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View Full Version : There are 221,184 ways to order a Whoper.



Kansaschaser
2011-02-11, 09:57 AM
There was a Burger King T-Shirt I saw that said how many different ways you can order a Whoper.

What I want to know, has anyone figured out how many different ways we can build(order) characters? I'm talking about just what class to pick, not feats, skills, magic items, or spells.

So if you consider 20 levels to be the different layers of a Whoper, how many different ways can you build a character in AD&D, D&D 3.X, and 4th edition? No Homebrew and only official material. I wouldn't consider Dungeon and Dragon magazines official.

I know in AD&D they had a Dual Class rule that let you take up a second and/or third class.

In D&D 3.X, you can Multi-Class.

I'm not sure what you can do in 4th edition.

Whammydill
2011-02-11, 10:00 AM
Just as EvilKingMaskPlaceBurgerKing has an upperlimit on what they have available to put on a whopper, you'd need to determine what books you would allow to calculate that.

Kansaschaser
2011-02-11, 10:04 AM
Just as EvilKingMaskPlaceBurgerKing has an upperlimit on what they have available to put on a whopper, you'd need to determine what books you would allow to calculate that.

For AD&D: Official AD&D material, excluding Dungeon and Dragon magazines.

For D&D 3.X: Official D&D material, no 3rd party material or Dungeon/Dragon magazines.

For 4th edition: No clue. What is there for 4th edition other than official material? Has anyone made 3rd party 4th edition material?

gbprime
2011-02-11, 10:05 AM
Has anyone made 3rd party 4th edition material?

That would imply there's a market for it. :smallamused:

Kansaschaser
2011-02-11, 10:07 AM
That would imply there's a market for it. :smallamused:

Oh snap! Was that a rag on 4th edition? :smallwink:

Douglas
2011-02-11, 10:09 AM
What I want to know, has anyone figured out how many different ways we can build(order) characters? I'm talking about just what class to pick, not feats, skills, magic items, or spells.
A lot. Billions at least, probably trillions or even quadrillions. Or maybe even more orders of magnitude than that.

Incidentally, the number you quoted for Whoppers implies that there are 13 binary (i.e. on/off) options and 3 trinary (none/some/lots) options for how to customize a Whopper.

Kansaschaser
2011-02-11, 10:14 AM
Ok, lets make it simpler and just stick with base classes for now. At my last count, there are 41 base classes for D&D 3.X.

I don't have any of my AD&D books, so I don't remember all the base classes for that system.

And, I don't have any 4th edition books, so I don't know what base classes are available for 4th edition.

So, if you have a max of 20 levels, a total of 41 base classes, and you can add any combination, how many would that be?

BlckDv
2011-02-11, 10:32 AM
Ok, lets make it simpler and just stick with base classes for now. At my last count, there are 41 base classes for D&D 3.X.

I don't have any of my AD&D books, so I don't remember all the base classes for that system.

And, I don't have any 4th edition books, so I don't know what base classes are available for 4th edition.

So, if you have a max of 20 levels, a total of 41 base classes, and you can add any combination, how many would that be?

If your 41 base class count is right, and you allow the selection of any class at each level (ignoring RAW limits such as once you leave class x you cannot go back), you could make 180,167,782,956,420,929,503,029,846,064,800 unique class/level combinations for a level 20 PC. If you count PCs of lower than level 20 as separate from the level 20 builds which include their progression, it gets a lot bigger.

That said I don't feel this metric provides any actual meaningful or useful data, as any claim that feat and prestige class selection does not separate characters as much if not more than base class levels is suspect. Further, it would be nonsensical if applied to 4e as the main leveling choice mechanism in 4e is based on power, not class, selection.

Eldan
2011-02-11, 10:34 AM
Well. I count 66 base classes, including NPC classes, but not counting variants. I'm not counting prestige classes.

That means, there are 1.40393832 10^19 ways to build your character, just with base classes. This does not take into account that there's classes where the order in which you take them matters, such as teh ToB classes.

Kurald Galain
2011-02-11, 10:37 AM
Annoyingly, a small fraction of those quazillion combinations isn't actually possible, because certain classes prohibit you from returning to them after you've left them.

Kansaschaser
2011-02-11, 10:44 AM
Further, it would be nonsensical if applied to 4e as the main leveling choice mechanism in 4e is based on power, not class, selection.

Wait, you can't multi-class in 4th edition? :smallconfused: I swear I've heard of people playing multi-class characters in 4th edition. So you can't play a Fighter 2 / Wizard 6 / Rogue 8 / Barbarian 2 / Bard 2?

Kurald Galain
2011-02-11, 10:49 AM
Wait, you can't multi-class in 4th edition?

The word has a different meaning across editions.

In 2E, you multiclass by picking two or three classes at character creation, and dividing your experience points equally among those as you level.

In 3E, you multiclass by picking a different class as you gain a level.

In 4E, you multiclass by taking a feat, which gives you a skill and minor ability related to that class, and which allows you to take other feats to swap a power from your base class for one of your multiclass.

dextercorvia
2011-02-11, 10:49 AM
Wait, you can't multi-class in 4th edition? :smallconfused: I swear I've heard of people playing multi-class characters in 4th edition. So you can't play a Fighter 2 / Wizard 6 / Rogue 8 / Barbarian 2 / Bard 2?

It's been a while since I read 4E stuff, so someone can correct me if I'm wrong. I believe you 'multiclass' in 4E by taking feats which give you a few of the powers of other classes. You also have different classes you can take as you advance through the paths (kind of like PrC's but you stick with one through the whole 10 level path).

