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Okay, so ages ago one of the battle.net posters, DianeE, once posted a thread on the battle.net forums about balance in computer games. Basically, it was a mathematical look at determining whether systems are balanced. I found it extremely interesting, but unfortunately very few other people did, and as DianeE posted only intermittently the thread soon died. However, I'm thinking that perhaps the people here, most of whom should be experienced with and interested in the balance issue, will find the idea more interesting than the battle.net posters did.

For those of you who don't understand what I'm getting at when I talk about balancing a game system, here's an example:

Units have a certain amount of attack and defense. The chance of one unit killing another is equal to its attack divided by the enemy unit's defense. Each race has one unit, with stats as stated below.

Race ... Attack ... Defense
Race 1 .... 5 .......... 100
Race 2 .... 2 .......... 250

This particular example would be balanced. However, if the units had the following stats:

Race ... Attack ... Defense
Race 1 .... 6 .......... 125
Race 2 .... 3 .......... 200

Then it would be unbalanced (Race 1 has a stronger unit than race 2).

Anyway, before the thread died, one thing became clear: As the complexity of a system increases, the process of determining whether or not it is balanced quickly approaches impossibility. We found that determining the balance evenof systems that were absurdly simple compared to most computer games could be extremely difficult.

So, I'm thinking that, with that considered, perhaps this thread should take the form not merely of a discussion on balance but also of a sort of implied contest, a contest to find one, who can come up with the most complex system that is still completely balanced, and two, who can determine whether or not a given system is balanced. Remember, mere approximations of balance are not acceptable! Oh, and if anyone wants to set up a mineral prize for a truly organized contest of this type, go ahead (I may even do it myself if I find it worthwhile).

But enough of that. Contest or no contest, what do you think? Have anything to ask about, or better yet, to add to the issue of game balance?

Well, it's an interesting issue but I don't think it will find that much interest because it's too technical. I'll move the topic to... Games, where it might get more exposure, but I'll say something about it too.

Like you said, I think the evaluation system proposed is too simple for anything approaching the complexity of a game like StarCraft.

I am going to guess that, if that system was applied to SC, then the game would appear to be grossly tilted in favour of the Protoss, which we know is not the case. They might look good on paper, in terms of unit stats for attack and defence, but then you have the fact that their units are costly etc.

Also, how would you factor in the ability to cloak and stuff?

I'll have a brief attempt at listing factors that should be considered:

Attack
Defence
Air Attack
Air Defence
Range
Speed
Terrain Ability (Air/Ground)
Cost
Build Time
Power of Spells
Cost of Spells
Cloaking Ability (Innate/Energy-Based/None)

And more...

Balance in games is not black and white due to the sheer number of factors; in a game like Warcraft 3, for example, each race has ~40 upgrades and spells, as well as 16 hero spells, ~15 different units with differently affecting upgrades and costs, all that.

It's also not black in white because even though the strength of the races would be the same, the enthusiasm of the players isn't. If you're playing the team with powerful spells as opposed to powerful normal attack, you'll probably be more enthusiastic because you have the more interesting race - or you may have too many spells that you can't control all units at same time and your units fall to the enemy units.

Some balance incorporates assuming the user has enough skill to properly use something. For example say you have a ranged unit who moves and attacks slowly but deals a lot of damage vs a melee unit who moves and attacks quickly but deals very little damage. The average person might view the ranged unit as being superior but the skill person might be able to say dodge attacks or flank with the melee unit to be more effective.

And that's where the beauty of games come in, IMO. It all depends on the player.

For the mathematical equation, there is no possible way to factor in all of the important numbers to determine a better unit, etc.

Yea, waaaay too many factors. It is indeed possible to list a million ways something may or may not be balanced, but it's really impossible to prove anything with such complex systems. To such an extent that even if all the greatest minds on earth got together to solve it, they couldn't come up with a perfect solution, because of all the unknowns: assumptions and variables that change depending on the situation.

It's like trying to determine a specific x value for 2X+Y=5. Sure, you can make a line out of it and comment on it but you can't determine a single specific value for x with the given data, and there is no more given data; it's simply impossible to get cuz it changes situationally.

