# Has AoE2 been locally maximized?

This is just a quick poll question. Those familiar with calculus can just skip to the question at the bottom. For those who need a quick and dirty refresher:

You can think of designing AoE2 as a maximization problem. Assuming the mechanics are established, the only question is how to set the thousands of parameter values like unit HP, civ bonus values, tech tree availability, etc. to achieve the best designed game the mechanics allow for.

The game currently “resides” at the point in the parameter space with the current unit stats, civ bonuses, tech trees, etc. A path through this space would consist of a list of small changes to various values such that you “travel” from one point to a new point in the space via some specific series of small steps.

Now a local maximum occurs when a small step along any path causes the design of the game to worsen. Keep in mind that these small steps can be along directions that involve multiple parameter changes at the same time. For example pikes train 1s faster, knights train 1s slower and squires costs 10f less would together form a small step.

So here is the poll question:

How much would you agree with the following statement? The design of AoE2 is locally maximized at the current parameter values. (Parameters include unit stats, civ bonuses, tech availability, etc. but do not include game mechanics)
• Agree strongly
• Agree somewhat
• Neither agree nor disagree
• Disagree somewhat
• Disagree strongly

0 voters

An equivalent phrasing for the above starement in question is “The design of AoE2 cannot be improved without changes in mechanics or large changes in parameter values.”

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What a coincidence to read this while studying for my Numerical Optimization exam next week 11.

there is no need to bring math into this and tbh it makes me question when you use stuff like “parameter space” relating to a videogame because I would be really curious of how you can trace a curve of (for example) HP vs “enjoyment” or “optimal game balance” and how you would go about measuring these last 2 objectively.

Regardless, no AoE hasn’t been locally maximized because maps and civs influence strats, there are dominant strats on some maps yes but that’s a good thing, you don’t want every strat to be “equally viable” else you have Knights trading perfectly evenly vs Crossbows and such and THAT’S a boring game.

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Such a nice way to offend whole industry of research field of soical science

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I think this is a bit of a weird question. Global maxima are only a theoretical thing, in the real world, they usually dont exist (or we can’t agree on what it would look like). The reason for this is that in practice, the possible space is infinite or rather unknown, only on theory it is defined. For example, any game can be warped into a completly different game, possibly even of a genre that does not exist yet; how do we judge if this imaginable new game is better than todays aoe2?

But when global maxima make little sense, their counterpart, local maxima, make little sense as a term either. You could just say “maximised” or “optimised”; or to rephrase the question again: Is AoE2 in a state where it can’t be improved anymore?
To which the answer is no.

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I disagree strongly.
Take the Siegetower (or don’t take it, I cannot blame you).
A mostly unviable in the current parameter space. Any change that would make them a little bit cheaper, give them more hp, faster, take less bonus damage from gunpowder, increase garrison space, take more garrisson speed boost, lower creation time would make them a bit more viable.
They would be a lot more useful, if they would not “flinch away” from arrow fire like villagers. This makes one of their intended uses (shielding Petards from castle fire) practically impossible, even if it was more cost-efficient. That on its own, also a small step.
And that would be fun and good and better. Therefore, we cannot be at a local maximum.

There may be many more nearest available local maxima, that one could approach by making small changes. But I do not care for those.
But I think game mechanics should be overhauled first, before trying for small optimizations.
Pathing, (un)garrisoning, formations, removing unfun frame delay, making armor classes more legible etc.

Actually I cant say this because it ignores an important relationship. Namely the ability to get to a maximum via a continuous path without making the game worse at any step.

If you are not at a local maximum (ignoring constraints and edge cases) it means you can improve something without making it worse. This is very important relationship for businesses dealing with a risk averse customer base or in an environment where you only have local knowledge and dont want to risk causing a massive problem on your way to a new point.

If you are simply “not at a maximum” the above relationship may or may not hold depending on where in the space you are. If youre at a local maximum you may be forced to make large jumps into an unknown part of the space or make smaller jumps that make the game worse in the short run. If you are not at a local maximum then neither of these things is necessary and you can make small changes and improve the game “safely”.

They dont need to be “objective” they only need to be consistent and map into some totally ordered space. The statement above is falsifiable for each individual but the only person who has the information necessary to check this is the individual because their choice of “good design” is subjective. But as long as that mapping of game parameters to design is totally ordered theres no problem.

Also mathematics is simply a way to describe relationships precisely. Being at a local maximum has an important relationship regarding whether you can improve the game in a non-decreasing manner.

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He is not concerning the objectiveness. He is questionning your intelligence

This thread is kinda showing why mathematicians should not rule society…

I’ve found usually people make those kinds of comments because they over-apply objectivity. Which is why I focused my critique there. Recognizing which problems involve preferences (and therefore are subjective) and which problems are independent of preferences is a learned skill after all. If it wasn’t then unis would never need to explicitly teach it to undergraduate econ students.

I assume this means you think mathematics is being misapplied here? I’d be interested in hearing why you think this.

It’s not necessarily being misapplied. It’s the fact that you’re consistently applying excessive maths to a video game, which is ridiculous in my opinion. Even though the game may revolve around maths, it is a game, and reducing it to maths equations seems like you aren’t enjoying it for what it is.

