Rough payoff times and exchange rates

[SevenSpirits]

Do citizens really cost 1 per turn in maintenance? I thought it was more like 0.4, divided about evenly between city and civic maintenance upkeep, plus a little bit for inflation and high difficulty. Are you abstractly factoring in costs like upkeep for police units and workers? Or even their initial build cost too?

Good question. The answer is, unfortunately, that I'm just fudging it and it seemed like a nice approximation. I hope it does account somewhat for the increased necessity of military protection, settling new land, and worker support (although not fully, since they are typically sunk costs at the time of deciding whether to grow or not). Although in pbem29 I've been noticing a pretty 1:1 correlation between whipped-off population and lowered maintenance costs in gold.

I also want to think about where do mines fit on the tile priority order? A grassland hill mine in your system is 23 points, minus the 19 for upkeep, which is pretty pedestrian. A plains mine is even worse at 20 - 19 = barely positive at all. This does feel like it matches my experience; I seem to work cottages over mines most of the time, the exception being when a city has really big food from resources such that it'll hit the happy cap unless it slows down growth by working mines.

Yeah, mines are interesting. Their value is generally poor, but this poverty is based on their lack of food. When building workers/settlers they are suddenly incredibly efficient since both food surplus and hammer surplus get converted to foodhammer surplus. A plains mine that you can afford the food cost of, building a worker, is worth net 2 foodhammers - 1b so 9 points - an incredible improvement. (Though keep in mind that whipping workers/settlers, or completing them with overflow, also carries increased value. Maybe it's best to think of there being a cost associated with every turn a worker/settler is in the queue. Or maybe I should just count foodhammers as 5, too - hm...)

Mines are also good when you can't whip, either because of no slavery or you're building wonders. And in a city with low food/production that needs to produce things, mines (well, grass mines at least) are a decent improvement that emphasizes this rather than commerce, although farms are usually better.

As for the growth of cottages... I tend to think of them in terms of their fully improved town value of +5 or +7 commerce.

That is an approximately correct way to think of them although you should really discount that +5/+7 for time. (You are getting an extra turn of +5/+7, but it's far in the future so not worth as much!) Doing so leads to thinking of a fresh cottage as I've valued it as about +3, and increasing slowly over time to reach +5/+7.

Am I right in thinking that this tool has been designed for use after about T40, T50 in a quick PBEM game? That it was calibrated using PBEM games, and not, for example, PB3?

Yeah, you could say that.

How are you accounting for GPP in this formula?

GPP are hard. I'm working on it.

[Krill]

Yeah, you could say that.

The tool makes some sense then, for already established cities that have basic infrastructure and tile improvements down already. I don't think it's possible to assign arbitrary values to food, hammers and beakers in the early game, the requirements of the start can vary too much...but as you said, you're assuming size 7-ish with a granary, so that pretty much agrees with my thoughts on the matter.

Question: Have you attempted to value workers in this, or city centre tiles? I'm thinking specifically because workers are an upfront investment but they have to be built and they can be built either via the slave or hills, and you haven't taken that into account. City centre tiles, well, I'm wondering how you would quantify the advantage of settling on that plains hill.

Also, how does all of this interact with that fickle idea of "Turn Advantage", that getting to something one turn quicker will speed up the snowball?

[darrelljs]

That leads to another area of the discussion: the overall cost to add a productive citizen to your empire.

Unconquered Sun gives an excellent analysis of this question in the context of Deity level play and Hereditary Rule. Probably the best post I've ever read, at least at CFC.

Darrell

[SevenSpirits]

I don't think it's possible to assign arbitrary values to food, hammers and beakers in the early game, the requirements of the start can vary too much...but as you said, you're assuming size 7-ish with a granary, so that pretty much agrees with my thoughts on the matter.

Right. Food's value goes up incredibly when you are growing onto resources. Production's value goes up incredibly when you can build a granary or a worker/settler that is necessary to improve/claim resources. Commerce's value goes up incredibly when you don't have the techs for basic tile improvements yet.

Question: Have you attempted to value workers in this, or city centre tiles? I'm thinking specifically because workers are an upfront investment but they have to be built and they can be built either via the slave or hills, and you haven't taken that into account. City centre tiles, well, I'm wondering how you would quantify the advantage of settling on that plains hill.

Well settling on a plains hill isn't that hard, it just gives an extra production every turn, so I would quantify that as +5 points/turn. (Though like you say the early turns have a lot of special circumstances that muddy this quite a bit.)

