Quantitative Spring Economics

[Caydr]

Isn't this what AI does, or have AI developers just been using random numbers all this time?

[Beherith]

As Caydr said; there are five resources, I would like to rank them by my perceived importance:

Command time
Game time
Energy
Buildpower
Metal

[Caydr]

Metal at the bottom? :S In what sense?

[AF]

There are various approaches, and whatsmore these formulae are predictive of the future actions results, they are not authorative of the current actions nature save by guidance.

[Caydr]

I need a coupon just to get through the first 10 words.

[JohannesH]

Game time is not a meaningful resource... Its same for both players, just dictates the rate of getting the other resources. If you wanted to get fancy, like when making an AI or something, you could say army and intel are kinda like resources though...

And BaNa, no you cant find relevant solutions to a question like how to best tech on dsd, or even how to rush adv fus on dsd with 3 mexes and no help in an optimal way. When you have to take into account all the ways the enemy can attack you while youre chilling, and what kind of attacking options you have when youre done... Should you share e/m/cons to allies etc etc..

[AF]

The existing algorithms in AIs that concern this kind of formula do not dictate what to do to the AI, rather they are used as a check or guide in decisions, not as decision makers in themselves.

For example, NTai has about 8 algorithms that attempt to predict whether the economy will stall or not if a new construction task is started, so as to prevent teching to tier 2 as soon as the first conbot has been built. Some of these algorithms work better than others, and one or two are quite simply attrocious, but they are not authorative, they are simply checks used in a logic flow, they hold no logic themselves.

As with all decisions though, the more accurate data you have, the better informed you are, and the more rationalizations you can make. Having newer algorithms and ideas based on different concepts is useful in that respect, and that is why these threads can sometimes yield useful insights or formula.

Sure they will always be aproximations of some kind, but what we have in our heads are mere approximations, and AIs have to rely on these systems, so why not refine them anyway for the purposes of a better computer opponent?

[hunterw]

Again, I'm saying: Find the optimal teching strat for exactly one map, one position on that map, assuming the enemy does not attack, and you don't need to worry about speed and nano distance.

There are standard methodologies for modeling error in these situations so it's not like you wouldn't be able to show in a reasonably rigorous way that you were probably pretty close.

pretty close is as close as we're ever going to get, and we are already there.

[squeakycleaners]

On the warfare side of things, I think this might be useful for modeling combat in TAS.
http://en.wikipedia.org/wiki/Lanchester%27s_laws

[Argh]

lol @ using a WWI theorist's concept for anything even vaguely approaching a reasonable result for modern combat, given that his equation doesn't even address shelter or dispersion

Or, to quote Ernest Adams, who already said it neatly:

Lanchester's Laws also don't take into account such considerations as terrain, morale, weapon range, movement and maneuver, surprise, weather, and many other issues that have decided battles over the centuries. In fact, various people have argued that in actual battle situations Lanchester's laws are well nigh useless. (See the works of Col. Trevor N. Dupuy for further criticism; Dupuy favored an empirical model of combat based on analysis of real, historical battles -- not numerical analysis.)

He goes on to say that Lanchester's Square can be applied to rough balance, but only with obvious caveats...

[Evil4Zerggin]

Previous topic on this subject:

http://springrts.com/phpbb/viewtopic.php?f=14&t=18228

[Gota]

You have all wrote that it is impossible to make an accurate equation that is elaborate enough to take all the game elements into consideration.

Well I bring you my equation.
It is very complex and takes time to understand all the different variables and the conclusions of such an elegant equation but once it sinks in you'll never think of game balance in the same way.

http://img28.imageshack.us/img28/5921/awesomea.jpg

[squeakycleaners]

lol @ using a WWI theorist's concept for anything even vaguely approaching a reasonable result for modern combat, given that his equation doesn't even address shelter or dispersion

Or, to quote Ernest Adams, who already said it neatly:

Lanchester's Laws also don't take into account such considerations as terrain, morale, weapon range, movement and maneuver, surprise, weather, and many other issues that have decided battles over the centuries. In fact, various people have argued that in actual battle situations Lanchester's laws are well nigh useless. (See the works of Col. Trevor N. Dupuy for further criticism; Dupuy favored an empirical model of combat based on analysis of real, historical battles -- not numerical analysis.)

He goes on to say that Lanchester's Square can be applied to rough balance, but only with obvious caveats...

You say that but Lanchester's laws have been applied to as unrelated a subject as buisness management. While I agree that full scale, combined force battles would be poorly modeled by these equations, small skirmishes with a handful of slow unmaneuverable units on each side and with all weapons in range and have low splash damage could provide useful predictions. Like 5 hammers vs. 7 hammers might be resonable.