BlckDv
2011-02-11, 10:51 AM
Wait, you can't multi-class in 4th edition? :smallconfused: I swear I've heard of people playing multi-class characters in 4th edition. So you can't play a Fighter 2 / Wizard 6 / Rogue 8 / Barbarian 2 / Bard 2?

There is a mechanic in 4E called Multiclassing, but it is a very diff. beast than what you call multiclassing in 3.x. A 4E multiclass character who was say a Fighter and multiclassed to Ranger at 10th level would still be a Fighter 10, not a Fighter 9/Ranger 1. He would just have access to some Ranger class features, and going forward could buy elements such as feats and Paragon Paths that have a "Ranger" pre-req. Only Bard base class is able to multiclass into more than one other class. I'm not going to get into the beast known as Paragon Multiclassing as that is way off topic.

There is a separate mechanic called Hybrid which is closer kin to the AD&D Dual-Classing systems of yore, and as such closer to 3.x multiclassing, but not apples to apples.

Douglas
2011-02-11, 10:52 AM
Wait, you can't multi-class in 4th edition? :smallconfused: I swear I've heard of people playing multi-class characters in 4th edition. So you can't play a Fighter 2 / Wizard 6 / Rogue 8 / Barbarian 2 / Bard 2?
There are feats that sort-of partway half imitate multiclassing, giving you a watered-down version of one of another class's basic abilities and letting you pick a portion of your powers from that class, but there's nothing even approaching 3.5's multiclassing. For the most part, in 4e you pick a class and that's your class, from level 1 to level 30.

Kansaschaser
2011-02-11, 10:52 AM
In 4E, you multiclass by taking a feat, which gives you a skill and minor ability related to that class, and which allows you to take other feats to swap a power from your base class for one of your multiclass.

Oh, well that kind of sucks. So you have to spend a feat to take an ability from another class. Do you get the hit points of that class for that level at least? When I play Wizards in D&D 3.X, I normally like to take levels in something that boosts my hit points.

Or, I'll take a few levels of Barbarian for the hit points and then go into the Rogue/Scout/Ranger/Bard/Factotum for the skills.

BlckDv
2011-02-11, 11:09 AM
Oh, well that kind of sucks. So you have to spend a feat to take an ability from another class. Do you get the hit points of that class for that level at least? When I play Wizards in D&D 3.X, I normally like to take levels in something that boosts my hit points.

Or, I'll take a few levels of Barbarian for the hit points and then go into the Rogue/Scout/Ranger/Bard/Factotum for the skills.

If you try to look at it from the PoV of building a 3.x PC, it isn't going to make sense, and the answers are just going to mislead you.

in 4E, there are no random HP, every class gets Con Score + (Class Number) at level 1, and then (Class Number) for every extra level. Multiclassing does not change this. It does mean that by giving yourself a high Con Score, any class can be made buffer for the first several levels, and it also gives more Healing Surges which makes you more survivable for the rest of the game.

Example: I have a party with two rogues. One (a sniper) has Con 8, the other (a thug) has Con 16. At level 1, the Con 8 rogue had 20 HP, the Con 16 had 33 (took the Toughness feat). At level 11, the Con 8 rogue has 65 HP, the Con 16 has 83 HP.

Staff wizards in 4E can be some of the toughest, hard to hit/kill PCs on the map, porting over 3.x expectations of what each class can and cannot do is just going to give false ideas.

Likewise, there are no skill points. All skills go up a bit from leveling, if you want extra skill training past level 1, you spend feats on it, raise the ability score, or get gear that improves your check. In 4e everyone gets a feat every other level, and so feats are much more spendable commodity, for that reason what feats do has been more normalized and is not at the same level as many 3.x feats.

RTGoodman
2011-02-11, 11:25 AM
Oh, well that kind of sucks.

Not if you want to play a straight Fighter, for instance, instead of some crazy amalgamation of Fighter/Barbarian/Rogue/PrC1/PrC2/PrC3/Whatever.

Multi-classing in 4E is all about taking your normal "job" (i.e., class) and adding a few tricks from another class. So you're a Fighter who picked up a few things from a Ranger or whatever. If you want to be a true combination, that's what Paragon Multiclassing and, to a greater extent, Hybrid characters are for.

Kansaschaser
2011-02-11, 11:31 AM
Not if you want to play a straight Fighter, for instance, instead of some crazy amalgamation of Fighter/Barbarian/Rogue/PrC1/PrC2/PrC3/Whatever.

Speaking of Prestige classes, my origianl question was going to be the number of combinations if you also added in prestige classes. But, I guess that number would be way too high to calculate.

Do they even have Prestige Classes in 4th edition?

Sillycomic
2011-02-11, 11:33 AM
I just don't think it makes any sense.

At least with the whopper, you can make it different ways and it will still be delicious. A whopper with extra pickles and no onions is still good and someone will eat it. A whopper with no mustard is still good.

A rogue 3, Monk 5, Paladin 2, Wizard 3, Ranger 4, Bard 2, Druid 1 is not a good character, and I doubt anyone would ever play it (order it off the menu)

Aside from that, you are forgetting important things that make characters unique, such as skills and feats.

2 level 20 fighters can be very different characters if they pick different feats.

Likewise any other character with feats, skills, spells, familiars/companions are very different characters from each other.

How does that work? A whopper with no tomato is different than this other whopper with no tomato?

Also, just because you built it doesn't mean your GM will let you play it... such as the monk who decides to become a barbarian and then feels as if he should be a monk again.

So, if you can't build it, it shouldn't be part of the equation which means there's a hidden parameter within the equation that says some combinations are just not allowed.

I suppose that would be like ordering a whopper with no cheese... oh and have the meat be on the outside of the bun. Is that considered a different whopper than the one with no cheese and the meat inside the bun?

