[SPOILERS] William discovers a source of horse. FDR of Mongolia

[suttree]

A few things:

The only (original) estimate of the growth rate in Civ4 I've seen is by Seven and he suggests a doubling every 30 turns on normal speed. The 5% number you quote reflects the growth rate on quick speed (a doubling every 20 turns) and even then 5% is misleading since it's better to model the economy as compounding.

An estimate of (or at least a lower bound on) the growth rate is really important because it allows you to calculate the present value of a per turn income. And this allows you to model an answer to many of the questions you ask.

Using Seven's model for the average growth rate, assuming the economy compounds every turn - which it doesn't - you get an average growth rate on normal speed of 2.34%.

So a per turn income of 1 resource per turn has a present value V=1 + r + r^2 + r^3 ..... where r~=1/1.0234.
That is V=1/(1-1/1.0234)~44. Seven rounds up to 45. Based on a model where the economy compounds less frequently, I suggest a lower number - 42 - because the answer is always 42.

You can find the full masturbatory episode here: link

This allows you to value your options pretty well.
IE is building X worth it? What is the trade off of 1h in to infrastructure vs. 1h in to gold?

Briefly:

*I think a worker turn has an opportunity cost of 2h + maintenance.

So this seems to lead to the heuristic that you're doing it right when you have just enough worker turns to improve while cities grow, and just enough cities to use tiles as they are improved, and no more of either.

*I think this is right. Your best investment is always going to be developing *new* resource tiles, plopping a granary on top, then making sure you get something out of the interim labour resulting from the whip-cycle. IE 30h or even 25h towards a settler/resources/granary combo is better than working a non-resouce tile (without whipping) at small sizes.

[WilliamLP]

You can find the full masturbatory episode here: link

This allows you to value your options pretty well.
IE is building X worth it? What is the trade off of 1h in to infrastructure vs. 1h in to gold?

Interesting, thanks for the thoughts. I confess I haven't read your PB11 thread - I met you only after that whole shit storm with Sisub went down. I'll read it now though, knowing there's equations in it, lol. I know that you and Oxy have been doing micro and planning in PB14 that's currently beyond me.

I speculate, also, that if you measure the global expansion rate it can still be a good idea to build things that return less than it. This is because the global rate includes a lot of very high return builds, like granaries in new cities, which drive the average value of a build above what the replacement value would be. (I.e. when deciding whether, say, a courthouse is worth it, it should be compared to what the alternative would be in that city, which may return less than the global average.)

It's also not a given that everything grows geometrically, especially later in the game when land is taken.

[suttree]

I'll read it now though, knowing there's equations in it, lol.

Well, since it was my first real game of Civ4, there was a lot of dumb stuff in it. I didn't know how granaries worked, for example.

I speculate, also, that if you measure the global expansion rate it can still be a good idea to build things that return less than it.

The idea is that post-Currency you always have the option to build wealth, so this would be false. In the model, an investment in the tech tree always has a return equal to the average growth rate. You have to use your judgement of course, but it does allow you to make consistent choices about wealth builds/fail gold versus infrastructure.

In the case of putting hammers in to a courthouse, for example, the model suggests that until your courthouse saves you ~3g/t you probably want to build wealth. Building wealth isn't the "right answer" - it's just the answer that follows from the model's assumptions. The model is useful because forces you to ask why the assumptions aren't true in the particular case.

If you're whipping below happy cap, then the model says you should whip the courthouse when the return on the courthouse is greater than the return on the labour you sacrifice. The model is useful, for example, because it allows you to calculate the present value of a cottage turn. Sometimes working cottages is better than sacrificing pop for the courthouse.

If the city is going to hit happy cap, things get a little more complicated. Killing the return on the granary by stagnating has a cost too.

It's also not a given that everything grows geometrically, especially later in the game when land is taken.

This is a bit tricky - remember that in the model a lot of value is being captured in the tech tree. What is the value of having access to Tanks when your opponent has only Spears, for example? The model captures that by saying every beaker invested in the tech tree pays interest (somehow) at the mean rate of interest.

