Has AoE2 been locally maximized?

Age of Empires II: DE II - Discussion
23

Actually, when reading the first post @Dagorad62 actually only refers to parameters that are already given and established
Which means, every new added mechanic, civilisatrion or unit or similar isn’t even part of the question.

So, regarless what is the result, Devs still are totally free to add new Mechanics, Units , Civs and so on.
And this would also be their only choice to add to the core game, as they wouldn’t be allowed to actually change anything already established…

But as I said, new things can be added, nothing said about the addition of new things… :face_with_monocle: :smile: :smile: :smile:

24

If you have the ability to rank the patches of AoE2 by whether you prefer one patch over another then your ranking fits this model just fine for the purposes of this question.

Such a ranking maps the entire game, including every parameter value, into a (weakly) ordered space. Realistically youll be indifferent over very small changes because theres no way to tell the difference. But you can think of small changes as the changes which are just big enough to notice. This mapping is likely not stationary and changes over time but thats not a big deal for a question asked at any given point in time.

In any case distance can be measured in the parameter space (though the choice of metric is arbitrary up to a point) and how much you like the game can be ranked. Which means the definition of local maxima is well defined with respect to A) whatever preferences you have for game design and B) whatever you qualify as “small”.

This is not perfectly rigorous it is good enough for the question. But its hard to ask people out of the blue “Hey what do you think about this extremely specific but subjective relationship?”.

25

No, thats not enough. By far not.
If i prefer patch A over patch B, all of the following are possible:
-A is the global optimum, B is a local optimum
-A is a local optimum, B isnt optimal at all
-A isnt optimal at all, B is a local optimum (!!!)
-A and B are local optima
-Neither A nor B are local optima, infinitesimal changes would improve them.

Actually, then only case such a ranking would exclude is B beeing a global optimum.

26

What about if I prefer B to A then? Surely that messes with stuff, as you no longer have a consensus on things. So it becomes irrelevant if you don’t have a significant majority agreeing one way or the other. You need a majority to be able to draw basically any of the conclusions you stated as possibilities.

27

If you can identify whether you prefer patch A over patch B, which ill write as P(A)>P(B) then presumably you also have the ability to determine the relationship between P(A) and P(A + dx) for small changes dx. Which means you would know which one of those states youre in at least up to local maximum knowledge.

The assumptions required for a player to be able to rank P(A) to P(B) but not between P(A) and P(A + dx) are a bit incredulous. I mean even a naive extrapolation is likely to be relatively accurate.

Design is inherently subjective. The question is about whether the design of the game is locally maximized for you.

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What model?

What paramenters?

Well, what about you. I mean you literally demand from other people to make a very complex mathematical analysis where you don’t even give the model neither the paramaters on which it should be built upon.
Maybe you should make the calcs you talk about first?

Meaning it’s absolutely arbitrary 11

Well, local maximum is well defined yeah. Doesn’t mean there have to be any of them. Which is probably what you mean, but from none you said it’s clear there is any local maximum.

But you literally make an objective assessment of “local maximum”, which is indeed an objective result of a well defined function. But in order to find this it’s necessary to first define that funciton… If the variables of the function are variable the local maximas may shift and/or even be non-existant. Which means a prediction where a local maximum is is actually impossible to make.

The preposition for the assessment where the local maximas are is a well described and specific function. By refusing to give this function you actually make that prediction impossible you ask for.

You basically demand from us to predict the prediction of the outcome of an analysis you only would make if you didn’t already know that outcome. Cause when you know the outcome you can just vary parameters as you like to get your prediction.

So yeah, this whole thread is from the perspective of anyone who understands the principle of science absolute bs. It doesn’t make any sense.

But that’s even intended in my opinion as you basically exclude anybody from the poll this way that just doesn’t thinks the game is “perfect as it is”. Cause them who think it’s exactly how it should be will just ignore any mathematical analysis anyways, as they already “know the answer”. All others just have to disagree with the whole setup of the poll.
Which means you rigged the poll in a way only those can realistically participate who actually agree with your underlying opinion the game would be in a perfect state.

