T-hawk Plays Alpha Centauri

[T-hawk]

I don't feel like I am playing the same game as you.

I'll sound arrogant, but, why aren't you?  The core of what I'm doing is beeline Industrial Automation, build the PTS with crawlers, rush-buy pods to expand hard horizontally.  Anyone can do that.  The details of micromanagement and terraforming and drone control are incremental margins on top of that.

If you aren't doing that because you want to play Blind Research or self-restrain from ICS or crawlers, then yes, you indeed aren't playing the same game.

Not sure if I missed some other consideration here, but a linear, quadratic, or cubic function is still a polynomial function. They are not exponential functions because they are still defined by a polynomial.

You're right, of course.  I was speaking colloquially where polynomial growth is often mistaken for exponential.  I half-knew I was describing it wrong but actually couldn't think of "polynomial" as the right word.

As for the red outline, I like it mostly because the visual indicator avoids me inadvertently terraforming a square outside my base radius.  Also helps me gauge just how much I'm overlapping and cramming in bases.

[induktio]

If there's some group that could be really triggered by using polynomial and exponential terminology interchangeably, it's probably the theoretical computer science people.

Most of the time the usefulness of algorithms is defined by whether they can be calculated in polynomial time (useful) or exponential time (often unusable). So that kind of issue is very commonly encountered. This distinction is also related to P vs. NP question, which is still the biggest open research question in CS.

[T-hawk]

You'll appreciate this bit then.

I played a couple practice and experimental starts without using the PTS. Bases would build a new colony pod roughly every 10 turns. But new bases didn't do that right away; they took about 10 turns to build formers and grow to size 2, then after that could produce a pod every 10 turns. That lag meant I wasn't exactly doubling my base count in every interval, but it was still exponential growth, I felt like the exponent was something like 1.6 for each time interval.

Then it hit me. At each step, my count of bases was the count from one step ago plus the count from two steps ago, since those bases had built new pods. Sum of the previous two steps... that's the Fibonacci sequence! Which grows by the exponent of the golden ratio, which is indeed just over 1.6.

[induktio]

Did you happen to plot the number of bases vs. turn to see how well it fit to the sequence?



Now that I think of it, there might be another special case too. Normally the growth is dominated by the building cost of new colony pods, but what if the movement cost instead was the limiting factor? Given very low building cost of new colony pods and very slow movement, the expansion might indeed be bounded to quadratic growth. Only a limited number of bases can be placed on given terrain and the new area being acquired can only increase in a quadratic fashion. I'm not sure where exactly the crossover point between exponential and quadratic growth is here though.

[T-hawk]

Man, we're gamer-nerd-mathematicians if we're looking for a closed-form solution to a 4X game.

I didn't keep track exactly.  It matched the sequence very closely by thinking in terms of it as 'generations'.  The turn numbers would be fuzzed a bit with the movement time and available food to grow, but I could pretty clearly see which group of bases comprised each generation/step of the sequence.  Each was double the actual Fibonacci numbers since we start with two colony pods.

Yes, movement time would eventually limit it to quadratic (and of course you're eventually bounded to zero growth once the map is full.)  But you can get lots of tricks to increase the movement: rover formers building roads, mag-tubes, needlejet colony pods or transports, drop-pods on the colony pods.  I could envision that on a real map it's possible to keep expanding the movement range enough that the Fibonacci sequence continues until the map is full, so that you go right from exponential to zero and there's never really a polynomial bound.  In fact I think that probably did happen in principle in that oldest tiny-map transcendence writeup.

How about other games? Civs 3 and 4 behave the same way, except it takes longer for a new base to mature than for a mature base to build a settler. The sequence is more like one step ago plus four steps ago, still Fibonacci-ish and exponential but with a lower exponent. Civ 5 doesn't do this - mature bases basically never build settlers, it's always cheaper to build them from the capital or buy with gold. Civ 6 I'm not sure how to evaluate with the escalating cost for each settler.

[shallow_thought]

I don't feel like I am playing the same game as you.

I'll sound arrogant, but, why aren't you?  The core of what I'm doing is beeline Industrial Automation, build the PTS with crawlers, rush-buy pods to expand hard horizontally.  Anyone can do that.  The details of micromanagement and terraforming and drone control are incremental margins on top of that.

If you aren't doing that because you want to play Blind Research or self-restrain from ICS or crawlers, then yes, you indeed aren't playing the same game.

I played AC and loved it for a long time while I had no idea what I was doing. I'm not dumb, but I used video games as a way to relax a busy mind, keep it ticking over, like motorway/freeway miles rather than racing/rallying like the day job. Once I realised quite how sub-optimally I had been playing I gave it another go. And enjoyed it less. Each to their own. Part of the genius of games like AC and Civ IV is how the are a layered experience, open to a range of players.

Now, I enjoy seeing the unexplored horizons, just as I love reading books about 19th century Antartic expeditions. And there is a strict sense in which play that wins faster, or at higher levels, or that would unquestionably win if going head to head is better ... but the other modes of playing this game still have value.

If there's some group that could be really triggered by using polynomial and exponential terminology interchangeably, it's probably the theoretical computer science people.

And in real life*, all that matters is staying O(log n) rather than accidentally introducing an O(n^2) dependency.

*Value of "real life" may vary.

[T-hawk]

Something to read on a summer Friday, have one more. http://dos486.com/alpha/drones/

[induktio]

At first I thought, T-Hawk playing the expansion, what is this heresy? But not surprisingly this was the case: "a playthrough of Alpha Centauri, with the base game not the Alien Crossfire expansion, but using an edited file to play as the Free Drones faction from the expansion."

I have to agree about the weak narrative qualities of the expansion factions, that's why smac-in-smacx mod was also combined with my Thinker AI improvement mod. One interesting new feature there is that one is able to select any custom/expansion factions while playing with the original SMAC ruleset, or as close to it as one can get while using the SMACX binary. The feature was needed because otherwise there was no easy way (without overwriting files) to change the set of factions used while playing in SMAC mode. Although you achieved the same end result with some kind of a smacx-in-smac mod.

[Modo]

And to think that not that long ago this section of your site had one old play through and now we ended up with a close to 200 bases one.
I'm sure it's plainly obvious but sometimes even the obvious is worth stating: you are taking us through some crazy rides, T-hawk, and it is very much appreciated.

[LKendter]

How much time did a single turn take with 180 bases?
WOW