RTGoodman
2011-02-11, 11:41 AM
Do they even have Prestige Classes in 4th edition?

Under a different name, yes. They're called Paragon Paths. Everyone chooses one at 10th or 11th level (I don't remember which) and it basically gives you extra class features and powers. Some require you to be from a specific base class, some are race-specific, and so on.

At Epic tier you also gain an Epic Destiny, which is like a second, even better PrC. These are things like Demigod, Legendary King, etc.

Kansaschaser
2011-02-11, 11:46 AM
I just don't think it makes any sense.

A rogue 3, Monk 5, Paladin 2, Wizard 3, Ranger 4, Bard 2, Druid 1 is not a good character, and I doubt anyone would ever play it (order it off the menu)

Aside from that, you are forgetting important things that make characters unique, such as skills and feats.

2 level 20 fighters can be very different characters if they pick different feats.

Likewise any other character with feats, skills, spells, familiars/companions are very different characters from each other.

If I sat down, I could make a decent Rogue 3 / Monk 5 / Paladin 2 / Wizard 3 / Ranger 4 / Bard 2 / Druid 1. It wouldn't be the best character in the world, but it would be unique and different.

The Feats, Skills, Abilities, Magic Items, Spells, Companions, and Familiars just add more dimensions to the equation. Asking someone to calculate the many different class combinations along with everything else is like asking how many different songs you can play with the 81 keys on a piano. It's practically infinite.

I just wanted to make a geeky T-shirt that shows the many different possible combinations available for D&D 3.X.


Under a different name, yes. They're called Paragon Paths. Everyone chooses one at 10th or 11th level (I don't remember which) and it basically gives you extra class features and powers. Some require you to be from a specific base class, some are race-specific, and so on.

At Epic tier you also gain an Epic Destiny, which is like a second, even better PrC. These are things like Demigod, Legendary King, etc.

So is there a limit to how many times you can multi-class and prestige class in 4th edition?

Amnestic
2011-02-11, 11:50 AM
So is there a limit to how many times you can multi-class and prestige class in 4th edition?

You sound almost shocked by this. It's hardly a new concept for D&D. :smalltongue:

Kansaschaser
2011-02-11, 11:51 AM
You sound almost shocked by this. It's hardly a new concept for D&D. :smalltongue:

I am kind of shocked. It seems less.... flexible.

Amnestic
2011-02-11, 11:57 AM
I am kind of shocked. It seems less.... flexible.

Less flexible doesn't necessarily mean it's bad. There's a beauty to simplicity too.

Part of me still thinks D&D should have the 2nd Edition version of multiclassing, where all your classes would progress at the same time, though dual-classing was pretty archaic and is best left behind I think.

CarpeGuitarrem
2011-02-11, 11:59 AM
I am kind of shocked. It seems less.... flexible.
3.5 veritably exploded flexibility out the window. More than anything, 4E reigns it in to a far more controllable (and less insane) level.

Sillycomic
2011-02-11, 12:01 PM
If I sat down, I could make a decent Rogue 3 / Monk 5 / Paladin 2 / Wizard 3 / Ranger 4 / Bard 2 / Druid 1. It wouldn't be the best character in the world, but it would be unique and different.

I would like to see that build. Please, go for it. I'll give you a 30 point buy and standard 20th WBL. Prove to me it will be useful at all in a group and will be able to toe the line against standard cr 20 creatures.

Besides, I never said it wasn't possible, I just said it wasn't good and no one would play it. Again, that goes to my point that just because it can be built doesn't mean someone will build it.

You have to narrow down your equation substantially (no skills, feats, prestige classes) just to get some arbitrary number that you know is wrong because you want to put a number on a t shirt?

Seriously? Just pick a number out of thin air, it will be about as useful as what you are asking for now.

There are 2,678,422 ways to built a character in D&D. There you go!

RTGoodman
2011-02-11, 12:05 PM
It's not really less flexible at all if you look at the system as a whole.

You only get one base class. So what? At first level, you get not only a race, class (and class variant/"build" for most classes), feat, skills, and weapons/equipment, but also two at-will powers (out of over a dozen for many classes), an encounter power (out of an equally big number), and a daily power (out of a handful of choices). And at EVERY SINGLE LEVEL AFTER THAT, I think, you get a choice about a new power and/or feat, or what two ability scores to increase, or whatever.

So yes, it's less flexible as far as choosing a class, but infinitely more flexible WITHIN your character build.

Kurald Galain
2011-02-11, 12:14 PM
I just wanted to make a geeky T-shirt that shows the many different possible combinations available for D&D 3.X.

The exact answer is 578759875248819037845093457345872438409238749475.

randomhero00
2011-02-11, 12:21 PM
For 41 base classes I get 41 ! = 3.34525266 10^49
for 66 I get
66 ! = 5.44344939 10^92

How are you guys doing the math? Isn't that the right way?

Kansaschaser
2011-02-11, 12:22 PM
So yes, it's less flexible as far as choosing a class, but infinitely more flexible WITHIN your character build.

Well, 3.X was already as flexible within each class. As pointed out earlier, no two level 20 fighters are the same.

I'm not saying 4th edition is bad or anything, I think it sounds pretty good. Playing the same class all the way to 30th level seems a little strange for some people, unless you play games like World of Warcraft (which I do). So being stuck with the same class isn't such a strange idea. You can specialize your class with certain abilities and equipment.

If you play a 4th edition character from level 1 to level 30, how many times can you "multi-class" and how many times can you "prestige"? Then factor in the number of base classes. That's the number I want to know for 4th edition. I don't care about feats, skills, spells, etc... That's way too many combinations.