So you imply that the function you want to analyze has to be monovariable?
Do you know the restrictions a monovariable function sets on the existence of global and local optima?
Also, how can you already make this restriction of being ############# I mean before hand you already spoka about parameters, which is plural. But now you imply a ############# function?
Which means you must already have found a way to merge all these parameters into one single variable which also restricts how these parameters can be designed of and how they influence the resulting function.
If I am correct this whole construct you set up here already implies that there actually can’t be a local maximum of this function, as this would already contradict the merge of the given initial parameters to one singular variable to form a function that is eligible for analytically finding local maxima.

Meaning in conclusion, that the only viable answer to your question would be “disagree strongly” as it’s actually impossible to have a local maximum in the way you already set up your function to analyze. Just from the (actually very few) informations you gave about that function.

Edit: @Dagorad62 I have absolutley no problem when people say they are happy with how the game is currently and don’t want anything changed. It’s an abolutely legitimate opinion. And there is absolutely no need to hide that. I don’t understand why you seem to have a need to hide it. Cause I don’t see why it wouldn need to be hidden. I respect that opinion.

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30

How is this a replay to my post? I dont understand the connection.

31

What?! If ## ##### away the extremly useless math expressions, what you just wrote is “if you can, after experiencing its effects, tell whether or not you liked a big change, then you can also judge a hypothetical and very small change”. This is very, very obviously wrong.

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33

Basically, yes. Why didn’t ask just that? (Although I worded mine as a yes or no question, to avoid using a Likert scale.)

Precise? You did nothing precise. You didn’t do any mathematics at all. You gave a vague proposal of an incomplete idea for a mathematical model, then left it to the reader to construct and analyse that model for themselves. And then, when challenged about it, you insist that it’s possible for any reader to do this, because an economics textbook told you so.

I’m not going to expend any more time or effort on this, but as a mathematician myself, I felt it was important to call out a bad attempt to apply maths. I agree 100% with what @casusincorrabil said:

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34

Well, this is an interesting question, but a weird one.

Itn particular weird to exclude “game mechanics”, as the game should be balanced around what players do. You shouldnt balance xbows vs mangonels the same way when you expect 100 apm players on 30 ping and when you expect 20 apm on 300 ping.

Also we cannot really expect a perfectly optimized games where all we have is rough theorycrafting and players actual gameplay with a patch every 3 months. And with stats + costs + tech tree etc, you have a ridiculous number of possibilities that you cannot navigate into.

And as other said, it is hard to get an insightful answer while staying so vague about your criteria. Like: is the balance objective assuming that civs are balanced on every map? Or civs can be stronger on some and weaker on others ?
When someone said it is optimized, he may recognize that there is a good balance despite nkt liking it (e.g. Champions too weak). People saying we are far from optimized game, they may just think that missing canon galleons on island make the game too one sided (or with op eco the civ would be op on land map).

35

Given that the ability to extrapolate over small changes is like a bare minimum requirement for like 90% of the change-related conversations had on this forum this presents a problem. I mean obviously no one can do this for every possible direction but generally enough directions that the answer to the question can be reasonably estimated.

So either this forum cant be trusted to gauge their own preference for how much they will like a change (because they have no ability to extrapolate over small changes) which renders most parameter changing discussions moot or the question is reasonable.

You really cant have it both ways that this forums population is similtaneously familiar enough with the causal effects of small changes to have reasonable balance or design discussions but also unable to reasonably discern whether the parameters of AoE2 create a kind of local maximum for them.

Local maxima has a precise definition. Yes? And that definition is usually conditioned on a metric on the domain and at minimum some kind of order in the codomain. I.e. f(x-star) >= f(x) for all x such that m(x-star, x) < I where m is the metric and I is some distance greater than 0.

Consider the set of points with integer coordinates on the x,y plane. The function from this space to the set {1,0} with ordering 1 >= 0. This set + function should in theory have enough structure such that a kind of local maximum can be defined. It wont be exactly the same definition because of the problems with defining a ball but its not hard to see what properties it should have. Maybe adjacent points are the relevant points for determining local maxima, idk. But the point is that making “local” well defined is not particularly hard even if its not super useful and is abuse of notation. Since the number of points to be checked is too high youd have to estimate (hence the Likert scale).

You can expand this up to AoE2 in a way that is useful for those who wish to view the problem that way. I never said this was the only way to view the problem, nor that one should view the problem this way. Just that you can. Maybe you map to the set {-1,0,1} for “worse, indifferent, better” and the ordering only has to be defined between where the game currently is and the change so you dont even a total order.

