Argh's Theory of Game Balance (very long).

Argh's Theory of Game Balance (very long).

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Argh
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Argh's Theory of Game Balance (very long).

Post by Argh »

Here is my theory of game balance. It's long, involved, and some of it involves logic exercises. I don't expect anybody to read it all the way through. If you'd like to argue a point, that's great, I'm always interested in peoples' perspectives, and I'm always learning new things about this topic.

Game Balance: Meaning and Terms.

1. One cannot refer to "game balance" in the context of Toys (see this article, for the definitive declaration on this subject). One may discuss "quality" in such contexts, but balance isn't appropriate.

2. While one can attach the term "game balance" to single-player titles, my feeling is that this is an example of a negative-sum game, where game designers are mainly just changing under what conditions and how often the "house" will win.

This is more an act of editing for proper dramatic impact- in a game where a single player takes on some sort of role (whether heroic or not is irrelevant) the game designer is trying to ramp play towards making the player's actions within the game feel properly relevant to the overall story that the game is telling. Single-player games, when you boil them down, are nothing more than problem-solving exercises with some sort of narrative (whether simplistic or not is besides the point- Asteroids and Space Invaders can sit next to Fallout and Bioshock- the level of "depth" is logically irrelevant, imo).

3. Therefore, all concepts pertaining to "game balance" take place within games which are played by more than one person.

4. While "game" is a fixed term with strongly fixed meaning, "balance" is not. Nor should it be.

The following essay defends this argument.



Essay: Introduction

Before I get into the meat of this, a little background is in order.

When people think of "game balance", they are mainly asking whether a game is "fair". After all, when we were little children, we were taught that we had to play simple games, like Tic-Tac-Toe (or insert a simple game for small children, for those of you who come from cultures that don't play that one) in a certain order, following certain very simple rules.

We were taught that if we didn't play by these rules, that we weren't being "fair"; i.e., that we weren't allowing the other person an equal shot at winning. Therefore, it is important to remember that "fair", in most cultures, is defined in games in the same ways- I'm sure there are human cultures that don't have a concept of "fair", but I can't recall any at the moment. Exploring this issue might be interesting, but it would be beside the main points here.

As we got older, most of us played sports and more and more complex games of various kinds. Some of us, like myself, loved games enough that we started making our own up, borrowing at first from other peoples' designs, and gradually making things that were our own.

I made my first game when I was 12. It was a clone of Car Wars (an ancient tabletop game), with a slightly different scale (I wanted to use Hot Wheels, because they were plentiful in my house) and rules that were designed to be simpler to play (Car Wars is a fairly complex game, when you actually look past the initial rules).

I was a big visitor to the local game shop, which back then meant board-games, RPGs and tabletop war games, and they invited me to test my new ruleset with a bunch of strangers. Fellow geeks all (this was back when "geek" was a major insult, young people- it didn't used to mean "smart person who knows technology"), they willingly sat down to play, with my collection of 1/72-scale rubber army men, and Hot Wheels I'd painted as if they were from a bad Mad Max ripoff, complete with toothpick spikes on their bumpers and lots of fake blood (Testors makes a model paint that is called "Ruby Red", IIRC, that looks like fresh blood, and I liberally applied it all over the cars).

It was a flop. An absolutely terrible, terrible game. I'd made several basic errors in my mathematics, and the element of flukey, random death introduced by my mistakes made the game entirely one of statistical chance. That, and one player had randomly rolled up an uber-weapon from my poorly-designed random table, that slaughtered half of us in one round of play.

While the older kids and young men were generally kind to me, I realized immediately that I'd made a terrible game, that it wasn't fair, and wasn't fun, and that I'd failed. I went home and fixed most of the major problems, but I was too embarrassed to show up at the game shop again with my creation, and it eventually ended up in the trash, along with a lot of other things like that I've thrown out over the years. The memory is the important thing- and 21 years later, it still stings.