Kurald Galain
2011-02-11, 12:23 PM
How are you guys doing the math? Isn't that the right way?

No, 41! is the number of different ways you can order 41 items. What you're looking for is (amount of levels) to the power of (amount of classes).

Amnestic
2011-02-11, 12:26 PM
If you play a 4th edition character from level 1 to level 30, how many times can you "multi-class" and how many times can you "prestige"? Then factor in the number of base classes. That's the number I want to know for 4th edition. I don't care about feats, skills, spells, etc... That's way too many combinations.

As far as I know, all classes can only take a single multiclass feat - the one exception to this rule being Bards, who can take as many as they like (Someone correct me if I'm mistaken on this, but I think that's correct.)

At Level 10 or 11, you enter a Paragon Path, which grants some new abilities and could arguably be called a "Prestige Class", then at 20 or 21 you enter your Epic Destiny, which is arguably "Prestige Class Mk.2"

So two 'Prestige Classes' in total (if you want to use that terminology. It's not quite accurate though), and one multiclass feat, with the exception of Bards who get two 'Prestige Classes' and as many multiclass feats as they want to spend.

Kurald Galain
2011-02-11, 12:27 PM
If you play a 4th edition character from level 1 to level 30, how many times can you "multi-class" and how many times can you "prestige"?
One multiclass (more if you're a bard), one paragon path, one epic destiny. There are tons and tons of paragon paths, in particular. Ironically, however, the way your class appears in-game is determined primarily by what powers you pick, not by your PP or ED.

BlckDv
2011-02-11, 12:28 PM
No, 41! is the number of different ways you can order 41 items. What you're looking for is (amount of levels) to the power of (amount of classes).

Shouldn't it be (# of Classes)^(Level) not (Level)^(# of Classes)?

At Level 1, you'd have 41 choices with 41 classes...

41^1= 41

1^41= 1

Kurald Galain
2011-02-11, 12:39 PM
Shouldn't it be (# of Classes)^(Level) not (Level)^(# of Classes)?
Oops. Yes, that's what I meant.

Jaidu
2011-02-11, 12:39 PM
In 4e, by my count, there are 324 possible class combinations, not including paragon paths and epic destinies. Not nearly as many as 3.x mostly due to the differences in multiclassing. If multiclass options, paragon paths, and epic destinies are taken into consideration, this would go up a ton, but would still be a lot lower than 3.x.

25 non-essentials classes
11 essentials classes
288 possible hybrid combinations

Sillycomic
2011-02-11, 12:39 PM
Something else I didn't even consider.

What about races?

Different races of the same class would be different characters.

How many base races are there? We considering Core for this concept? So... does that mean anything in the Monster Manual with LA is a playable character?

Kurald Galain
2011-02-11, 12:42 PM
What about races?

Different races of the same class would be different characters.
That may depend on whether the race makes a noticeable difference in play; some races don't.

Please don't tell me you want to count all the 9001 different elf variants as different "races" :smallbiggrin:

dextercorvia
2011-02-11, 12:45 PM
Shouldn't it be (# of Classes)^(Level) not (Level)^(# of Classes)?

At Level 1, you'd have 41 choices with 41 classes...

41^1= 41

1^41= 1

This is correct. So I get either

41^20=1.801677829564209295030298460648e+32

or

66^20=2.4596805720250036121275867055794e+36

if you remove all multiclass restrictions.

Kansaschaser
2011-02-11, 12:45 PM
Something else I didn't even consider.

What about races?

Different races of the same class would be different characters.

How many base races are there? We considering Core for this concept? So... does that mean anything in the Monster Manual with LA is a playable character?

That's a gigantic number. I was thinking just classes themselves, not races. Then you would have to take the answers given before and multiply them by the number of playable races.

That would be a Googleplex of combinations.

Sillycomic
2011-02-11, 12:52 PM
Google sounds about right.

There are a google number of characters to play in D&D. *

Oh, and it fits nicely on a t shirt.

Just be careful not to get sued.



*This does not include races, feat selection, skill selection, spell selection, animal companion selection, familiar selection, variants, substitution levels or templates. The actual number is much higher but I wanted to wear a t shirt with a lower number on it...

NichG
2011-02-11, 12:54 PM
The best way to understand numbers like this is to only bother with the logarithm of the numbers.

Lets say you have three independent degrees of freedom (I know they're actually not independent, but for sake of example) that you can control to design your character: Feats from levels, Classes/Templates, and Race/0 LA templates

If you figure out the combinatorics of each of them, lets say the number of combinations is something like 10^16 (100 feats, allocated into 8 feat slots), 10^60, and 10^3 (say 50 races and 20 0LA templates)

The entropy associated with feat selection is then roughly 48 bits (2^48 ~= 10^16), with classes is roughly 180 bits, and with race and templates is roughly 9 bits.

So such a D&D character could be described by a 237 bit data block, and there are 2^237 possible characters of this sort.

Of course, then you'd want to add on the 6 stats, which are each about 4 bits worth of information, so thats another 24 bits, and so on and so on...

Kansaschaser
2011-02-11, 01:01 PM
The best way to understand numbers like this is to only bother with the logarithm of the numbers.

Lets say you have three independent degrees of freedom (I know they're actually not independent, but for sake of example) that you can control to design your character: Feats from levels, Classes/Templates, and Race/0 LA templates

If you figure out the combinatorics of each of them, lets say the number of combinations is something like 10^16 (100 feats, allocated into 8 feat slots), 10^60, and 10^3 (say 50 races and 20 0LA templates)

The entropy associated with feat selection is then roughly 48 bits (2^48 ~= 10^16), with classes is roughly 180 bits, and with race and templates is roughly 9 bits.

