How many power combinations exist in game to date?

[Bionic_Flea]

2 minutes ago, ZemX said:

And I declare myself the thread's Pedant in Chief for reminding him that it's 11 epic/patron choices... since "none" is a choice.   *pushes up glasses*

 

Can confirm.  Source:  If you choose not to decide you still have made a choice. 

                                          --Neil Peart of Rush, in Freewill from the Permanent Waves album.

[lemming]

15 minutes ago, ZemX said:

And I declare myself the thread's Pedant in Chief for reminding him that it's 11 epic/patron choices... since "none" is a choice.   *pushes up glasses*

Can't resist.    You have to pick at least two pools with the number of power picks requiring six powers plus Primary & Secondary...  (unless there's a six power pool that I'm forgetting about)

[Andreah]

Let's look at Scrappers for a start.

 

Scrappers can choose from 21 primary powersets and 14 secondary. 21 x 14 = 294 combinations of those, except for the specific combinations that are disallowed, such as (katana, staff fighting, titan weapons, claws, dual blades) which can't be combined with shield defense. That's five combinations we subtract out, for a total of 289 combinations. Correct me if I've missed any forbidden scrapper combos.

 

Then, scrappers can choose up to 4 out of 12 power pools, and then one out of 10 ancillary/patron pools.

 

For power pools, we have to account for possibly choosing 0 of these (one way to do that), 1 of these (12 ways to choose one), 2 of these (66 ways), 3 of them (220 ways), or 4 of them (495 ways) for a total of 794 unique ways to choose from power pools.

 

For ancillary/patron pools, there's 1 way to choose none of them, and 11 ways to choose one of them, for a total of 12.

 

The total number of unique scrapper powerset choices is the product of these totals, or 289 x 794 x 12 = 2,753,592.

 

After that, there's many, many numbers of ways to powers from each set.

 

 

As an aside, the way to figure out how many unique ways there are to choose K things out of a set of N choices is called "N choose K", or C(n,k) which is equal to n! / ( k! (n-k)! ), where x! is the factorial function, which is where all the whole integers from 1 up to x are multiplied together.

 

 

Counting the unique ways one could choose powers is much harder to work out, and I suspect, vastly higher yet. 

 

 

 

[ZemX]

1 hour ago, lemming said:

Can't resist.    You have to pick at least two pools with the number of power picks requiring six powers plus Primary & Secondary...  (unless there's a six power pool that I'm forgetting about)

 

I know that, but as I explained, I am not counting standard power pools as a "powerset combination".  As such, your pedantry on top of my pedantry is denied!

[Snarky]

2 hours ago, ZemX said:

 

To be serious about this (unlike my other reply) the useful answer here is the simplest one (number of primary choices multiplied by number of secondary choices) summed across all ATs.   If you think about how we most often talk about what characters we are playing, we tend to just give the pri/sec combo. e.g. "I am playing a Katana/Regen Brute!"

 

Less often, people will throw in that epic/patron pick and say they are playing a Dark/Dark/Dark Blaster, so that's fair game too, I think.

 

Pools are much less differentiating, however.  It's not that the powers themselves are unimportant.  Just that nobody introduces themselves as a Fire/Fire/Flying/Speed/Concealment/Mace Blaster.

 

As such I declare @Snarky the winner of this thread:

 

And I declare myself the thread's Pedant in Chief for reminding him that it's 11 epic/patron choices... since "none" is a choice.   *pushes up glasses*

None…funny.  Also, now they are talking about various only take this or that so if we are talking actual power choice combinations and not possible primary/secondary/epic it is about to get maddeningly more complicated. 

[ZemX]

1 hour ago, Andreah said:

For power pools, we have to account for possibly choosing 0 of these (one way to do that), 1 of these (12 ways to choose one), 2 of these (66 ways), 3 of them (220 ways), or 4 of them (495 ways) for a total of 794 unique ways to choose from power pools.

 

For ancillary/patron pools, there's 1 way to choose none of them, and 11 ways to choose one of them, for a total of 12.

 

The total number of unique scrapper powerset choices is the product of these totals, or 289 x 794 x 12 = 2,753,592.

 

Must... resist... can't... okay, we're doing this:

 

If you really want to count standard pools, it's a bit more complicated.  You can't choose zero standard pools.   You have 24 powers to pick and can only fill 18 of them by taking all primary and secondary powers.  That leaves six, as @lemming has also noted.  This means two pools must be chosen, one of which or neither of which can be an epic/patron.

 

So you have one of these cases:

1. Two pools. (12 choose 2 is 66 but 3 of these are illegal combinations of two specialized travel pools, so 63)

2. One pool and one epic. (12 times 10 choices = 120)

3. Three pools (12 choose 3 is 220 but this time there are 9x3 illegal combos of one standard and two specialized pools, and one illegal combo of all three spec pools, so 220-28 = 192).