Essay: Three Views on Game Balance

1. Game balance is the perception, by all parties, that their skill and some luck will secure victory. Not the absolute certainty. Good game balance presents players with enough choices that they feel they have a fighting chance.

Balance isn't about two sides being entirely identical, and having entirely identical starting positions. That's a logical fallacy. I hate it when people drag this argument out, and having heard it multiple times, I'd like to clear things up.

First off, we have to look at the game design in strict terms. Is the game zero-sum, positive or negative-sum? Multiplayer games may fall under any of these categories.

For example, online gambling games feature game balance, in the sense that I'm talking about this topic. They're negative-sum games- i.e., the odds favor the "house" overall. The degree to which they favor the "house" or individual players is a very strong part of their game designs (and one of the biggest trade secrets, for obvious reasons).

Gambling games don't even pretend that all sides start off with even chances of victory- in a poker game, you may be hosed no matter what choices you make, as a player, and this is an accepted part of the game. While many Spring players would probably find this reprehensible, and whine about how things are "imba", the fact is that almost many people gamble with real money, with full knowledge that they're probably going to lose, than play video games. Heck, it may even be more people- I'll have to check the stats on that. At any rate, a game or games that are inherently "imba" may still be considered to be "fair", if all participants (aside from the "house") are considered to have equal chances- Lady Luck may be fickle, but she may also be kind. And skillful players may work with human psychology and the odds and come out ahead, on average, due to factors that aren't inherently part of the game design itself.

I'd never play poker, or even blackjack (traditionally, the best odds of any gambling game that I know of are in blackjack, because it's so simple) for money against people online. I can't bluff them, and I have no way to see how the "house" is screwing with the odds. Whereas if I play it in a casino, I can do both things, and maybe put this knowledge to my advantage. Not to mention putting on a nice sportcoat and a tie, and pretending I'm James Bond for a minute ;)

Examples of positive-sum games abound. They're called MMORGs. Y'know... the most popular form of video game, and most profitable, period? While I personally don't get into them, I understand that a very huge number of people do, and I get why- they can live out fantasies of being someone else- from the trivial power-gamer, who wants to be a super-heroic wizard or warrior, to somebody who wants to be an Elf from a fantasy world they've invented in their spare time... they can get together with other people, and create a game that is more than the sum of the parts. WoW would be extremely boring, if all you could do was solo. I've watched people play it, and compared to, say, Oblivion, it's a mere sketch of an RPG in the single-player sense.

However, as a social game, it and many others have proven excellent draws, and I think a lot of it has to do with the fact that they contain both positive-sum and zero-sum games within them- positive, when one is in a party and hunting for treasure against the server, zero-sum when one is playing in the various competitive "wars" between factions within the game-world.

Nobody in a MMORG who is not a complete power-gamer gets all that worried about asymmetry between classes and races. "Game balance" in such a title, even for the zero-sum parts, implies social cooperation- my Wizard can stun and hurt the other side at a distance, your Warrior can hack away at them up close and tank, and my other friend, playing the Priest, can keep us both alive with buffs and heals. Nobody worries a lot about whether a Warrior and a Priest are "equivalent"- they're supposed to complement and contrast one another. And when two or more factions meet, with their own weird sets of complementary powers, nobody expects them to be identical. WoW's two factions are an excellent example of this- while game-balance in raw stats is a factor, there are all of the human elements that also matter- good stats won't make up for poor teamwork or coordination.

The only positive-sum game type I've ever really gotten into is the FPS genre. Here, again, we encounter positive-sum games, within what looks like a zero-sum game framework.

Before everybody jumps on my statement... let's examine it for a second. While a game like Counter-Strike is clearly zero-sum- one team wins, another loses- the experience of playing can vary considerably, depending on how both teams choose to play. If you've played CS for more than a minute, you'll understand what I'm saying immediately- there's a giant difference in a game played with a hardcore bunch who take teamwork seriously, irregardless of skill levels, and a game played with random pub people, who are mainly playing for Kill:Death ratios.

