Forged Alliance Forever

Re: Exponential or Linear (on-topic)

2012-08-16T00:22:29+02:00

Damn college level math... Calculus II was bad enough... Now we have TA going all smart on us.
*tries to understand*
*fails*
*goes back to not upgrading mass and spamming t1*

Statistics: Posted by Cerberus — 16 Aug 2012, 00:22

Re: Exponential or Linear (on-topic)

2012-08-15T22:58:23+02:00

M - mass income
t - time
f(t) the fraction of the mass that the player chooses to invest back into eco, adjusted by the efficiency of this project(mass invested in a t1 to t2 ugprade gives a different return than mass invested in a t2 to t3 upgrade)

The main principle of supcom fa economy, the more you invest the more you get back.

dM/dt = f(t)M

The solution to this differential equation is dependent on the specific form of f(t).

If we approximate f(t) as a series of step functions in time
f(t) = {a for t=0..t_1, b for t=t_1..t_2, ... , z for t = t_n..t_final}
the problem can be split up into n parts and solved on each separately then put back together:
M(t) = {exp(a*t) for t=0..t_1, exp(b*t) for t=t_1..t_2, ... , exp(z*t) for t = t_n..t_final}

In other words the supcom fa economy is exponential anytime the above assumptions hold, but the exponent constant varies as the player changes the number of engies assisting mass extractors or when there is a switch between the type of upgrades.

One example of when the assumptions do not hold is when a player has 0 mass in storage and their mass income is fluctuating randomly due to mass reclaim. In this situation the function could be a whole bunch of different things.

Statistics: Posted by SeraphimLeftNut — 15 Aug 2012, 22:58

Re: Exponential or Linear (on-topic)

2012-08-15T21:45:09+02:00

I played the game to back up the statement that if someone plays sim city their eco will be exponential. Thank Ghoti for this, it was him that suggested it wasn't obvious enough.

The only way to have a linear economy is to reduce the proportion of you mass that you invest into it as your eco gets better. I'm not talking about an approximation of the entire game here, as I stated before I'm talking about how your economy will increase via one method of upgrading it. Necessarily you will move onto less efficient ways of upgrading it as time goes on (causing the gradient of our income graph to go down again), which may give some people the mistaken impression that it is indeed linear.

Nor am I saying that all the time your eco is increasing on an exponential function. In fact I do recall saying that a graph of income is a series of horizontal and vertical lines, aka its not a continuous function. What I am saying is that while you are putting mass into economy, broadly this will approximate to an exponential curve in every case at every point in the game. This is because you put more mass into your eco as time goes on. That is the basic premise. If thats not happening then you're either losing or will be fairly shortly.

Statistics: Posted by Softly — 15 Aug 2012, 21:45

Re: Exponential or Linear (on-topic)

2012-08-15T21:13:32+02:00

SeraphimLeftNut wrote:
Thank you Cerberus. This should now all be clear to everyone.

why all the party pooping? if it is obvious to you, dont click on the thread.

Statistics: Posted by rootbeer23 — 15 Aug 2012, 21:13

Re: Exponential or Linear (on-topic)

2012-08-15T20:56:36+02:00

SeraphimLeftNut wrote:
Are the hopes of getting raw data from replays completely gone? Is the problem too difficult?

it seems to be possible. but i have to get my ass up. You may want to lobby Ghoti, he seems to be more proficient with lua.
Converting base64 to csv data is comparatively trivial.

Statistics: Posted by rootbeer23 — 15 Aug 2012, 20:56

Re: Exponential or Linear (on-topic)

2012-08-15T20:47:01+02:00

Thank you Cerberus. This should now all be clear to everyone.

Statistics: Posted by SeraphimLeftNut — 15 Aug 2012, 20:47

Re: Exponential or Linear (on-topic)

2012-08-15T20:41:49+02:00

Maybe I am Either incredibly gifted, or stupid, because All I know about the economy without all this damn college level math (which I hate) boils down to this.
A guy with 5 Mex will be able to exponentially skyrocket his Eco over a guy with 4 Mex, because he has that small extra boost, to be put into more Mex, which in turn puts into even more Mex....
While the guy with 4 Mex points, will be able to do the same thing, but the increase is less steep.

So, In a game, when someone takes 80% of their Mex, dedicated to army, and 20% to more Eco, They will increase their Eco exponentially over the guy who dedicates 90% to army, and 10% to Eco... Assuming he survives, ofc.