Does the above really seem like some kind of unrealistic framework? Sure “local” has been abused but its precise enough to fill in the details is it not?

The bottom line is if you take the question in good faith the precision is there. Like I always say its not hard to construct an intepretation that makes the other person look like a fool. But that doesnt mean they are a fool.

Because its broadly equivalent which means that it doesnt matter which question one answers. If someone doesnt like or understand one version they can answer the other. Moreover if that phrasing makes sense then it can be used to infer what is meant for the more technical phrasing.

I used to think this community was always looking for new ways to view things to have better discussions regarding changes. But this thread just makes it clear this community doesnt care about incorporating new ways of looking at things that might help solve problems. This was not a good faith discussion where people asked what I was trying to get at. This was a bad faith discussion where people assumed I didnt know what I was talking about and ran with that assumption.

36

This guy gets it. Why should “design” be totally ordered? You can’t just apply math words to abstract concepts and expect it to make sense.

Replacing the word “design” with “balance” and you get a far more defined question. It still has problems, but you’re at least in the ball park of an actual question you might be able to answer.

37

This is a strange thread.

On the one hand, the poll is entirely intelligible enough for me to answer it (although I’d expect 90+% of people to answer as I did if they interpreted it the same way). On the other hand, a simpler phrasing would have yielded better results, with far less friction. The beginnings of a framework to (partially) view the game through a lens of maths optimization problems is there, but the people who point out its limitations and incompleteness are right. And I don’t think that “bad faith” cuts it as an explanation for why so many people have a problem with the characterization.

I’ve found some of your other posts interesting because they involve potentially useful contextualization of specific problems. But this thread has all of the abstraction that I find off-putting and none of the practical solutions that I find interesting. The “mathematical model” framing will be perceived by many as burdensome or incomplete, and unless you show it solving problems that people care about, it will (rightly) be rejected in favor of simpler and more intuitive models.

I don’t think this is a fair (or correct) conclusion. As far as I can tell, there’s nothing to imply that OP wants a static game. From what I’ve seen, he’s interested in improving balance/unit interactions by using tools from economics, among other things, but he would have to confirm that.

Also don’t think this is fair to the community, or is particularly the case beyond merely being the “human nature” of its human components. In my experience, people are highly predisposed to not care about your ideas, theories and frameworks until you’ve proven their value. Yes, that’s demanding, and perhaps you could call it “unfair,” but that’s the way of the world.

So I reckon you’re at a fork in the road. You can choose to lean into the “bad faith” interpretation and view this community as stagnant or regressive and not willing to engage with you in a productive way. Or you can learn from the feedback you’ve gotten by fleshing out your model further and showing the benefit of thinking of the game in that way, as opposed to simpler models or trial and error. And I think optimizing your communication for a general audience would be a net positive.

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39

By reading this thread it looks like the starter of this threads wants to know what we think about the current balance. Instead fo asking that straight forward, he askes it very strangely. I think the current balance is fine. Every time we will see some tweaks to keep the balance fresh again.

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40

I appreciate the constructive feedback.

The context behind this is that the developers make very infrequent changes and it often appears as if most changes are made simply to adjust balance. However depending on what design people want (e.g. viable elephants, nomad balance, less knight spam, whatever) these kinds of changes might not address that.

However large changes are trickier to predict. Which presents a problem: If you think point X would provide better design, but you cant reasonably expect to jump to it, what is the next best alternative plan to improve the design?

Assuming for simplicity that mechanics changes are off the table, one alternative would involve constructing a path through the parameter space from where we are to where we want to go such that we do not make the game appreciably worse at any point along the way. This path will probably not be a straight line in this high dimensional space and would ideally be constructed such that it can be stopped at any point without making the game worse than is now, nor infringing on the ability to get to other important points via a new path with similar properties. How to construct such a path via a combination of human intuition and analysis would be interesting to analyze. Also has applications beyond balancing a video game.

However doing so presumes that we can even get started without violating the “do no harm” principle. Which is equivalent to asking players “Do you think the parameters of AoE2 can be slightly changed without harming the game?” Now I just took 10ish minutes to write the original post and it was written from this context which is why it was phrased the way it is. I didnt expect a bunch of pushback on why this is analogous to abuse of mathematics.