In the first type of game, people are playing for team wins. In the other, players are playing for individual wins. Both types of players are in the same framework of rules, however their definition of "win" within that zero-sum framework are entirely different. The team players are playing within CS's specified rules. The Kill:Death people are ignoring the rules, and are playing for a score that is nowhere in the round system or objective system of the game.

Having played lots of CS, I am very reluctant to condemn either way of playing as "wrong", even though the second type of play is not used in serious competition. But I think it's fair to put forth the argument that while the strict, by-the-book CS "round" play has a zero-sum element, a pub player with the top K:D ratio can fairly define themselves as winners, even if their "team" is losing, because they're not really playing that game at all, and the "rounds" mainly serve as a way for everybody to respawn and attempt new tactical approaches to killing each other, as opposed to the stated objectives- a slow-motion variant of Quake, as it were.

When we get into purely zero-sum games, like a 1-vs-1 game of Spring, then we get into the more familiar channels and discussions of what "game balance" means. Moreover, we start very quickly getting to the root of this issue- that "balance" is a perception, not a mathematical certainty- when we examine the true level of complexity in a modern RTS.

Simply put, balance in a sufficiently complex game is usually statistically unprovable, short of exhaustive analysis. Don't believe me? Do your homework, and hunt down people's game-theory theses on Monopoly sometime. Heck, I'll make it easy- go here. It won't be fun reading, I promise you, but you will very quickly see that even a game that "simple" is extraordinarily complicated, and difficult to analyze.



Now that you've gotten a glimpse behind the curtain, and hopefully arrived at this paragraph with an open mind... let's do a thought experiment.

Ask some BA players, "does one Tremor beat four Flashes, on a map with flat ground?". I'll bet that, if I go to the Lobby right now, and can get them to stop cursing randomly at me for being a "nub" for a minute, that everybody will say, "no".

A good game designer is going to ask, "how far away are the Flashes, and do both players know their relative starting positions"? Because this is directly relevant. The other question to ask is, "how much starting E do both sides have?", because that's also directly relevant. If the Flashes start far enough away, and the Tremor player knows their location, and the player has unlimited E, then the Tremor actually has a chance to win this confrontation.

However, the larger the map gets, the less determination can be made by the Tremor player as to the probable paths of the Flashes- it cuts both ways. In the end, the Tremor probably loses, irregardless of skill levels on both sides. But it's an uncertain equation, with an element of luck.

Players know jack squat about this kind of problem-solving.

It's not that they're stupid. Don't get me wrong. They're just focused on the elements of play, as opposed to theory. I suspect that the very best players of any RTS aren't like this, but the only person I know who's truly expert-level is DRB, and he's not a typical player.

I think it's very interesting, though, that when you see the Korean players at the top levels of StarCraft play, that they aren't just random punks who happen to be good button-pushers. I strongly suspect that they probably are quite capable of using, and understanding, the deeper mathematics of that particular game.

However, most players often don't think past the things they've learned from a relative handful of games, against handfuls of people. They end up in all sorts of pattern behavior, because most of them don't ever bother learning enough about the game design's fundamentals to really know what is effective, and why. It's even worse with the Spring community, where the number of really excellent players is very low, compared to a commercial RTS. Think about it, fellow game-designers.

And yet, players often feel like their judgments supersede anything a game designer has to say, and dismiss our arguments, even though we're the ones having to do the hard work, under the hood.

To be fair, they're the ones who see any egregious flaws in the designer's logic, and their patterns often reflect areas where the designer, either intentionally or accidentally, created probability curves that favor a given strategy. Such is the world of "game balance"- where the game designer has to take the deep view, and analyze all elements, the players take the broad view, and see the totality. Which is why any good game designer playtests, and playtests frequently, before releasing a product.

But they're just seeing the results, not the underlying phenomena. They don't really understand when you say, "this unit is now using a different Armor Table rating, therefore its total effectiveness against every other possible unit must be re-evaluated".

