Trizshjen said:
Grouchy Imp said:
Well if you want to calculate permutaions generally speaking you use factorials, and 14!=87,178,291,200 - so what, they have 14 different options in character creation? Don't get me wrong, I'm looking forward to Diablo 3, but that doen't sound like too many. Even taking long scale (rather than short scale) billions into account, that's only 16 options. Then again, I suppose if that's 14 (or 16) options for each class then that looks a bit more like it.
the factorial calculation is an oversimplification because you are just saying that there are 16 different objects which can be arranged in any order with each one counting as an option. unfortunately when skill branching and prerequisite skills come into play the maths gets much messier.
They're still all factorials, for example k samples out of a population of n with respect to ordering but without replacement is n!/(n-k)!
I'd say the 'messiest' one is with replacement but without respect to ordering, but that's still just the binomial (n+k)-1 over k, in other words (n+k-1)! / k!(n-1)!
And for any extraneous cases it's just the multiplicative principle, so although unwieldy to do by hand, I wouldn't call it messy.
Neither would I call Grouchy Imp's numbers oversimplified, if we abstract out 14 unique choices, that you chose in order (ie through progression) then indeed you get close to 9*10^10. In mathematical terms: we choose fourteen samples out of a population of fourteen, without replacement but with respect to ordering =>
n = k = 14 =>
14!/(14-14)! =>
14!
.
In other words, fourteen choices (w/o replacement, wrt ordering) are enough to get ~90 billion permutations and that's the important part.
Of course, the order in which we choose these defines what a "build" is, so those abstract choices might be a lot more complex than, say, a stat/skill increase or a skill rune.
Probably we could find a better abstraction using k out of n w/o respect to ordering, but with replacement (ie spend k skill points on n skills), but it probably won't tell us anything more than the 14! one. We call it a heuristic, apply Occam's and accept 14! as our measure.
So, during your leveling up you will make about 14 choices about where to take your character that will be defining for your build. Now that sounds pretty good, imo!