I have not really attempted to value workers except that apparently they are a good deal compared to growing your size 7 granary city approximately when worker turns are worth more than 2 foodhammers/turn to you.

Also, how does all of this interact with that fickle idea of "Turn Advantage", that getting to something one turn quicker will speed up the snowball?

Well on average this idea is accounted for by the interest rate and the basic idea that stuff now is worth more than stuff later. But there are so many special circumstances and edge cases. Like I said in the intro paragraphs, before you complete something your interest is not compounding at all. After you complete it it's probably worth a little bit more than the average interest rate, so that it all balances out.

Typically these edge cases are where you can make concrete calculations about what you are gaining and losing, like growing a turn sooner may result in +3f, -7h, +4c. And if you want to look ahead farther to the next time you grow, and the next, you can see further whether that 3f you gained has above or below average value. And similarly you could find out how much time on your next building the 7h will save you, or whether the 4c will save you a turn on an important tech. At some point this is too much work and you just want a rough estimate, and that's what the formulas are nice for.

[mackoti]

Your link has a single problem,darrel its for SP not for MP.In my SP game i can get Comunism very fast(500- 1000ad) so cottage has no value there,if it isnt in buro capitol,but in MP getting that will be very dificult becasue my oponents might not agree(if its not pbem24 or 23),and i need Military techs and there cotage became more stronger than a mine,i need pop to whip for emergency and again cottage its stronger and i have to build military anyway so i can put those at good use.

[luddite]

The tile yields sound about right. The civ4 AI evaluates tile yields as 5:3:2. If we assume that commerce= beakers, that's basically the same comparison as the values you've given (not quite the same, but very close). This thread argues that windmills are actually the best tile improvement in the late game (combined with towns) since they maximize those values. That being said, I think that might overemphasize food- you always see the civ AIs building too many farms, and then stagnating on health and happiness. GPPs also give a diminishing return with more farms.

For interest rate... I dunno. I've thought about that as well, and I'm not sure it's possible to calculate a fixed "interest rate" like that. If the interest is constant, that would imply (by math) that your total yields should all follow a simple exponential curve. In the beginning that might be true, but in the late game the growth seems more linear than exponential. At any rate, the rate of growth is going to depend a lot on how resource-rich the map is, how good your micro is, and how much military you have to build. It's definitely worth thinking about long-term profit vs. short-term profit, but I don't think you can use a single number like 20 turns for all game situations.

[mackoti]

Yeah windimils are very good.

[Compromise]

Interesting discussion. I've found that unit builds are particularly difficult to put a value on because their payback depends on who your neighbors are and what they're doing.

[Krill]

OK, some points from my experiences: http://realmsbeyond.net/forums/showpost....tcount=287

From PBEM4V:

OK, extra Information...

t105 - Breakeven @ c 310 bpt (Lib)
t118 - Breakeven @ c.560 bpt (after PP)
t125 - Breakeven @ 825 bpt (just before 1st GA)
t133 - Breakeven @ 1255 bpt (just after 1st GA)
t144 - Breakeven @ 1910 bpt (which is about 96-97% of the slider)

The first 3 figures have no Bureaucracy or Academy, the t133 figure has FS and Academy, and the fourth figure is purely theoretical because of the slider restrictions

That's a fair bit faster that 3.5% growth, even excluding the effect of civics and the Academy.

Unconquered Sun gives an excellent analysis of this question in the context of Deity level play and Hereditary Rule. Probably the best post I've ever read, at least at CFC.

Darrell

As mackoti says, that's for high level SP games. I've only seen that idea done twice: in the MTDG and PBEM23. In the MTDG it only worked because tech trading was on and it was 3v1.5, and I almost pulled that one off. In PBEM23 mackoti managed to stop the snowball (I know that is a simplistic explanation but it's also true). A counter point would be PBEM2 up until about Astro, because after that the diplomacy broke that game...(no, I'm not going to forget that either, Darrell )

Typically these edge cases are where you can make concrete calculations about what you are gaining and losing, like growing a turn sooner may result in +3f, -7h, +4c. And if you want to look ahead farther to the next time you grow, and the next, you can see further whether that 3f you gained has above or below average value. And similarly you could find out how much time on your next building the 7h will save you, or whether the 4c will save you a turn on an important tech. At some point this is too much work and you just want a rough estimate, and that's what the formulas are nice for.

Yeah...tbh, I kinda want to stay out of this discussion because I will usually work all of this out in advance to make decisions. However, a series of case studies would probably be much more informative and helpful in explaining how and why the numbers you're using work well.

[darrelljs]

I wasn't aware this was an MP only thread .

Darrell