You can tell 'em that, but they're not going to understand you, even if you break it down to case-by-case basics. They may even spout some numbers, in isolation, in their paragraphs about how you've "ruined" their game. But they don't get it, and we shouldn't even ask them to. They play for fun. We design to make something we hope is fun. They know what they've played that was fun before. We know what we're trying to do, that's different enough that it might be interesting. And we're the people with months, or even years, hanging on their reactions. It's not the same thing at all.

When I made NanoBlobs, I didn't give a shit about what people wanted, frankly. With PURE, I decided to give a shit. Hopefully I'll make something people like. But that's the view, from the other side of things. Maybe it explains why me, and most of the other designers, seem a little bit cranky sometimes.



2. Most good game designs include an element of chance. This is not a cultural fluke- look at games throughout the world, and this is almost always the case, aside from purely physical games such as soccer. And even a game like soccer contains elements of statistical probability- what the conditions of the field will be like today, the conditions of the stadium, the weather, etc. Ask any bookie, or serious fan.

When elements of chance are thrown into the mix, any concept of statistical balance becomes more and more problematical, because you're looking at intersecting curves of probability, and the same mixes rarely recur often enough, in practice, to arrive at a final judgment.

Let's take a look at a typical game-designer puzzle for a minute.

If you have a unit that, once in 100 shots, will automatically kill whatever it shoots at, is it 1% effective, and thus worth 1 / 100th of a unit that will kill another unit every time it fires?

No. Because, for 50 of the supposedly crappy unit, I would have a 50% chance of a kill on the supposedly vastly-superior unit, on the first round, then 49%, and so forth. Therefore, probability is entirely in favor of the 1% unit. In fact, it isn't until we get around 10 of the supposedly-crappy units that probability overwhelmingly favors the unit that kills every time. Even at 25 of the crappy units, probability says that a hit will occur before they're all dead.

If you don't believe simple probability theory, it's easy to set something up to test this, with turrets on Greenfield. Try it out.

Players don't think that logic through. They just don't. They like to attach all sorts of worth to stuff that's not even worth mentioning, like DPS, when in fact, there is no such thing, outside of isolation cases, where you are strictly comparing two units, without terrain as a factor. Take that Tremor, for example- get three, put them against 12 Flashes, re-run the scenario.

Now probability favors the Tremors, by a long shot, because the probability of hits has increased threefold, whereas the Flashs' movement speed across the map is static. It's simple math.

Put the Tremors on a smooth cone- now the probability changes again (for the math-inclined... figure who is favored, it's actually interesting).



3. Elements of chance are a factor insofar as "fairness" is perceived. This has to do with human psychology. Elements of chance often distort human expectations of outcomes. We often hope that something will be true, even when the raw math states that it is unlikely.

This is one of the things that, especially within the complex world of computer game design, is rather important- when an event has a low probability of occurring, but gives a player a "jackpot" when it does, it generally generates more excitement when it occurs than disappointment when it doesn't. Nothing is more boring than a game where every single time a situation occurs, and a player executes the same moves, the same results happen.

Examples of this abound, but the most classical one in modern game-design history is the probability of headshots in Counter-Strike. The game designers of that title, realizing that headshots are one of the single-most important elements of perceived balance, put enormous amounts of work into this area. I know- I've read some of their commentary. It's very, very interesting stuff... if you're a game designer. Expert-level players favor accurate weapons and identical outcomes. Less expert-level players strongly favored more random chance, so that they'd be able to survive long enough to maybe "contribute" to their team's victory- or even get lucky and take someone out. Counter-Strike's designers, knowing this, have been trying to get this formula right.

I don't like where they eventually arrived- but I was a hardcore player. When I play now, it feels very dumbed-down and flukey. But I understand the reasoning behind it. Most players simply don't think about it, or just adjust without examining the reasoning overmuch.

Chess is often cited as the counter-example of these concepts. If I had a dollar for every pompous ass who said that chess was the ultimate example of a game without elements of probability, and thus was the gold standard for fairness...

However, this is not really true.