So such a D&D character could be described by a 237 bit data block, and there are 2^237 possible characters of this sort.

Of course, then you'd want to add on the 6 stats, which are each about 4 bits worth of information, so thats another 24 bits, and so on and so on...

So, would you agree that there are more D&D character combinations than the number of humans that have ever lived on the planet?

dextercorvia
2011-02-11, 01:06 PM
It isn't Google (http://en.wikipedia.org/wiki/Googol).

Knaight
2011-02-11, 01:12 PM
So, would you agree that there are more D&D character combinations than the number of humans that have ever lived on the planet?

Every seriously quoted number on this thread states that there are orders of magnitude more D&D build combinations than the number of humans that have ever lived on the planet. If you look at the math behind the total possibilities inherent in a system, you can see that getting beyond easily understood numbers is to be expected in all but the simplest. Burger Kings' 221,184 ways to order a Whoper isn't even impressive.

Kansaschaser
2011-02-11, 01:16 PM
Every seriously quoted number on this thread states that there are orders of magnitude more D&D build combinations than the number of humans that have ever lived on the planet. If you look at the math behind the total possibilities inherent in a system, you can see that getting beyond easily understood numbers is to be expected in all but the simplest. Burger Kings' 221,184 ways to order a Whoper isn't even impressive.

Yeah, I thought it would be in the millions, maybe even the billions. But the playgrounders have made me realize that, once again, I was waaaaaaaay wrong. :smalleek:

If the number for the possible combinations didn't reach a million, then I was going to ask to add in prestige classes. You can forget that request now!

Eldan
2011-02-11, 01:19 PM
This is correct. So I get either

41^20=1.801677829564209295030298460648e+32

or

66^20=2.4596805720250036121275867055794e+36

if you remove all multiclass restrictions.

That isn't entirely correct either. What you want is (n+k-1)!/(k!(n-1)!), which is Combination with Repetition (or at least it's called that in German). n is the number of classes, k is number of levels.

Kansaschaser
2011-02-11, 01:27 PM
In 4e, by my count, there are 324 possible class combinations, not including paragon paths and epic destinies. Not nearly as many as 3.x mostly due to the differences in multiclassing. If multiclass options, paragon paths, and epic destinies are taken into consideration, this would go up a ton, but would still be a lot lower than 3.x.

25 non-essentials classes
11 essentials classes
288 possible hybrid combinations

Would this translate into 25,660,800 possible combinations?

324 x 25 x 11 x 288 = 25,660,800

Or did I misunderstand how building a 4th edition character works again? I probably did. Please don't kill me. :smalleek:

Eldan
2011-02-11, 01:28 PM
In 4E, you have one class and you stay that class. Done, if you don't go into feats.

NichG
2011-02-11, 01:28 PM
So, would you agree that there are more D&D character combinations than the number of humans that have ever lived on the planet?

Once the word 'combination' shows up, its usually a fair bet that there are more of whatever the subject of discussion is than atoms in the universe :smallsmile:

Eldan
2011-02-11, 01:30 PM
Wasn't there something like 10^49 atoms, or am I misremembering?

dextercorvia
2011-02-11, 01:42 PM
That isn't entirely correct either. What you want is (n+k-1)!/(k!(n-1)!), which is Combination with Repetition (or at least it's called that in German). n is the number of classes, k is number of levels.

Try it. If there are 3 base classes (A,B, and C) to choose from and only 2 levels, then it is easy to list them

AA
AB
AC
BA
BB
BC
CA
CB
CC

That is nine possiblities which is 3^2.

Your formula yields 4!/(2!*(3-1)!)=6.

Eldan
2011-02-11, 01:43 PM
Partially true. However, by normal D&D rules, CA is the same as AC.

dextercorvia
2011-02-11, 01:45 PM
Partially true. However, by normal D&D rules, CA is the same as AC.

Not when you consider things like skill points, hit points, IL for selecting Maneuvers...

Edited for comprehensiveness. There is probably more.

Mystic Muse
2011-02-11, 01:46 PM
For 4th edition: No clue. What is there for 4th edition other than official material? Has anyone made 3rd party 4th edition material?

I have a 3rd party book for it called "Scythe and shroud"

Amnestic
2011-02-11, 02:17 PM
For 4th edition: No clue. What is there for 4th edition other than official material? Has anyone made 3rd party 4th edition material?

There is some 4e 3rd party material. Campaign settings, a bunch of races, monsters, gear...

I've not actually checked any of it out, but it is out there, and it's not just a few pieces either. I doubt there's as much as 3.X, but then, 3.X has had a lot longer to have material made for it (~7 years vs. 2-3).

Also, wow, has it been that long since 4th was released? Years pass surprisingly quickly.

Squark
2011-02-11, 02:30 PM
One multiclass (more if you're a bard), one paragon path, one epic destiny. There are tons and tons of paragon paths, in particular. Ironically, however, the way your class appears in-game is determined primarily by what powers you pick, not by your PP or ED.

Unless I'm mistaken, Half-Elves do also have some degree of flexibility in that regard, but I don't have my PHB II with me at the moment. 4e Does have a fair amount of flexibility, but, since It's designed to be player friendly, things like multiclassing where toned down and hybrid classes only appeared in the PHB III



Also, I actually liked Dual Classing in 2e, at least the way the Baldur's Gate games did it (At any point after they reach level 2, a human character of most classes (Bards, Rangers, and Paladins can't) can choose to start over at level 1, loosing all their original classes abilities (keeping their HP, though, I think). Once their level in the new class exceeds their old level, they can begin using their old class again.


Of course, in vanilla 2e, you could only use your old class's abilities if you wanted to take a horendous penalty to your XP, I believe.

