ljw1004 said:*Sigh*. Let's try again. There are three options, as you say. The first asks: are you good or evil. The second asks: are you red or green. The third asks: do you help Irenicus or hinder him.
Now consider the end scene. How many variants are there? Eight:
(1) a good red hero helps Irenicus
(2) a good green hero helps Irenicus
(3) an evil red hero helps Irenicus
(4) an evil green hero helps Irenicus
(5) a good red hero hinders Irenicus
(6) a good green hero hinders Irenicus
(7) an evil red hero hinders Irenicus
(8) an evil green hero hinders Irenicus.
I.e. there are 2^3 variants of the end-scene. An exponential.
Let me explain to you a mathematical concept called independence. There are often cases where good or evil has nothing to do with red or green. Being red or green may not even affect dialogue in the slightest, and may just affect how a player performs a quest, or how fast the player is, or some other physical thing. So, you often don't have to write the red/good, red/evil, green/good, and green/evil dialogues. In fact, you can present the same gosh darned dialogue to the player and add a couple of conditions if that dialogue doesn't require a judgement on the player's color type or even his stance on morality.
Now, in a real game example, say you have thief, fighter, and priest classes. They can be either good or evil. A person wants you to recover a trinket from an evil wizard. You certainly wouldn't need 2^class + 2^alignment choices here. The quest giver probably wouldn't give a rat's ass what skills you used to get that trinket, only that you got it. Depending on the alignment of the quest giver, he may or may not give a rat's ass how the hell you do it, either. The player's responses might be governed by the good or evil alignment of the player, though. Therefore, that is probably where you need to do a little more work.
When you get to the wizard, the wizard might try to bribe you. If you're going to kill him, then he'll probably try to bribe you regardless of your class or alignment. If you're a thief, he probably won't see you since you rely on stealth. If you're good and pacifistic, you may want to bribe HIM for the trinket.
None of that is exponential, because it's a case by case basis and many of those events won't matter in relation to one another. You can't justify this taking 2^class * 2^alignment, since those typically wouldn't involve more than an extra tree or maybe putting a back way in that a thief can do without ever seeing the wizard, and so forth. You've gone from what you've been saying would require 32 design features to a few conditional statements in the main set of dialogue on that quest and responses in addition to adding a locked backdoor with some traps.
After all, you don't have to write two sets of dialogue for good versus evil, just a few different branches of that tree. Adding the backroom door is trivial. That's why it's not expontential, because you don't have to write a whole set of features for each thing, they're merely something tacked on to the main thing, getting that trinket.
Except it's not quite like that, because the red-green encounter actually has variants itself (where a good hero chooses red, a good hero chooses green, an evil hero chooses red, an evil hero chooses green). That makes us have to do a sum of exponentials. But the result is still an exponential. So let's just say 2^n.
Which would end up being linear independence, which a good chunk of everything you're talking about either dropping out because they're not involved in a lot of dialogues or map features.
However, as you explained with your example, a major arc change doesn't have to change every single dialog. It need only change one in fifty dialogs, for instance. (although how one can call it "major" if it has such little effect, I don't see). That puts us at roughly 2^(n/50). Which is still an exponential.
Actually, it puts us at just 50 + fractional extra choice, since for one out of fifty dialogue groups, you have to write an extra choice. Huzzah!
PS. Yes, exponential increases are part of complexity theory, which was part of my course at university. I went on to teach it to undergraduates. The exponentiality of story arcs is a standard problem to set. I do know what I'm talking about.
Good for you, now let us have a moment of slience for the future.