I was wondering which forum to post it in myself, and finally decided on Miscellaneous. Maybe I was wrong. Anyway, no harm done, I guess.

You mean my example? Well duh, that was meant to be simple, it's an example. DianeE started her thread off with a very similar example, and then slowly progressed into more complex (but still simple) systems.

Or do you mean the system I used to figure out whether the examples were balanced? Well, remember, all that has to be done is to make sure you're taking every aspect of the system into account. For the sake of keeping it from becoming completely unsolvable, we can assume to begin with that all players play perfectly. That is to say, things like slow reaction time and low multitasking ability are not included (these things vary from player to player and therefore become essentially unknowable).

Keep in mind that this does get very complicated. I suspect that as the systems get more complex, calculus will be required to determine if they are balanced or not. I hope there are some people on here who are good at calculus, because I'm not.

Well, if it is still inaccurate even if we assume perfect play, then obviously there's something the theory wouldn't be taking into account.

Anyway, you should keep in mind that I'm not proposing that this system be applied to StarCraft, at least not at this stage. As we proved in DianeE's thread, StarCraft is absurdly complex in terms of determining its balance, and with standard mathematical tools it could possibly require more work than the human race has ever done in the field of mathematics and may not be possible at all.

Instead, the idea here is to sort of lay a framework for investigation of...let's called it Balance Theory. My guess is that there exist certain mathematical tools and functions which could go a long way towards simplifying Balance Theory, and perhaps bring the evaluation of systems equivelant to most RTS games into the realm of possiblity. But whatever happens, as usual we have to start from the ground up.

Again, we can start by simplifying the idea. For example, you could take a system like the following:

There are two races, each with 1 unit. Each unit has 100 defense and 10 attack. The unit belonging to Race 1 has energy, which for each unit increases by 1 every generation (a generation is the basic quantity of time in any computer simulation, and can be considered to be something like the planck time in our own universe), starting at 0. At any given generation, one of these units can use up 2 of its energy (provided it has at least 2) to make itself invincible (cloaked) for that generation (cloaking does not force it to forgo its +1 energy per generation).

Obviously this system is not balanced to begin with because the races are exactly the same except for one advantage belonging to Race 1. What I want to do here is to find out how much more power Race 2's unit should have for it to be balanced. By 'power', I mean its overall value in the game; for the purposes of combat in real strategy games, this can be estimated by offensive power multiplied by defensive power. For this system, this is sufficient because the only two abilities Race 2's unit has are attack and defense.

Okay, so we can reason that Race 1's unit can remain cloaked for half of the total time it exists (because it uses up energy to cloak at twice the rate at which it gains energy). Therefore it seems that any increase in the power of Race 2's unit by a factor of 2 will balance this system. The resulting stats of Race 2's unit could therefore be 10A/200D, 20A/100D, 4A/500D, etc. But be careful! It's not quite as simple as that. As Race 2's unit passes the 100 attack mark, additional attack becomes absolutely useless, because the unit can already guarantee a one hit kill every time it hits. Therefore in this system all attack values for Race 2's unit past 100 are effectively 100. This means that stats of 99999999A/20D are balanced, so long as the defense of Race 1's unit remains the same.

Well, that was easy enough. Or was it?

Not too fast. Race 1's unit can only be hit half the time, but because it starts at 0 energy, we can assume that it will be cloaked not on random generations (which would result in the above system being balanced) but rather on every even-numbered generation with the generation on which it was built being 1. And this disadvantage, interestingly, suddenly makes a difference between the attack and defense of Race 2; attack has now become more useful for Race 2 than the same factor of defense.

I'm not sure how exactly to solve this part. However, I did think up the idea of considering each set of two generations as one generation. In this case, we have five possibilities:
1. No one dies on either turn
2. Race 1 dies on the first turn
3. Race 2 dies on the first turn
4. Both races die on the first turn
5. Race 2 dies on the second turn
I'm not entirely sure that this is a valid way of considering it, however so far I haven't though up any flaws in it. Unfortunately, when I plug it into OpenOffice, the total probability of all the possiblities adds up to more than 1, even counting in the fact that number 4 doesn't count because it is included in both number 2 and number 3. I may be able to figure out what I did wrong later, but for now I'm sorry to be anticlimactic but I can't come up with a precise number for Race 2's attack.