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I reject the premises of the question. Specifically:

No I can’t. At least not in any helpful way. You’ve even partially answered for yourself why I can’t:

You haven’t actually said what you think that totally ordered space is supposed to be – I think the nearest you’ve come is saying this:

So I think you mean the codomain of the function I’m optimising is supposed to have elements that represent my possible evaluations of the quality of the game design in some way. I can just about believe that one could define such a set, but it isn’t going to be totally ordered. For it to be totally ordered, my evaluation of the quality of the game design essentially has to be a single number. (I say “essentially” here because I realise I’m simplifying – there are other possibilities, but as a human, it’s not going to be practical for me to use any of them for this purpose.) The end result will be so over-simplified that it will be unhelpful.

Even if there was such a totally ordered “design quality space”, there’s then the question of whether there’s a well-defined function from the parameter space to the design quality space. There isn’t; my evaluation of the quality of the game design depends on variables other than the parameters – including variables that have nothing to do with AoE2.

But let’s assume that both the design quality space and the function into it do actually exist. There’s no way I can know what that function is – even knowing how it behaves close to the current set of parameters is difficult, and I absolutely need to know that to answer the question.

(There’s also a fourth issue, that the parameter space is discrete and optimising in this way requires continuity. I’m less bothered about that because I don’t see much problem with modelling it continuously – but I suspect this might not have occurred to you, since in another thread you suggested irrational numbers as population costs.)

See above. But also, I think you could just have asked something like “do you think AoE2 could be improved by small changes to unit stats, civ bonuses, tech availability, etc.?” and you would have got the information you wanted, with more respondents and clearer answers. The use of maths here is unnecessary, will be off-putting to plenty of people whose opinions you might actually be interested in, and makes it more difficult to understand what it is you actually want.

I suspect that @Dagorad62 has also recently learnt about numerical optimisation, and in their enthusiasm is trying to apply it to everything. At least, that’s the best case scenario…

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This whole thread is just such an abonimation…
It’s just absurd even attempt thinking about a game this way.

A question that could maybe ask realistically:

“Does the current design of the game allow for new interesting units/mechanics?”

But the whole way this is set up… Just…This is a computer game, it’s intentionally designed in a way certain strats are more effective than others (which then develops to meta). And every strat has counterstrats that can be executed against them.
What are we even talking about here.

Is this your attempt to close up the game and say: “I think it’s perfect as it is rn. I’m against any further changes!” But in a very cringy way?

Maybe you are happy with the current meta.
But trying to use mathematics to “objectively” support your personal preferences and try to stop any change is… absolutely weird. Are you sure mathematics is the right choice for you?

Edit: After reading I actually think you don’t actually know what you’re even talking about… This is such a nonsense. No mathematician would ever make a thread like this. It just doen’t makes sense. It’s absurd.

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I mean I dont use much maths to play the game beyond getting an idea of breakpoints and other small but useful things.

But personally I would not feel comfortable trying to make changes to the game without at least employing some rigor regarding describing the problem.

You mean like this?

I gave the quick and dirty non mathematical option but I preferred to express it slightly more precise.

Most of your qualms with the underlying mathematics are moot. As long as an individual has the ability to prefer or be indifferent between any two sets of game parameter values they have the ability to evaluate some the function which maps game parameter values to a totally weakly ordered set. It is not exactly unbelievable that people can do this, especially at a local level where only small changes from the current status quo are in question. Which means the question is reasonable at minimum. I made a mistake by using total order rather than weak order but the point is similar.

While none of us know what that function is we can nonetheless ask questions of its properties at a local level. Such as “Do you as an individual view the game parameters to create a local maximum?”

I am not going to say this question is phrased and framed perfectly. But the property of whether the game has paths of sufficiently small step size to some preferred state that dont cause bad effects is not unreasonable.

Trouble with the question is that it apparently nerdsnipes people into arguing about the phrasing and definitions instead of engaging with it in good faith, apparently

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The question is actually:

“I think the Game is currently in a Perfect state. Do you agree?”

But @Dagorad62 made it a two pages long column of showcasing his evasive language skils while touching subjects he doesn’t knows anything about. It’s like watching a whole Jordan Peterson podcast.

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That is not the question at all.

Again I am trying to get at a very specific property: does there exist a path with sufficiently small step sizes to get from the current state to a perferred state without causing the game to get worse at any step along the way? The equivalent phrase for this is “are we at a local maxima?”

This is a much more specific property than “Do you think the game is perfect?”

I thought people would have the maturity to engage with this in good faith. Instead what seems to be happening is everyone is assuming im trying to ask one question Q and then criticizing it on the basis that I didnt ask that question. But I dont want to ask Q I want to ask something different.

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Yeah, also Jordan Peterson:

“I didn’t said that.”

Yeah you actually didn’t said anything.

Therefore:

I refuse to vote as your question is just nonsensical. From a mathematical point of few it’s just not well describend.

What does locally maximized even means for a game. This question is stated as a true/false question, but it is just subjective. What does best designed mathematically means? Too vague to answer.

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The problem is that models are just that: Models. They are not right or wrong, instead, they are useful or useless. A useful model takes the reality, makes some simplifications, then does some math magic and can say something about reality. A useles model tries the same, but made too many simplifications and therefor does NOT say something about reality.

Now your “model” (sorry but it kinda hurts to call it such) is very far from reality. Not only do you talk about local maxima (and therefor imply that there is a global maximum, a kind of a holy grail of video games), you also fail to ask what a maximum (global or local) even means. You also do not really define “step” (you only give a meaningless example).

Therefor, your model does not help us understand AoE2 at all.

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