Psychological studies of chess players have determined that even the greatest masters cannot see every single possible move more than a few moves ahead- they certainly cannot see the finite tree of all outcomes. While they can and certainly do memorize all patterns that lead to consistent victory, they frequently are playing in large part within a framework of probability- the only certainties are the patterns they have memorized.

While it's strictly accurate that this reflects their human limitations, and not the logic of the game design, it doesn't really matter much- chess players, even at the highest levels, engage in classical risk-taking behaviors.




To summarize:

1. Game balance is perceptual. It is frequently resistant to analysis. I don't mind that players want to endlessly argue about stupid stuff that they don't really understand, and create fake terminology, like "DPS", which they then use to argue amongst themselves- that's OK. However, game designers should read between the lines, and then look at the depths, to arrive at an appropriate answer. Most of the time, players are basically arguing about whether or not a particular unit is worth building, for what it can achieve. This is frequently a very complex argument- a Jeffy, for example, may have some utility in combat, but its primary role, in most alphabet-soup mods, is that of a scout. Therefore, game designers should ask themselves, frequently, "what is the purpose of this unit? Why is it important? Why should it be in the game?" If you don't have a good answer, you should take it out, until you do, or perform a crazy experiment, like doubling / halving an important variable.

2. Most good game designs include an element of chance. In games involving Spring, this has implications all over the place. Weapons may have random chances to hit a target, so you can only talk about probability, not certainty. Even a weapon with a 100% probability to hit within its blast radius of a given target is not the same weapon every time, if you've used EdgeEffectiveness or other variables to influence the outcome. Such tools are in Spring because they provide game designers with small tools for small adjustments- not every game design problem requires a sledgehammer. Use what's available. Ask questions. Use Spring to its fullest- most alphabet-soup mods barely even touch the surface, and look shockingly crude, next to many of the other games that have been made. Ignorance is not a good excuse.

3. Elements of chance are a factor insofar as "fairness" is perceived. If you're going to build my "every time it shoots, something dies" unit, then you'd better have something like the 1% unit in the game design, too, and price them very, very carefully. Probability is your friend, because it helps make balance even more contextual, and less linear. Less linear balance makes for a more exciting and interesting game design, and rewards micro. You don't have to go this route, of course, but keep in mind what you're sacrificing.



That's it- that's really all I have to say about this topic, short of releasing PURE. I hope you found some of it useful.
Last edited by Argh on 23 Nov 2007, 05:43, edited 1 time in total.
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knorke
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Post by knorke »

sorry, seems like lots of words with little context ;)

I dont really understand what you are trying to say. Even noobs will understand that AOE weapons like the tremor are better the more you have of them and that there is often a sizelimit for an effective army...
2. One cannot refer to "game balance" in a game where only one human participates, or where multiple humans participate against a mathematical construct. There is no such thing as a "balanced single-player FPS". Nor could one ever be built. This is a mis-use of the term.
That has nothing do with playing against a "mathematical construct" but with the fact that in an FPS the enemies must have an disadvantage to the player, otherwise the game would be impossible to finish. Singleplayergames are imbalanced by concept.

[/quote]I'm sure there are human cultures that don't have a concept of "fair", but I can't recall any at the moment.[/quote]
Ordos from the Dune universe! ;)


I dont really understand the difference between
Most of the time, players are basically arguing about whether or not a particular unit is worth building
and
Therefore, game designers should ask themselves, frequently, "what is the purpose of this unit? Why is it important? Why should it be in the game?"
Why is the first a bad and the second one a good thing?