The assumption is that, most of the time, the game is balanced so that investment in the tech tree is worthwhile. If that assumption is false, then you probably should be building troops and smashing your neighbour - not making commerce investments.

[WilliamLP]

I speculate, also, that if you measure the global expansion rate it can still be a good idea to build things that return less than it.

The idea is that post-Currency you always have the option to build wealth, so this would be false. In the model, an investment in the tech tree always has a return equal to the average growth rate. You have to use your judgement of course, but it does allow you to make consistent choices about wealth builds/fail gold versus infrastructure.

So I can conclude then (can't I?) that post-Currency, the value of the average build must be greater or equal to building wealth. Or else I'd just build wealth everywhere, and nobody does that. (Obviously it's not linear though, some things like units and workers are crucial to a certain number, and then decline in value over that threshold.) Yet, wealth may be the best build at some times or in some cities, despite it being less productive than the global average, because it's locally the best choice (perhaps at a certain time to speed a tech).

(By "value" I'm not just talking about value in beakers or gold but something more abstract.)

In the case of putting hammers in to a courthouse, for example, the model suggests that until your courthouse saves you ~3g/t you probably want to build wealth. Building wealth isn't the "right answer" - it's just the answer that follows from the model's assumptions. The model is useful because forces you to ask why the assumptions aren't true in the particular case.

Even ignoring benefits of EP and enabling FP, the model has to be more complicated than that, doesn't it? Because it doesn't just save you 3gpt, it saves you half of the maintenance of the city forever which should eventually rise. I'm sure you could still put reasonable bounds on what the net present value of that is, though.

If you're whipping below happy cap, then the model says you should whip the courthouse when the return on the courthouse is greater than the return on the labour you sacrifice. The model is useful, for example, because it allows you to calculate the present value of a cottage turn. Sometimes working cottages is better than sacrificing pop for the courthouse.

If the city is going to hit happy cap, things get a little more complicated. Killing the return on the granary by stagnating has a cost too.

Interesting, and yeah I can see that. It seems like in RBMod a granary in the capital is a much less valuable build because whipping is not nearly as useful and it has already probably grown to its cap by the time you can build one

The assumption is that, most of the time, the game is balanced so that investment in the tech tree is worthwhile.

Challenging assumptions is what I'm looking to do... There seem to be a lot of places in the tech tree where investment is more worthwhile than others. Knights are an obvious quantum leap. If you get knights and cats quickly, you can fight with that for a long time before anything new comes up that makes them obsolete.

Of course, what I may end up doing is looking for ebbs and flows and discrete break points around models while making plays that are just simply bad by any reasonable measure.

[SevenSpirits]

I speculate, also, that if you measure the global expansion rate it can still be a good idea to build things that return less than it.

The idea is that post-Currency you always have the option to build wealth, so this would be false. In the model, an investment in the tech tree always has a return equal to the average growth rate. You have to use your judgement of course, but it does allow you to make consistent choices about wealth builds/fail gold versus infrastructure.

So I can conclude then (can't I?) that post-Currency, the value of the average build must be greater or equal to building wealth. Or else I'd just build wealth everywhere, and nobody does that. (Obviously it's not linear though, some things like units and workers are crucial to a certain number, and then decline in value over that threshold.) Yet, wealth may be the best build at some times or in some cities, despite it being less productive than the global average, because it's locally the best choice (perhaps at a certain time to speed a tech).

I disagree with suttree's claim here. If a point of commerce is taken to be worth 3/5 of a hammer, then spending hammers to build wealth to get tech is 3/5 efficient* and does not necessarily meet the baseline standard.

I think wealth is often good to build in cities with extremely low hammer output. If you have the choice between building 1 gpt or spending 120 turns building a courthouse, you should just take the 1gpt. (But if you can whip the courthouse after 30t, maybe the calculus changes.) The longer something is going to take to finish, the worse of a deal it is.

On a side note, techs are interesting and strange because a significant part of the value of a tech is its prerequisite value for other other techs. Like, a significant part of the value of math is the fact that it's required for calendar, and practically required for currency. And it's even harder to judge because a significant part of the value of the later techs is in unlocking military units.

* Though this can be improved by having beaker multipliers in your civilization.