Statistics: Posted by Cerberus — 15 Aug 2012, 20:41

Re: Exponential or Linear (on-topic)

2012-08-15T20:23:40+02:00

rootbeer23 wrote:
more like: (a+b)^2 != c^2

ok, i see that this diagram is geometric proof of pyths law. no need to correct me.
But since the lengths of the shapes are not measured and added up, that is a real proof applying to all right triangles.

Statistics: Posted by rootbeer23 — 15 Aug 2012, 20:23

Re: Exponential or Linear (on-topic)

2012-08-15T19:38:35+02:00

This whole discussion is going nowhere, since you guys can't agree on what it means for economy to be linear or exponential. Since in Supcom FA the player has control over economy, the actual mass vs time curve will be different for every single game.

I think the most that can be said that in some cases the player has the ability to have their economy grow exponentially for some period of time during the game.

Are the hopes of getting raw data from replays completely gone? Is the problem too difficult?

Statistics: Posted by SeraphimLeftNut — 15 Aug 2012, 19:38

Re: Exponential or Linear (on-topic)

2012-08-15T19:23:08+02:00

Ghoti wrote:

more like: (a+b)^2 != c^2

Statistics: Posted by rootbeer23 — 15 Aug 2012, 19:23

Re: Exponential or Linear (on-topic)

2012-08-15T19:21:47+02:00

rootbeer23 wrote:
but go ahead, draw another graph. If you want best results, look at the air spot.

So that's a no then to one of yours? kk.

Statistics: Posted by Ghoti — 15 Aug 2012, 19:21

Re: Exponential or Linear (on-topic)

2012-08-15T19:11:38+02:00

Ghoti wrote:
Personally, I'm here to find out what forged alliances economy does in an all out tech when you factor in build time, the increasing cost of investment, and the whimsy of the random number god.

That's why I wanted to see root at air in sentons. I don't have 3599 so I can't launch these: http://supcomfaguide.uw.hu/challenge.html

You can study any game of setons, and any of the army positions. as long as the game does not contain some unlucky destruction of mass extractors, each of the 8 economies will be exponential with varying degree.
I was really hoping that you could get your answer without a replay (it's not rocket science), but go ahead, draw another graph. If you want best results, look at the air spot.

Statistics: Posted by rootbeer23 — 15 Aug 2012, 19:11

Re: Exponential or Linear (on-topic)

2012-08-15T19:10:46+02:00

rootbeer23 wrote:
Playing a game to prove that eco is exponential is like proving pythagora's law by drawing triang

seems pretty pointless doesn't it? Yet, someone took the time.

Statistics: Posted by Ghoti — 15 Aug 2012, 19:10

Re: Exponential or Linear (on-topic)

2012-08-15T19:03:30+02:00

Anaryl wrote:
DilliDalli wrote:Played a game where all I did was build kennels mass fabs and pgens (both t2)

So we've discovered that if you do nothing but eco, cherry pick the results, you can achieve exponential growth.

It proves that Dillis eco in one particular game was exponential. That is if you consider a bunch of numbers a proof. I would not. There are infinitely many polynomials that would generate the same few numbers. But ok, lets be practical.

Anaryl wrote:
So that proves FA ecos (under real conditions) are not linear?

[/quote]

It proves that an economy can be exponential. I hope i dont have to make a similar stunt to "prove" the statement:

If Dilli had started a landfac at minute 1 and produced infinite tanks (linear production), his eco would still have been exponential.
If Dilli had started a landfac at each full minute and produced inifinite tanks from all (quadratic production), his eco would still have been exponential.
If Dilli had invested only 1% of his mass income to produce an ever increasing amount of factories and tanks, his eco would have been exponential.
If Dilli had invested 99% of his mass income to produce units and 1% to produce more eco, his eco would have been exponential.

Statistics: Posted by rootbeer23 — 15 Aug 2012, 19:03

Re: Exponential or Linear (on-topic)

2012-08-15T18:50:49+02:00

DilliDalli wrote:
Played a game where all I did was build kennels mass fabs and pgens (both t2)

interesting how the topic still survives. Playing a game to prove that eco is exponential is like proving pythagora's law by drawing triangles. I now that the idea was actually Ghotis, i am not blaming you Dilli. BTW. that previous longer post in this thread was an excellent description of the problem. As for the results: nothing unexpected.

Statistics: Posted by rootbeer23 — 15 Aug 2012, 18:50