4. Two pools and one epic (line 1 times 10 = 630).

5. Four pools (12 choose 4 is 495 but again more illegal combos. We'll need a footnote here!^(a). Total = 495 - 45 = 450.

6. Three pools and one epic (line 3 times 10 = 1920.  whew!

 

Sum of all these is 63+120+192+630+450+1920 = 3375 (but I'll be shocked if I didn't make a mistake in here somewhere).  This 3375 is what you'd multiply by primary and secondary choices you have from your post.  So 289 times 3375 = 975,375.   Almost a million scrappers combos! And you thought ONE on the team was trouble!

 

Footnote (a): Illegal combos of two specialized pools is 3 combined with two choices of the other 9 (9 choose 2 = 36.  Illegal combos of all 3 spec pools is 1 times a choice of the other 9.  So 9.  Total is the sum of 36 + 9 = 45.

 

What was that you posted while I was in the middle of all this @Snarky?

5 minutes ago, Snarky said:

it is about to get maddeningly more complicated. 

 

Tooooo laaaaate!

[lemming]

52 minutes ago, Snarky said:

it is about to get maddeningly more complicated.

Hence my sticking to Pri/Sec

Blaster -> 225 - 15
Brute -> 286 - 22
Controller -> 187 - 17
Corruptor -> 255 - 17
Defender -> 255 - 17
Dominator -> 143 - 13
Mastermind -> 119 - 17
Scrapper -> 294 - 21
Sentinal -> 195 - 15
Stalker -> 252 - 18
Tanker -> 242 - 22
Epic -> 4 - 4
Combo: 2457 - 198

 

Nice work @ZemX; so for all, looks like 8,292,375 before subtracting .

 

As a side note, @Andreah Spines doesn't work with shield either.  And for Brutes & Tankers, they have the shield restriction, and no claws with Stone.  So dropping total combos to before pools to 2438 and a total of 8,228,250

So if you want, with 3 builds each, you could have 2,742,750 needing only 2,743 accounts.   Sounds like a very long project

[Scarlet Shocker]

4 hours ago, Bionic_Flea said:

 

Wait.  Are you calculating number of possible power set combinations or number of possible POWER combinations?  If you are doing sets then you can only have 4 pools and one epic, so you only have to multiply by 5, not 50. 

 

If looking at powers, then I think you have to do factorials for each power set (9 powers each) and pool, as you can choose to take or skip powers.  And that probably has to be limited by the total number of power picks (24 not including inherents).  Ugh!  Math!

 

I was trying to discover what are the maximum number of power variants in the game, across all ATs and powers: In other words, what is the maximum possible PCs you could build, at level 50 where no two characters had exactly the same power sets. Every PC would be different even if by a magnitude of just one

 

 

turns out to be pretty bloody difficult!

 

Edited September 11 by Scarlet Shocker

[lemming]

5 minutes ago, Scarlet Shocker said:

turns out to be pretty bloody difficult!

Well, then you have the choices in slotting...

[Scarlet Shocker]

1 hour ago, ZemX said:

 

Must... resist... can't... okay, we're doing this:

 

If you really want to count standard pools, it's a bit more complicated.  You can't choose zero standard pools.   You have 24 powers to pick and can only fill 18 of them by taking all primary and secondary powers.  That leaves six, as @lemming has also noted.  This means two pools must be chosen, one of which or neither of which can be an epic/patron.

 

So you have one of these cases:

1. Two pools. (12 choose 2 is 66 but 3 of these are illegal combinations of two specialized travel pools, so 63)

2. One pool and one epic. (12 times 10 choices = 120)

3. Three pools (12 choose 3 is 220 but this time there are 9x3 illegal combos of one standard and two specialized pools, and one illegal combo of all three spec pools, so 220-28 = 192).

4. Two pools and one epic (line 1 times 10 = 630).

5. Four pools (12 choose 4 is 495 but again more illegal combos. We'll need a footnote here!^(a). Total = 495 - 45 = 450.

6. Three pools and one epic (line 3 times 10 = 1920.  whew!

 

Sum of all these is 63+120+192+630+450+1920 = 3375 (but I'll be shocked if I didn't make a mistake in here somewhere).  This 3375 is what you'd multiply by primary and secondary choices you have from your post.  So 289 times 3375 = 975,375.   Almost a million scrappers combos! And you thought ONE on the team was trouble!

