Min maxing and fractal mechanics

Some people are crazy.

Ok, lots of people are crazy. All of us, in fact. But this is a particular kind of crazy I want to talk about. The min-maxers. The munchkins, the optimizers and power gamers who will spend hours poring over sourcebooks trying to find half a percentage more dodge rating. The kind of person who will spend literally forty minutes taking a turn just so they're sure they've eked out every last scrape of advantage. Randy. Err... someone who's name I've certainly changed to not reflect on the guilty parties. Let me start over.

Last night I spent a couple hours playing Torchlight for the first time. Yeah, I know it's been out for a while, but I just don't play new video games nearly as much anymore. Torchlight is mostly a repackaging of Diablo II. Close enough that, after spending years playing D2 in high school, I was preemptively sick of torchlight. Even so, I was reluctant to put the game down when it came well past time to go to bed. So naturally I fell asleep reflecting on what made Diablo II a good game to begin with. In my mind, one of the most significant factors is the character creation process, together with the vast range of potential equipment. (Even if you do go for the Burrito Dough Cannon every time.) Which brings me to my topic:

What if I design a game that offers min-maxers unparalleled opportunities to manipulate the rules to maximize their character?

Now check your mouth. For most of you, the bile is rising in the back of your throat. That's good news. It means you're (relatively) normal, and that you should hit your "back" button and flee for your life. This way madness lies. If, on the other hand, you're unconsciously salivating, well, this is the place for you.

So what would be the characteristics of such a game? Well, it'd necessarily be single player. Waiting for five other players to take long, complicated actions and then explain them to everyone else sounds perfectly miserable to me. Maybe two player, if you can convince them to do their setup elsewhere, on their own time.

The main thing is, the rules have to be incredibly complicated. Or at least they have to have incredibly complicated implications. Just having the rules pointlessly complicated is frustrating and boring. So Fizzbin wouldn't qualify. No, we want rules that allow for any amount of complexity you're willing to endure, and most importantly we need a buzzword to describe it:

Fractal mechanics

Fractals are... you know what? Let the power of song explain it, if you don't already know. Here; build your own. Draw a triangle. Then make it into a triforce by drawing an upside down triangle in the middle. Continue by drawing upside down triangles in the rightside up triangles until you can't draw anymore; they're too small. You've made a Sierpinski sieve. The point is, it only requires a simple procedure to make, and yet you can make it as complicated as you want. Neat, huh?

So how would you make fractal mechanics? Well, let's define fractal mechanics to have three basic properties:

The main principle of the rules is easy to grasp; like the way you draw the sieve.
The majority of the benefit gained from the mechanic has to be in the first one or two iterations
The more effort you're willing to put into maximizing the mechanic, the more benefit you'll get out of it.

Let's talk about this in the context of a fantasy RPG. In most of these games (I can't think of a counterexample, but one might exist) the relationship between your character's strength and the damage he does swinging his sword is linear. That is, you add +10 strength you get +20 attack power (WoW), or going from ST 10 to ST 12 increases your basic thrust by the same amount that going from ST 12 to ST 14 would (GURPS). Let's say we change that.

If your sword damage went up proportional to the Square Root of your strength, you get some interesting results. Larding on more strength will always increase your damage, regardless. But the more strength you add the less and less it benefits you. Now, if we also allow that the game has items that either increase or decrease your strength, you have the option of using those. The more strength you have, the less the penalty of decreasing it somewhat, particularly if the item has better bonuses to compensate for the normally large minus.

That's three levels of complexity (+str is always good-> +str gets worse and worse -> items that reduce str aren't always as bad as they seem). The fourth level is much more difficult. Suppose you start with a low strength, and use items to push it in the negatives. What happens? Most games would just redefine that as zero strength to make the math easier, but suppose we don't. If you take the square root of a negative number, you get an imaginary amount of damage. What's that mean? Anything we want it to. Let's say it works like elemental damage in normal games; I can attack for 200 damage +50 fire damage. Instead I'm attacking for 100 real damage and 40 imaginary damage. As long as imaginary damage takes away real hit points, we're still in business.

That's a fourth level of complexity; modulating into imaginary damage for whatever benefits that provides you.

So there you go, a fractal mechanic. Four isn't infinity, but it's close. Is it possible to do better? I'm sure it is, I'm coming up with an example on the fly here. Let's broaden our horizons a bit, to see what that'd accomplish.

Imagine a game where every single one of your stats worked like that; a simple relationship that encompassed hidden depths of complexity. Imagine that every item and modifier you got changes one or more of your stats, or offers other benefits. Imagine doing all that arithmetic by hand. Yeah, I'm thinking this will necessarily have to be a computer game of one sort or another just so you don't have to work things out yourself.

It's an interesting idea. It's only marketable to a certain type of hardcore gamer, and games that require you to be hardcore don't generate fans easily, so I don't see making this as a for profit venture. Maybe as a project, after the Terrible Secret of Space winds up. Actually, I'd better get back to that.