Assuming you are playing a Barbarian with Elective Mode:
There are 22 active abilities to choose from, with 5 runes apiece. (realistically, you will never use an unruned skill at max level)
There are 16 passive abilities to choose from.
This gives you:
22x5 = 110 possibilities for your first active slot
21x5 = 105 possibilities for your second active slot
20x5 = 100 possibilities for your third active slot
19x5 = 95 possibilities for your fourth active slot
18x5 = 90 possibilities for your fifth active slot
17x5 = 85 possibilities for your sixth active slot
16 possibilities for your first passive slot
15 possibilities for your second passive slot
14 possibilities for your third passive slot
This is a total of 110*105*100*95*90*85*16*15*14 = 2,820,371,400,000,000 theoretically possible skill builds.
If you had a penny for every possible build, you would have 28.2 trillion dollars - nearly twice the U.S. National Debt.
If you tried a new build every 15 seconds (the skill swap cooldown), it would take you 1.3 billion years to try every possible build. 1.3 billion years ago, multicellular life hadn't yet evolved.
If you had a shot glass full of water for each possible build, you would have 120 trillion liters of water. That is enough to fill 50 million Olympic swimming pools, or roughly a quarter the volume of Lake Erie.
If you had a fine grain of sand for each possible build and lined them up end-to-end, you would get a line of sand that could reach from the Earth to the Sun and back.
Let's just say that we are not going to run out of possible builds to try anytime soon.
Sure, I guess.
But when you take into account that ONE rune, or ONE passive, isn't going to DRASTICALLY make a difference in the way you play, you bump that number back down to:
22X21X20X19X18X17 = 53,721,360 builds that could be considered "drastically different" in my opinion. Still a huge number lol.
That's true - you could have multiple "builds" with exactly the same skills in a different order. To get the number of unique builds you'd have to divide the # of active skill combos by 6! and the # of passive skill combos by 3!. This leaves us with roughly 650 billion builds. Somewhat less impressive than 2.8 quadrillion.
Still, you could argue that having the skills in a different order (assuming you are sticking to the mouse1 mouse2 1-2-3-4 hotkeys) is a different way to play a character.
Well the builds will really rely on the mobs you are facing, in the end. You wont have the same build through out the game, especially in inferno. There you will be swapping out by acts and even areas I will assume. With all of the modifiers on all of the mobs, the degree of strategy that you will need it will be more specific to situation rather than play style or preference. The good thing is we have tons of gear with their own modifiers and lots of other goodies to keep up different, and DYES!
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Sometimes you don't always know where you stand... until you know that you won't run away.
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There are 22 active abilities to choose from, with 5 runes apiece. (realistically, you will never use an unruned skill at max level)
There are 16 passive abilities to choose from.
This gives you:
22x5 = 110 possibilities for your first active slot
21x5 = 105 possibilities for your second active slot
20x5 = 100 possibilities for your third active slot
19x5 = 95 possibilities for your fourth active slot
18x5 = 90 possibilities for your fifth active slot
17x5 = 85 possibilities for your sixth active slot
16 possibilities for your first passive slot
15 possibilities for your second passive slot
14 possibilities for your third passive slot
This is a total of 110*105*100*95*90*85*16*15*14 = 2,820,371,400,000,000 theoretically possible skill builds.
But when you take into account that ONE rune, or ONE passive, isn't going to DRASTICALLY make a difference in the way you play, you bump that number back down to:
22X21X20X19X18X17 = 53,721,360 builds that could be considered "drastically different" in my opinion. Still a huge number lol.
X=abilities for your class
y = number of passives
Number of builds:
X!/(x-6)! * 5 * y!/(y-3)!
Mod- NO NOOB BAHAHAHAHA! *goes to play beta*
Me- /wrists
Still, you could argue that having the skills in a different order (assuming you are sticking to the mouse1 mouse2 1-2-3-4 hotkeys) is a different way to play a character.
Try: (x!/(x-6)!) / 6! * 5^6 * (y!/(y-3)!) / 3!