Kansaschaser
2011-02-11, 02:35 PM
Unless I'm mistaken, Half-Elves do also have some degree of flexibility in that regard, but I don't have my PHB II with me at the moment. 4e Does have a fair amount of flexibility, but, since It's designed to be player friendly, things like multiclassing where toned down and hybrid classes only appeared in the PHB III



Also, I actually liked Dual Classing in 2e, at least the way the Baldur's Gate games did it (At any point after they reach level 2, a human character of most classes (Bards, Rangers, and Paladins can't) can choose to start over at level 1, loosing all their original classes abilities (keeping their HP, though, I think). Once their level in the new class exceeds their old level, they can begin using their old class again.


Of course, in vanilla 2e, you could only use your old class's abilities if you wanted to take a horendous penalty to your XP, I believe.

And, unless you played a human, there was a maximum level you could obtain by playing other race/class combinations. Humans could be unlimited in any class and Half-Elfs could be unlimited for Bards. Other than that, most other races were limited to level 9-17 in most classes, if they could even be of a certain class.

Squark
2011-02-11, 02:43 PM
Yet another thing Baldur's Gate was improved by excluding, frankly.

Kurald Galain
2011-02-11, 03:00 PM
Unless I'm mistaken, Half-Elves do also have some degree of flexibility in that regard, but I don't have my PHB II with me at the moment.
That's PHB1. Yes, half-elves can get an at-will power from another class, which they can use 1/encounter. This is not generally very impressive, except with specific combos or paragon feats.


Of course, in vanilla 2e, you could only use your old class's abilities if you wanted to take a horendous penalty to your XP, I believe.Yes, as long as your new class was lower-level.


And, unless you played a human, there was a maximum level you could obtain by playing other race/class combinations.
Yes, but I've never been in a campaign where that was at all relevant. Either the campaign never made it that high, or the DM handwaved that particular arbitrary limit.

Sillycomic
2011-02-11, 03:50 PM
Try it. If there are 3 base classes (A,B, and C) to choose from and only 2 levels, then it is easy to list them

AA
AB
AC
BA
BB
BC
CA
CB
CC

That is nine possiblities which is 3^2.

Your formula yields 4!/(2!*(3-1)!)=6.

Isn't that true though? There are only 6.

AA, AB, AC, BB, BC, CC.

We can't count CB as a separate class combination from BC, can we? A rogue that takes a level in fighter is a different character than a fighter that takes a level in rogue?

If feat and skill selection isn't important, then it doesn't matter if the fighter or the rogue class come first, only that the combination of rogue/fighter is listed in the equation.

That would be like saying a whopper with pickles on top of the onions is different than a whopper with onions on top of the pickles.

Kansaschaser
2011-02-11, 04:02 PM
Isn't that true though? There are only 6.

AA, AB, AC, BB, BC, CC.

We can't count CB as a separate class combination from BC, can we? A rogue that takes a level in fighter is a different character than a fighter that takes a level in rogue?

If feat and skill selection isn't important, then it doesn't matter if the fighter or the rogue class come first, only that the combination of rogue/fighter is listed in the equation.

That would be like saying a whopper with pickles on top of the onions is different than a whopper with onions on top of the pickles.

It only really matters at first level, when you receive maximum hit points and x4 skill points.

In your example, you used Fighter 1 / Rogue 1. Lets say you have an Intelligence of 14 and a Constitution of 14.

If you take Rogue at first level, then you receive 40 skill points and you will have 8 hit points. At second level, you would then add Fighter 1. If you take average hit points, then you would have a total of 15. You would also have 44 skill points.

On the flip side, if you take Fighter first, then you would have 16 skill points and 12 hit points. Then at second level when you add the Rogue, you would have 26 skill points and 17 hit points.

1. Rogue 1 then Fighter 1 = 44 skill points and 15 hit points
2. Fighter 1 then Rogue 1 = 26 skill points and 17 hit points

So there is a difference between a Fighter 1 / Rogue 1 and a Rogue 1 / Fighter 1.

Sillycomic
2011-02-11, 04:26 PM
Ahh, but you said skill points don't matter. in fact, I even argued that they did and you said adamantly that they did not. Remember?

So, it shouldn't matter if the first level you get more skill points then the second level.

Unless you are factoring in that the first level does indeed count. That's fine. It just makes your math problem infinitely more complicated, but considering I'm not the one doing the math I don't mind at all.

Does the order matter at the second and all other levels? Does the order matter at important levels, like say when you get your ability increases or feats?

If it's important when you get those bonus skills, I don't see why it isn't important when you get these bonus feats. A dip in fighter when you get a bonus feat means two feats, much different then if you take a dip in rogue at that time.

So, the order doesn't matter for all levels above first?

Let's say the first level is rogue. Then the second level is fighter and the third level is wizard.

Is that the same as a rogue with a second level in wizard and a third level in fighter?



We never even discussed Hit points. Do they matter when calculating this thing out? Because some races (dwarves) give a bonus to Con. So any character combination that happens to be a dwarf will automatically have an extra hit point than those that don't. Do we count those as well?

A level 1 fighter with 14 con gets 12 hitpoints.

A level 1 dwarf fighter with 16 con gets 13 hitpoints.

A level 1 dwarf fighter with toughness and 16 con gets 16hitpoints.

Are these three different character combinations... not because of race or feat selection, but because the resounding hit points are different?


You said Races don't count, but if different Hit Points are now a factor in your equation it seems like they should. I don't know. I'm just going on what you're giving me.

Kansaschaser
2011-02-11, 04:33 PM
Ahh, but you said skill points don't matter. in fact, I even argued that they did and you said adamantly that they did not. Remember?