So from my perspective this question only had value as a way to quickly gauge how strongly people feel the game can be improved with small tweaks around where it is. If people felt like the game was approximately locally maximized then clearly it would be very hard to find a path out which means jumps should be looked at closer. It wasnt meant to be rigorous only precise enough to get at what I wanted.

I could have phrased it using natural language but hindsight is 20-20. I thought the blurb at the bottom would be enough. I often dont know how to avoid aliasing certain concepts that I dont want aliased when using natural language and thats when I tend to just use whatever relationship is closest, whether it be mathematical, economic, psychological, comp sci, etc.

I will point out a subtly regarding good/bad faith here. Some of the responses were good like criticising the lack of specification regarding what “design” meant. Thats fair and I should have made clear that its subjective. But many of the responses critical of this whole idea added assumption which didnt need to be made or were unrealistic. Its the introduction of these unnecessary assumptions that is imo bad faith.

I mean yes the formal definition of local maximum will never work. But its intuitive that something analogous is attempting to be described and quibbling over how the precise defintion used in math is not going to work here is, at least to me, bad faith.

People like yourself might find my analysis interesting but my compulsive nature to answer these kinds of criticisms means I cant keep posting things and unpacking assumptions place on me that I didnt make. Its not worth the effort.

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41

Locally maximized are simply confusing to me.

If you put the game state as S and the scoring function is F, the issue is that F is not purely a function of S to me.

To put an example, at one day I may be feeling sick and weird and found that I cannot micro as good, then I would find some cav civs to be overpowered (than other days where I am not sick).
Sometimes I play Arabia, sometimes I play Arena, the weight of Arabia:Arena changes as my mood changes.
Sometimes a new rule is invented (e.g. 9 vills rule) and my view of the game changes. In particular, there are infinite rules from the game so you can derive infinite subsequent states S’ from S.

Therefore F = f(S, time, random), which changes without S changing, so the game is sometimes (close to) locally maximum and sometimes far from it.

Also I am not sure what is the relationship between locally maximized and big / small changes? I always thought it is a psychological problem (resistance to change) rather than economic problem - in paritcular, regardless of the changes are net positive or not, people will always dislike changes.

42

Also, just for all people who are curious what a “local maximum” actually is:

image
image1563×1176 20.3 KB

This Function has a local Maximum at the Point (0,0).
So right in the Center, not the big Bumps on the Outside. Ofc the big bums are also local maxima, but from a sheer mathematical understanding the very flat bump in the middle is basically categorized with the same name: Local maximum.

So idk what this has for a significance here. It’s just a mathematical term that probably sounds good, but unless you know what it actually really means, it’s pretty useless.

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43

Extremely misleading diagram. It’s a local maximum because everywhere around is slightly lower. It’s just hard to see clearly (and you put the x^6 term last as if it were a quartic which would make an extra bump in the middle impossible). It’s not the “flatness” that makes it counterintuitive, just the lack of zoom.

44

??? ehm no??? The x^6 is only to make the outer bumps. The bump in the middle would be there without the x^6 term.

It’s not misleading, it’s showcasing exactly that. A local maximum can be as “flat” as you want it to be. So flat indeed, that you can’t “see” it anymore.
It’s absolutelyi intended to show exactly that.

Local maxima aren’t intuitive. They are well described mathematical properties of functions. It has nothing to do with intuition.
I can understand your confusion as the TO tried to use an “intuitive” interpretation of a local maximum. But he failed dramatically, as there are seemingly a lot of people in the forum who actually understand what it really is and not what the TO thought it would be.
It’s actually very embarassing for the TO that he tried to use a mathematical property to hide his real intentions, but as he failed to understand what this mathematical property really is, he only exposed himself to derision.

Just as an advise to everybody: If you don’t know what you’re talking about. Better don’t even try. Or you’ll be taken apart by the people who understand that stuff.

Right click the picture. Select to show the picture in a new tab. Use ctr+ ore ctr- to zoom in and out.
You’re welcome.

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45

He actually makes a very good point. It looks “counter intuitive” because it was chosen to look counter intuitive. It looks flat to highlight the difference with really high values at -4 and +4.
When you look for a local optimum, you dont know where you will get, and it may be a very bad local optimum.
There is no reason why the local optimum in aoe2 wouldnt look like this 0 optimum and there is no reason why people saying we are at a local optimum wouldnt think we at at such a 0 optimum.

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