 

Footnote (a): Illegal combos of two specialized pools is 3 combined with two choices of the other 9 (9 choose 2 = 36.  Illegal combos of all 3 spec pools is 1 times a choice of the other 9.  So 9.  Total is the sum of 36 + 9 = 45.

 

What was that you posted while I was in the middle of all this @Snarky?

 

Tooooo laaaaate!

I think Zem is closest here. I may not be right but I guess one thing I haven't factored in is the rules about the number of pool powers  - and indeed the variance of them - and the Patrons

[Scarlet Shocker]

10 minutes ago, lemming said:

Well, then you have the choices in slotting...

 

I almost hate you (no I truly do not! 😃 ) but you are saved by the fact that I was only interested in powers. If you add slotting to the mix that would mean that almost every power taken could be multiplied by 6.

 

It would be a large number.

Edited September 11 by Scarlet Shocker
too harsh man, too harsh. Dayyyyyyyyyyooooooooooooooooooh

[Scarlet Shocker]

Thinking aloud here: We need to establish the definitive rules here: What is the minimum number of pool powers and/or sets we MUST pick...  I think I'm right in believing we don't have to pick an EP (EPicatron) if we don't wish.

 

That way we can at least get a baseline for the non V/EAT ATs

 

[Andreah]

4 hours ago, Scarlet Shocker said:

 

I almost hate you (no I truly do not! 😃 ) but you are saved by the fact that I was only interested in powers. If you add slotting to the mix that would mean that almost every power taken could be multiplied by 6.

 

It would be a large number.

But that's just number of slots -- that's not in itself very interesting if they're empty. It matters what you put in them! There are LOT more combinations of that than I care to think about.

[Andreah]

5 hours ago, ZemX said:

 

Must... resist... can't... okay, we're doing this:

 

If you really want to count standard pools, it's a bit more complicated.  You can't choose zero standard pools.   You have 24 powers to pick and can only fill 18 of them by taking all primary and secondary powers.  That leaves six, as @lemming has also noted.  This means two pools must be chosen, one of which or neither of which can be an epic/patron.

 

So you have one of these cases:

1. Two pools. (12 choose 2 is 66 but 3 of these are illegal combinations of two specialized travel pools, so 63)

2. One pool and one epic. (12 times 10 choices = 120)

3. Three pools (12 choose 3 is 220 but this time there are 9x3 illegal combos of one standard and two specialized pools, and one illegal combo of all three spec pools, so 220-28 = 192).

4. Two pools and one epic (line 1 times 10 = 630).

5. Four pools (12 choose 4 is 495 but again more illegal combos. We'll need a footnote here!^(a). Total = 495 - 45 = 450.

6. Three pools and one epic (line 3 times 10 = 1920.  whew!

 

Sum of all these is 63+120+192+630+450+1920 = 3375 (but I'll be shocked if I didn't make a mistake in here somewhere).  This 3375 is what you'd multiply by primary and secondary choices you have from your post.  So 289 times 3375 = 975,375.   Almost a million scrappers combos! And you thought ONE on the team was trouble!

 

Footnote (a): Illegal combos of two specialized pools is 3 combined with two choices of the other 9 (9 choose 2 = 36.  Illegal combos of all 3 spec pools is 1 times a choice of the other 9.  So 9.  Total is the sum of 36 + 9 = 45.

 

What was that you posted while I was in the middle of all this @Snarky?

 

Tooooo laaaaate!

Outstanding!

 

It's not impossible to work these numbers out, and IMO, different combinations of pools can make otherwise identical primary/secondary choice characters play very differently.

[Snarky]

at this point madness consumes me looking at the conversation.  @Scarlet Shocker did indeed mention pool powers.  but are we counting each different pick within a power as a different unique "combo" or just "some from this" and "some from that"?

[Andreah]

I remind myself what the OP is asking about, and here's one way to look at this, kind of superficially, to figure out the total number of uqnique powers choice options within one build.

 

Let's say you choose a primary and secondary, we don't care which, each has up to nine powers, and then also four power pools, each with five choices, and then also one patron or ancillary pool, also with five choices. 

 

So, let's estimate a lower bound on how many options there would be. This is a total of 9+9+5x4+5, or 43 potential power picks. From these, the character can pick 24 choices -- that's 43 choose 24 combinations, or 800,472,431,850. That's over 800 Billion.

 

But wait, there's more constraints. There's a minimum number of power choices that have to go into the primary and secondary, and that can't go into any pool, and the number that can go into pools is also limited in some ways.