By the way, I have left out one possible (essentially useless, but still possible) solution which is very simple to come up with. This is to give Race 2 infinity defense and 0 attack, guaranteeing that neither race's unit can ever win, therefore making it balanced. I might as well just say now that we're looking for a solution other than that.

No, you don't quite get it. It is a matter of black and white (in the same sort of sense that 1-(1/infinity) being less than 1 is black and white), it's just that more factors to consider makes it that much harder to determine whether it's black or white.

We're assuming perfect play, because it is impossible to know how skilled the players are just from the game itself. We are also not assuming any particular 'map', in a system that includes landscape.

Except that there is. That's the whole point. Of course most games are absurdly complex for these purposes, but that's why I'm starting at the bottom.

If the situation only includes definite factors inside the game, then it is still theoretically possible. It's only when you include player skill (which is something we aren't doing) that it becomes unknowable.

OK fine-You could theoretically calculate an answer for every possible in-game situation. That means about 9.9x10^99999999999999999 situations, each one with it's own special factors dependant on all sorts of external factors that aren't even a direct measure of skill.

If everyone on earth were to attempt to solve this, it would never be completed. The earth would be burninated by the sun first.

And even then you wouldn't get 1 answer....you would get 9.9x10^99999999999999999 answers.

So for all practical purposes, you can't put game balance such as this into specific quantity.

The nice thing is, sometimes you don't have to do every single possible situation. There are ways of abstracting and condensing the necessary calculations into much simpler equations. This is one of the key points of balance theory.

And in the end, all you are really saying is 'keep things simple and don't be a retard when designing games'. Which is totally cool, that is about all you can do.

I've never found StarCraft or Warcraft imbalanced.

I believe the experts say StarCraft is slightly imbalanced, that if anything the protoss are the weakest and the zerg are the toughest. However it is very difficult to say.

As for WarCraft, well, WarCraft II was horribly imbalanced, and WarCraft III, while better balanced in terms of races alone, was very unbalanced in terms of units and strategies (there's a reason words like 'gruntapult' and 'riflecaster' exist).

Anyway, as DianeE proved, it is unlikely that any of Blizzard's RTS games are truly balanced.

StarCraft is pretty balanced for how simple it is. Company of Heroes is pretty darn balanced (much more so than StarCraft), especially considering how complex it is. True, it only has two sides (Germans and Americans), but there is so much more to consider when playing it.

I don't know. In Starcraft, not only units and stratagies factor in, talkings do too. Like a fag opponent like me, I like to lie about my race when I random. And make them talk right before I talk(slow reaction, no micro).

Another thing to consider in balance is the maps that they are played on. You can't compare races in a combat situation unless you somehow find a perfectly neutrally designed map... And in some cases, races are dependent on advantages given by maps... Its a very touchy subject.

The simple scenarios we've looked at so far didn't include landscape at all, so up to now that hasn't been much of a problem. However, yeah, when you add in sufficiently complex landscapes it does make things harder. One question when you do that is, how do you include such neutral factors in the definition of 'balanced'? Must they be balanced on average on all possible maps? Balanced in simple limited situations (such as having one unit on top of a cliff and the other on the low ground)? Merely set up such that there can exist maps on which they are exactly balanced and assume the players will try to make such maps? It depends how you look at it. The latter may be valid provided we assume the existence of a map editor, and if it is then it would certainly be the easiest one to evaluate.

And zerg's units are the weakest there is.

Weakest how? Weakest per individual, yes. But what about weakest per resource cost, or per supply point?

Actualy, zerg has by far the poorest unit strength:resource cost ratio.

Which is why blizzard made them so they could expand like a night elf.




Anyway meklar, you stated about how terrain isn't a factor because you are invisioning these situations flatplane-style. There's a big issue-very few maps are like that at all, and it's pretty obvious that right from the start, terran sucks on '
big empty' maps in a non-mirror game.

Really? Seems to me the zerglings in particular are actually quite tough for their cost.

Actually, as I believe I stated before, the simple scenarios I've tried evaluating so far did not include terrain at all.