[Argh]

Oh, sure... it works just dandily, for like-vs-like.

Problem is, RTS designs aren't about like-vs-like. It's not even apples and oranges... more like small orangutans named Sue vs. a small kinetic sculpture.

Seriously, guy. Read at least some of the massive walls of text that have come before you even got here, this is a subject that's been explored a lot. I still like my theory of probability spaces in the context of time, but I haven't the slightest inclination to talk more about it atm.

[JohannesH]

I still like my theory of probability spaces in the context of time, but I haven't the slightest inclination to talk more about it atm.

Sounds really awesome but can you actually translate that theory into playing well?

[Argh]

The theory isn't for playing, per se. It's a design concept- how to figure out how far you can push your assumptions about balance, and when they're going to go out the window, other than the biggest items of leverage. My theory is mainly concerned with when the probability space gets too large to model any more, even if you dumb things down.

In terms of play, i.e., application... it's stuff that's obvious to anybody who's played an RTS competitively: there are distinct stages, they differ based on the map and the faction, and knowing what they are and which stage your opponent is at is usually the key to winning, all other things being equal. No theoretical model can factor in completely failing to scout, not knowing how to kite, etc., of course.

[YokoZar]

You say that but Lanchester's laws have been applied to as unrelated a subject as buisness management. While I agree that full scale, combined force battles would be poorly modeled by these equations, small skirmishes with a handful of slow unmaneuverable units on each side and with all weapons in range and have low splash damage could provide useful predictions. Like 5 hammers vs. 7 hammers might be resonable.

This is close enough to true when the units stand in a line and shoot eachother Napoleanic style.

Spring has an implicit outnumbering bonus though - the bonus damage you do when you hit an enemy from multiple directions. Larger forces of the same unit are much more able to surround the enemy, meaning they have an even bigger advantage than the n^2 law would suggest.

At ideal positioning (units opposite eachother attacking the same unit), you do on average 50% more damage per shot. I believe this means that while the smaller group has power n^2 the larger group has power (1.5n)^2, or n^(2.25)

[squeakycleaners]

This is very interesting. Is this bonus programmed in or is it a result of the units having greater difficulty firing on targets from different directions? I would think that envelopment would be the same as being lined up as long as the units are all within range of each other, however I might be missing something.

I am getting tired of people saying this has been discussed before; It hasn't. Sure mathematical balancing has been discussed, however a rational approach to optimum game play has only been lightly touched. They are only distantly related.

Also, for you people who lack faith in formulaic methods:
What would you propose would be the best way to optimize gameplay?
Simulation?
Emperical data & statistics?
Manual trial and error?

[Argh]

This is very interesting. Is this bonus programmed in or is it a result of the units having greater difficulty firing on targets from different directions? I would think that envelopment would be the same as being lined up as long as the units are all within range of each other, however I might be missing something.

It's an auto-bonus, basically all Units have a "shield" that reduces damage when attacked by one enemy, but if hit by more than one during a short timeframe, the second shot does damage based on how much arc it is away from the "shield's" center. Most games other than BA don't use it, it was an obscure part of the source and until a couple of years ago, we didn't know it was there, even though we knew our numbers weren't coming out right...

Sure mathematical balancing has been discussed, however a rational approach to optimum game play has only been lightly touched. They are only distantly related.

No, actually they're very tightly related subjects. If you know how a game is balanced, ergo, you know how it's imbalanced, and therefore can structure your strategy around using those imbalances to your advantage.

IOW, you can't form a strategy for burning the forest down, if you can't see the trees or know that pouring gasoline in a circle around yourself and tossing a match might 'succeed', but hardly be optimal.


Basically, what you want, if you're looking for optimal strategy, is to determine your scope until you hit the chaos point (in OTA games, depending on the map, that's 4-8 minutes) and to develop strategies for that map that optimize for the resource you think is most important. The big key is, what resource do you want to have more than your opponent of, all other things being equal?

Time, as in, you've had more time to consider each move or micro-manage your units?
Knowledge of enemy dispositions?
Raw materials (M&E)
Map control, i.e. you have established areas where the enemy may not expand without exchanging at a loss?
Assault forces?

I'll leave it to expert BA players to define what they think is the key thing to have, by the time you reach the chaos point (commonly referred to as, "early midgame"), but you get the idea. It should be possible to empirically design, test and evaluate strategies that produce the optimal results for each resource... on a per-map basis. You will find that it's utterly impossible to apply it carte-blanche to every single map, or even every start position on a given map (see: north player on DSD vs. playing on the southern plain).

[hunterw]

I haven't the slightest inclination to talk more about it atm.