Imo, the "feel" of the game is much more important than pure numbers.
ie in Counterstrike you basicly sneak around and when you see an enemy you start clicking on his head. Every other tactic usually fails, ie moving away hardly works because your aim gets worse when moving while your enemy can keep shooting. Also bullets from most (all?) weapons slow you down when you are hit.
Playing COD, Quake or has a different feel and this is what really makes the gameplay.

short of releasing PURE
hurry, hurry!
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Argh
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Post by Argh »

I dont really understand the difference between
Most of the time, players are basically arguing about whether or not a particular unit is worth building
and
Therefore, game designers should ask themselves, frequently, "what is the purpose of this unit? Why is it important? Why should it be in the game?"
Why is the first a bad and the second one a good thing?
I'm not saying that either is bad. I'm saying that when players are arguing, and creating terminology to talk to one another about what is "balanced", that game designers need to get to the root of the issue.

In a typical RTS, the resources are time, the map, any fixed / linear / random resources (or "counters", in classical terms) that may be used, the units and their many capabilities. Game designers should, imho, evaluate changes to the units, which is the main thing they can control in something like Spring, based on their design goals. If a unit is supposed to be support- is it support, or is it really something else? Keeping clear goals for each unit is a big priority. Listening to players' feedback, and reading between the lines to arrive at accurate conclusions, is an important part of the process. Game designers should ask more questions of their audience- "does this unit do this job, when you play?"- and then evaluate whether or not they can achieve this goal. Players are always going to key on the things that work, or used to work, for them- game designers need to ask questions that avoid essentially meaningless statistical chatter, and keep an eye on their design concept.

A game designer's goal is to have a game that plays as it was designed to, which will hopefully make players happy :-)
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Zpock
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Post by Zpock »

IMO, things that work like they "should" are boring. It's the novel ways of using something that are interesting.

If you fix everything to just work as you intended only... not good I think.
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Argh
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Post by Argh »

Things that work as they "should" is a very vague concept ;) You're fixated on very simple game designs, methinks, broaden your horizons.

For example, the Heavy Shell in PURE would have a design role that reads something like this:

"For its costs, a Heavy Shell should be an effective, multipurpose assault unit, able to counter ground and aerial threats, especially in situations where wreckage plays a significant role in the flow of combat."

It's not a pigeonhole. It's not a, "this thing only does X". You're right- if that's how things work, it's frequently boring. However, keeping a concept in mind, once you've fleshed out the initial design goals, is a good idea- it keeps you from wandering all over the place.
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Zpock
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Post by Zpock »

I agree, if its what you mean, that the concept of how you actually want to set up your gameplay is what's most important. Interesting units, mechanics etcetera. I mean if the design sucks, the game will suck even if you can implement your design just as you want it to work in practice (what I consider the goal of balancing).

That was just to point out that, for example, if they fixed some of the funny supposedly unintended stuff in a game like starcraft, it would suck bad.
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Argh
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Post by Argh »

if they fixed some of the funny supposedly unintended stuff in a game like starcraft, it would suck bad.
That's actually an excellent example of how when your game design encounters players, that it's important to listen- not just to what people say, but what perceptions of relative worth emerge. StarCraft has become a game that most players would label, "balanced", in large part because Blizzard has put a lot of time and energy into listening to their players (both directly, through forums, etc., but also through studying bNet and replays).
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rcdraco
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yea

Post by rcdraco »

I'll have to agree with both of you, for example, I KNOW THIS NEVER HAPPENS.

In starcraft, I like to use the siege tanks as supplemental defense, a really effective defensive strategy, that the developers may or may not have added. In my mod, I want something like that though. Units will all have a purpose, and knowing the little nit-picky features of each one allows you to become an effective player.
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Zpock
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Post by Zpock »

An important aspect is that they "let go" of the game tough. Starcraft hasn't had balance changes since 2001 or thereabout. The original design is also pretty much intact. The exception would be the total remake of how WC3 works in the expansion. However it should be noted that they changed everything in one fell swipe, not gradually.

Listening to players has 2 problems:

A: 99% has no idea what their talking about, have no clue about the big picture, are plain idiots.

B: the game has to be balanced before players get their hands on it. You can't release a shitty first version and think that players will flock and help you balance or even design the game. To put it short: The first impression will be bad and then your game is dead.