So, it shouldn't matter if the first level you get more skill points then the second level.

Unless you are factoring in that the first level does indeed count. That's fine. It just makes your math problem infinitely more complicated, but considering I'm not the one doing the math I don't mind at all.

Does the order matter at the second and all other levels? Does the order matter at important levels, like say when you get your ability increases or feats?

If it's important when you get those bonus skills, I don't see why it isn't important when you get these bonus feats. A dip in fighter when you get a bonus feat means two feats, much different then if you take a dip in rogue at that time.

So, the order doesn't matter for all levels above first?

Let's say the first level is rogue. Then the second level is fighter and the third level is wizard.

Is that the same as a rogue with a second level in wizard and a third level in fighter?



We never even discussed Hit points. Do they matter when calculating this thing out? Because some races (dwarves) give a bonus to Con. So any character combination that happens to be a dwarf will automatically have an extra hit point than those that don't. Do we count those as well?

A level 1 fighter with 14 con gets 12 hitpoints.

A level 1 dwarf fighter with 16 con gets 13 hitpoints.

A level 1 dwarf fighter with toughness and 16 con gets 16hitpoints.

Are these three different character combinations... not because of race or feat selection, but because the resounding hit points are different?


You said Races don't count, but if different Hit Points are now a factor in your equation it seems like they should. I don't know. I'm just going on what you're giving me.

Heh, I wasn't counting hit points, skill points, feats, and such into the level builds. But lets just agree that a Fighter 1 / Rogue 1 is still different than building a Rogue 1 / Fighter 1. The order the classes are gained will have an impact on the final level 20 character, so they are considered different.

Just like when I go to Subway, I prefer my toppings to go on in a specific order. They always seem to add them in just the opposite order that I want. I want my mayonase next to the bread and lettuce and they squirt it on the meat and cheese. Yuck.

Sillycomic
2011-02-11, 04:55 PM
Well, these things are important for a mathematician to help you figure out your number.

And yes, at this point you need someone with a degree who deals with logic and numbers for a living to help you.

I just gave you three different fighter character.... basically I just showed you three different sandwiches with different amounts of mayo on them. And you told me they were all the same.

Yet one sandwich with mayo next to the bread is different than a sandwich with mayo next to the meat?

All right then, if that's your opinion.

Like I said, it's your equation, you can make up whatever you want. What goes into it, what doesn't, what counts as a different character, what is the same.

Just so long as you understand the total number (whatever it is you get) is wrong, and will in no way reflect the actual number of ways to make a character in D&D, I don't mind at all.

Squark
2011-02-11, 05:30 PM
That's PHB1. Yes, half-elves can get an at-will power from another class, which they can use 1/encounter. This is not generally very impressive, except with specific combos or paragon feats.

I wasn't talking about that. In the lieu of a racial paragon path, Half-elves can choose to take the Versatile Master Paragon-Tier Feat, which lets them use the aforementioned power at will, and, if they choose to paragomn multiclass (not a good idea, IMHO), they can choose their powers from any class, and they can spend an action point to regain an encounter attack power they've used.

Personally, I despise Paragon Multiclassing (You lose out on the cool abilities from a paragon path). You're better off choosing a path from your second class's paragon path.

Jayabalard
2011-02-11, 05:38 PM
If your 41 base class count is right, and you allow the selection of any class at each level (ignoring RAW limits such as once you leave class x you cannot go back), you could make 180,167,782,956,420,929,503,029,846,064,800 unique class/level combinations for a level 20 PC. If you count PCs of lower than level 20 as separate from the level 20 builds which include their progression, it gets a lot bigger.it's actually about 1.025 * the number you came up with... not really that much more (at least, in context)
Since the powers are kind of big, I went with something that could be done on paper. So, all of the lower level builds added together would be
411 + 412 + 413 + ... + 4118 + 4119 + 4120
= 4120 + 4119 + 4118 + ... + 413 + 412 + 411
= (1/410) *4120 + (1/411) * 4120 + (1/412) * 4120 + ... + (1/4118) * 4120 + (1/4119) * 4120
= [(1/410) + (1/411) + (1/412) ... + (1/4118) (1/4119) ] * 4120

=(sum (1/(41i)) where 0<=i<20) * 4120

We can estimate this using the infinite sum; it won't be exact but it's pretty close.
(sum (1/(41i)) where 0<=i<20) < (sum (1/(41i)) where 0<=i )

(sum (1/(41i)) where 0<=i ) = 1 / (1 - (1 / 41)) ~= 1.02500

so the answer is just slightly less than 1.02500 * 4120

Haarkla
2011-02-12, 06:15 PM
Unless you are factoring in that the first level does indeed count. That's fine. It just makes your math problem infinitely more complicated, but considering I'm not the one doing the math I don't mind at all.

Actually, factoring in that the first level just makes the equation:

n(n+k-2)!/((k-1)!(n-1)!)

instead of (n+k-1)!/(k!(n-1)!).
n is the number of classes, k is number of levels.

Knaight
2011-02-12, 06:34 PM
If the number for the possible combinations didn't reach a million, then I was going to ask to add in prestige classes. You can forget that request now!

If the term combination show's up when looking at anything in the real world, its likely to hit a million. Which is why Burger King's 221,184 is a joke. Even staying within food, one can reach more. For instance:

I'm making an omelet. I have 2 dozen eggs, of which I will choose 4 (locally grown eggs tend to vary a bit), due to being a hungry teenager. That's 24*23*22*21 combination right there. There are 3 types of cheese that might see use (white cheddar, orange cheddar, parmesan), each of which is going to have either 0 cups 1/4 cup, 1/3 cup, 1/2 cup, 3/4 cup, or 1 cup, depending on taste. That's another 6*6*6. Without even considering vegetables, there are a good 55 million combinations. Without considering the cheese at all, there are still over 250 thousand combinations.

