R R R A - 210 * 220 * 10 = 462000

Total number = 48400 + 242000 + 242000 + 462000 + 635250 + 462000 = 2091650


With new classes and new limits numbers will be different. Thanks to guys from Stoic for creating so many possibilities. If you enjoyed reading this and want to calculate something else, write it down and I will try to do it.

Leartes
04-04-2013, 09:39 AM
I don't really get where your numbers come from. Like "R R R" there are 3 options for 3x team and 3x2 options for a 2+1 team. Then there is all 1x so in total we have 10 raider combinations. (the same holds for archers). Therefore I'd say there are 100 raider + archer combinations.

I see, if you count base-classes you get 4+4x3+4=20 combinations. I keep the above for others that make the same error as I did.

Aleonymous
04-10-2013, 07:31 AM
Hello Kuba. I'm a little lazy in following the math there, but I guess the final number (12960) does not account for different permutations, right? For instance, a team of 6 different units can be ordered in 6!=720 different ways.

Imagine how that would grow when taking unit-ranks also into account! Finally, somebody attempted on another thread to calculate the Renown needed to purchase the units needed to build any of those lineups... :)

KamikazeDurrrp
04-10-2013, 09:41 AM
Yeah I took a probability class and your math is entirely wrong. Looking at your first grouping of "RRRAAA" group, you would start out with a 6! different combinations that you could have. Since there are 3 repetitions of "R" and of "A", you would divide the 6! combinations by 3!*3! to account for those repetitions. Thus, overall you would have 6!/(3!*3!)=720/36=20 for just RRRAAA without advanced classes.

Now factoring advanced classes is a lot easier. Since you already determine the combinations of RRRAAA all you need to do is find the number combinations for RRR and AAA respectively. Since in this case you can have repetitions of the same class (3 RM, 3 BM, etc etc) that means that finding the number of combinations for RRR means that you would just multiply the possibilities for each event, meaning that the overall combinations of advanced classes for RRR is 3*3*3=27, and you do the same for AAA. Take those number and multiply by the overall combinations that you have and you get 20*27*27=14580 different combinations for just "RRRAAA" alone. Yeah.......

(BTW MOST RANDOM PLACE TO APPLY WHAT I LEARNED FROM MY PROBABILITY CLASS EVAAAAARRRR)

Edit: after looking again at some of the posts what you were trying to do, which was just find unique teams without factoring in turn order I found that your math is correct. My bad :P

Kuba
04-12-2013, 05:00 PM
Thank you guys for your responses, I updated my first post, ranks are now taken into consideration.