This is where playtesters come in, however their very different from the actual players.
Warlord Zsinj
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Post by Warlord Zsinj »

Argh, no! bad! *taps forehead sternly*

Go work on pure!
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Argh
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Post by Argh »

<laughs>

Thank you, Zsinj, I will now return to my regularly-scheduled round of work-out-eat-go-to-sleep-and-Work, so that I can do that ;)
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LordMatt
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Post by LordMatt »

I didn't read your post, but my experience with nanoblobs suggests that Argh is a good game balancer, and probably worth listening to. :-)
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ianmac
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Post by ianmac »

A+ for the easy.
Argh I couldn't agree with you more. I love games where there is chance per say put you have to think as well.

P.S. I read it in one sitting :wink: .
P.P.S. Do you have a vauge releas date for pure? I realy want to play it!
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Felix the Cat
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Post by Felix the Cat »

2. One cannot refer to "game balance" in a game where only one human participates, or where multiple humans participate against a mathematical construct. There is no such thing as a "balanced single-player FPS". Nor could one ever be built. This is a mis-use of the term.
It is you who misuses the term. Every game must be balanced, in terms of difficulty of the game versus time spent in game versus average intelligence and experience of the audience, among other things. Multiplayer RTS balancing is a subset of game balancing.
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smoth
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Post by smoth »

Eh, yeah zero sum exists.

http://en.wikipedia.org/wiki/Zero-sum

Whatever, we all have a perception of balance when devs who have been making shit before you crapped in your first diaper. Meh, we are not really qualified to say what is the best perspective of balance. In the end we can only say that some units need to be more or less useful. It is just an abstract concept.
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KDR_11k
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Post by KDR_11k »

I prefer the definition of balance that is: "every valid approach is viable". With this definition any game with multiple approaches (even an FPS with weapons) can be balanced and the absense of this type of balance will hurt the game by making approaches that were intended to be valid not viable since other approaches are always "better".
tombom
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Post by tombom »

Zero-sum means that a possible move results in a loss for all parties. Not that it happens every time. There are games, like variants of poker and many other gambling games, which have zero-sum elements, where the house will win every time if players do certain things to each other.
This isn't what zero-sum means at all :?
Wikipedia wrote:In game theory, zero-sum describes a situation in which a participant's gain or loss is exactly balanced by the losses or gains of the other participant(s). It is so named because when the total gains of the participants are added up, and the total losses are subtracted, they will sum to zero. Chess and Go are examples of a zero-sum game: it is impossible for both players to win. Zero-sum can be thought of more generally as constant sum where the benefits and losses to all players sum to the same value. Cutting a cake is zero- or constant-sum because taking a larger piece reduces the amount of cake available for others. In contrast, non-zero-sum describes a situation in which the interacting parties' aggregate gains and losses is either less than or more than zero.
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Argh
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Joined: 21 Feb 2005, 03:38

Post by Argh »

First off, everybody pointing out my abuse of "zero-sum" is correct. I'll correct my terminology in my essay, later.

What I was trying to get at is the assumption made by many that games that have exactly-matching pieces given to each player are inherently balanced, and that it all goes downhill from there- if that were so, nobody would ever play Risk, among other asymmetrical games.

Secondly, I understand that everybody brings their own perspective to the table. I'm not trying to impose mine, just explaining why I do certain things- there's a philosophy here, even if I don't always explain it as well as I should ;)

What I wanted to do was to explain mine, since I'm getting tired of people not understanding why I regard statistical approaches with a certain level of skepticism, having built several games where I've honestly beaten that horse to death (go look at Silent Dark, my own private monument to "universal system" game design)...
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Zoombie
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Joined: 15 Mar 2005, 07:08

Post by Zoombie »

Interesting. However, I suffer from an acute lack of being able to actually build a modification, mostly because I'm lazy.

But still, interesting and good for mulling over a warm cup of blood.
Tobi
Spring Developer
Posts: 4598
Joined: 01 Jun 2005, 11:36

Post by Tobi »

removed off topic posts

if you don't want to talk about something just dont post, k thx
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