Inyssius Tor
2011-02-12, 08:05 PM
If the term combination show's up when looking at anything in the real world, its likely to hit a million. Which is why Burger King's 221,184 is a joke. Even staying within food, one can reach more. For instance:

I'm making an omelet. I have 2 dozen eggs, of which I will choose 4 (locally grown eggs tend to vary a bit), due to being a hungry teenager. That's 24*23*22*21 combination right there. There are 3 types of cheese that might see use (white cheddar, orange cheddar, parmesan), each of which is going to have either 0 cups 1/4 cup, 1/3 cup, 1/2 cup, 3/4 cup, or 1 cup, depending on taste. That's another 6*6*6. Without even considering vegetables, there are a good 55 million combinations. Without considering the cheese at all, there are still over 250 thousand combinations.

Have you ever tried asking a Burger King employee to add one-third of the normal amount of cheese to your Whopper?

Jayabalard
2011-02-14, 09:28 AM
Actually, factoring in that the first level just makes the equation:

n(n+k-2)!/((k-1)!(n-1)!)

instead of (n+k-1)!/(k!(n-1)!).
n is the number of classes, k is number of levels.There's no reason to have factorial; the only reason to use that is if you can't repick items from the list (it's how you represent the list of options shrinking as choices are made).

This isn't an issue, since you can still pick any of the n base classes at each level... So at first level you have n choices; at second level you have n choices again for a total n2 + n possibilities; at third level you have n choices again for a total n3 + n2 + n possibilities; etc. No factorial, just a straight up geometric series.

so it's just the sum (ni) where i = 1 to k, n = the number of classes and k = the number of levels. I don't know of a general form for that (I know there's one for an infinite sum, as long as you're talking values where |x| < 1, so I used that above in my estimate)

Douglas
2011-02-14, 09:36 AM
There's no reason to have factorial; the only reason to use that is if you can't repick items from the list (it's how you represent the list of options shrinking as choices are made).

This isn't an issue, since you can still pick any of the n base classes at each level... So at first level you have n choices; at second level you have n choices again for a total n2 + n possibilities; at third level you have n choices again for a total n3 + n2 + n possibilities; etc. No factorial, just a straight up geometric series.

so it's just the sum (ni) where i = 1 to k, n = the number of classes and k = the number of levels. I don't know of a general form for that (I know there's one for an infinite sum, as long as you're talking values where |x| < 1, so I used that above in my estimate)
Ah, but if you're ignoring feats and skills, the order of levels doesn't matter and that substantially reduces the total. ABC is the same as ACB, which your formula does not account for. That is the detail that the factorials are necessary for, and Haarkla's formula is correct for the case where order matters only for which class is taken at level 1.

Lord Raziere
2011-02-14, 09:53 AM
In 4E, you have one class and you stay that class. Done, if you don't go into feats.

there is also hybrid classing.

pick two classes, cut them in half at character creation put em together voila you play two classes.

Kansaschaser
2011-02-14, 11:05 AM
there is also hybrid classing.

pick two classes, cut them in half at character creation put em together voila you play two classes.

I think someone figured out the total combinations for 4th edition to be around 25,000,000.

Sillycomic
2011-02-14, 01:51 PM
There's no reason to have factorial; the only reason to use that is if you can't repick items from the list (it's how you represent the list of options shrinking as choices are made).

This isn't an issue, since you can still pick any of the n base classes at each level... So at first level you have n choices; at second level you have n choices again for a total n2 + n possibilities; at third level you have n choices again for a total n3 + n2 + n possibilities; etc. No factorial, just a straight up geometric series.


I have to disagree, order should not matter except at the first level. If we're going for an accurate account of the total number of character concepts based only on class combination's, then what does if matter if a 19 monk/1 wizard took that 1 level of wizard at 8th or 18th level?

Those are not two different character combination's. You end up with a 19 monk/1 wizard at 20th level either way.

First level is important because it gives you nice things that the other levels don't. But if you take away feats and Ability score increases, none of the other levels are distinguishable from each other. Level 2 or 4 or 8 or 12 or 16 are all the same.

dextercorvia
2011-02-14, 02:24 PM
Initiator Level cares. My martial character cares whether it gets Pounce at 2nd or 20th level as well.

Beguiler1/Factotum1/Beguiler+18 ends up with vastly different skill layout than Beguiler19/Factotum1.

cfalcon
2011-02-14, 02:50 PM
Not if you want to play a straight Fighter, for instance, instead of some crazy amalgamation of Fighter/Barbarian/Rogue/PrC1/PrC2/PrC3/Whatever.

The inability to play straight fighter is a balance problem in 3.x, and one that most groups handle at their table. Whether fighter is too weak or the other stuff is too strong is up for debate, of course. But it's not an inherent problem in 3.x unless your DM doesn't know how to houserule stuff like that.

I'm not impressed with 4ed's non-support for multiclassing, but w/e. I'm more disappointed by the use of the term- 4ed seems to want to use the older game's terms as homage or something, but it steps on you if you want to implement the ability for real.

Sillycomic
2011-02-14, 02:52 PM
Beguiler1/Factotum1/Beguiler+18 ends up with vastly different skill layout than Beguiler19/Factotum1.


Those are 2 different sets of class levels. So, I would agree with you in saying they would count as different characters.

It's already been said that skill selection and feat layout, while important and can make even the same classes (fighter, rogue) completely different as far as play style and character, aren't factored into this.

Your martial character may care when it gets pounce, but this thought exercise does not.