 

A better approach would be to think about how many permitted choices there are at each level up, which would also account for the sequence that powers open up by level. So, how many choices do you have at level 1, then how many at level 2, at level 4, and so on, for each level you choice make a choice at. It gets complicated whenever you could choose a pool, because then we need to track separately how your choices change from that point on based on whether you chose a pool or not. This forms a tree of choices, and we have to add across the nodes of, and multiply as we ascend the branches. This would be best done by a computer program to keep track of it all, but as I think about it, it feels to me that it should be tractable to do by hand, or with a spreadsheet, since the number of pools is in the single digits, and worst case there would be five pools? (I rarely use them, so I don't know, can you have an epic/ancillary and a patron pool? So six?) That's 32 (64?) tree branchings to track. Sounds tedious, but doable. Ideally done by computing through, using recursion.

[lemming]

41 minutes ago, Andreah said:

can you have an epic/ancillary and a patron pool

Nope.  Just one from those.  I think @ZemX laid out the combos decently enough.

 

I think your methodology is the way to go.   And at that point, we can have a program just spit out a build...

[Apogee]

I wasn't a math major so I am going to say the answer is...

 

[Scarlet Shocker]

7 hours ago, Snarky said:

at this point madness consumes me looking at the conversation.  @Scarlet Shocker did indeed mention pool powers.  but are we counting each different pick within a power as a different unique "combo" or just "some from this" and "some from that"?

 

You must have a minimum of... 5 pool slots I believe and a maximum of 20. I fiddled around wtih Mids last night and actually taking 20 pool powers is very difficult. I don't even think it's permissible.

 

@Andreah makes a good point about the number of combos but for most EPs there are 10 options. (MM get 9 for some reason. Devs hate MMs)

[Andreah]

4 hours ago, Scarlet Shocker said:

You must have a minimum of... 5 pool slots I believe and a maximum of 20. I fiddled around wtih Mids last night and actually taking 20 pool powers is very difficult. I don't even think it's permissible.

 

Good to know! From that we can further limit the choices down. I'm busy for the moment, but I'll think about it some more later.

[ZemX]

17 hours ago, ZemX said:

Sum of all these is 63+120+192+630+450+1920 = 3375 (but I'll be shocked if I didn't make a mistake in here somewhere). 

 

Aaand I did.    Forgot one last line:

 

7. Fours pools AND one epic/patron (line 5 in my previous post times 10 epic/patron choices = 4500 more options).

 

So total of 7875 pool/epic combos times 289 pri/sec combos = 2,275,875... wow... so many Scrappers!

 

5 hours ago, Scarlet Shocker said:

You must have a minimum of... 5 pool slots I believe and a maximum of 20. I fiddled around wtih Mids last night and actually taking 20 pool powers is very difficult. I don't even think it's permissible.

 

Minimum six.  You have 24 power picks to make and can only fill 18 of them with primary and secondary if you choose all of those.   Max is actually 21 though since your first pool is picked at level 4, hence 3 picks to make before that (2 at creation and one at level 2).  But I'll let someone crazier than myself prove it.  Read this old thread by @Spaghetti Betty... and despair! (and yes, it reads in the thumbnail as "Show me your poo..." to me too).

[Snarky]

Are we zeroing in on a number? Or at least a set of rules?

 

If we disregard the madness of counting the different picks in primary/secondary/pool/patron/epic and just focus on WHICH sets are taken my mind starts to settle.  Then you have the standard A x B x C x D.  Except pools are odd in that you can pick 1 to 4.  Which suggests the pool multiplier will be not be #pool but #pool+3.  Likewise epic/patron is #epic/patron+1.  For none.  You cannot take no pool.  Even if you take all primary secondary and epic/patron you still have one power pick left. 
 

so the method would be (Archetype Primary) x (Archetype Secondary) x (Pool+3) x (Epic/Patron+1) - invalid choices processed for each Archetype and then summed.  
 

If you want to talk about the variations of each power pick within the sets I will tap out.  I like math but the navel gazing gets stupid at a certain point, and pretty sure that is the point in this discussion.

[ZemX]

13 minutes ago, Snarky said:

Are we zeroing in on a number? Or at least a set of rules?

 

Despite indulging in some math nonsense up there I think I am with @lemming.   Stick with just the AT, primary, and secondary combos.  Everything else after that is just build variation you can mix, match, and respec at will.  And there are effectively an infinite number of build variations because all of us together will never try all of them or even more than a fraction of them.

[Snarky]

3 minutes ago, ZemX said:

 

Despite indulging in some math nonsense up there I think I am with @lemming.   Stick with just the AT, primary, and secondary combos.  Everything else after that is just build variation you can mix, match, and respec at will.  And there are effectively an infinite number of build variations because all of us together will never try all of them or even more than a fraction of them.

I agree, but the OP wanted pools and epics/patrons

[Mopery]

Accounting for every possible slot/enhancement combination, I'd wager the number is greater than the number of particles in the known universe.