[suttree]

By "value" I'm not just talking about value in beakers or gold but something more abstract.

Let's distinguish between the game and the economy. The goal of the game is to achieve a victory condition, so the value of a given position may or may not correlate to a measure of the economy. The problem is that the value of a given position is really really hard to determine. So we substitute something simpler - the economy: the sum of food, hammers, and beakers over time - and use that to save effort and compare options.

That is, I set a strategic goal (that may or may not have anything to do with the economy) and use a model of the economy to compare the various means of achieving that goal. If I have two options for achieving the goal, I choose the one that the model predicts will produce a better economy in the long run. If I'm faced with a decision that has no clear connection to my strategic goal, I choose the option that the model predicts will produce a better economy in the long run - for no reason except that, whatever my goals, I prefer a stronger economy to a weaker.

We ought not to try and build a more abstract notion of value in to our model of the economy because that defeats the purpose for modelling the economy in the first place: to simplify decisions that have to do with, all else being equal, maximizing food, hammers, and beakers.

There is a feedback effect of course: the player might conclude from the model that emphasizing food in the early game is key to maximizing beakers later in the game (the model informs the strategy) but a simple model makes it easy to avoid making false assumptions.

There are always going to be a range of investments whose value is a function of the behaviour of other players in space (the map) and over time. We don't want the economic model to rely on assumptions about how other players are going to behave.

So I can conclude then (can't I?) that post-Currency, the value of the average build must be greater or equal to building wealth. Or else I'd just build wealth everywhere, and nobody does that.

If you don't have other strategic priorities, a commerce city doesn't need much (~16c/t) to prefer a library to wealth. A market can be pretty awesome if you have market happy or you start to fall below 50% science. Courthouses (ignoring EP's) look good once maintenance is above 6g/t. Forges in cities that average more than 12h/t. But again, it's not about the specific numbers, it's about making consistent decisions and adjusting assumptions based on evidence. For example, you build a courthouse in a far away city but not in your capital. I want to be consistent about what it means to be "far away" so that I can honestly evaluate my working model and improve from game to game.

Wealth may be the best build at some times or in some cities, despite it being less productive than the global average, because it's locally the best choice (perhaps at a certain time to speed a tech).

Any model is going to be about growth, on average, over a long time. The micro fiend is still attuned to breakpoints. For good or evil, it's still the case that a single beaker or hammer can be worth an entire turn's worth of production in the special case.

In the case of putting hammers in to a courthouse, for example, the model suggests that until your courthouse saves you ~3g/t you probably want to build wealth. Building wealth isn't the "right answer" - it's just the answer that follows from the model's assumptions. The model is useful because forces you to ask why the assumptions aren't true in the particular case.

Even ignoring benefits of EP and enabling FP, the model has to be more complicated than that, doesn't it? Because it doesn't just save you 3gpt, it saves you half of the maintenance of the city forever which should eventually rise. I'm sure you could still put reasonable bounds on what the net present value of that is, though.

The idea is that it's a good approximation to simply make decisions at the margin. If you want, you can micro out a detailed growth plan for the city and predict exactly how the maintenance will change and determine how long it will take before the courthouse is finished and your investment starts compounding and smush that all in to some sort of present value and then compare that to the value of your tech path over a similar time period and somehow try to calculate the present value of that.... but you're probably not going to make a better decision than the decision you would make by comparing the marginal return on a courthouse vs the marginal return on something else. You don't start building the courthouse until the former is greater than the latter. And once the return on the courthouse is greater than the return on labour you finish it immediately by the whip.

You can use your judgement to identify the outlying cases: perhaps you anticipate a demand for EP's, or you plan to build the Forbidden Palace soon, or you know that maintenance is going to spike soon. But the default mode is to simply maximize marginal return - that's the reason for having a simplifying model.

Of course, what I may end up doing is looking for ebbs and flows and discrete break points around models while making plays that are just simply bad by any reasonable measure.

Or you may find a specific sequence of investments that gives you an advantage at exactly the right time and place. The purpose of whatever model you build for yourself is to simplify the majority of your decisions with a reasonable approximation of reality so that you can focus your attention on the "big picture" decisions that win you the game.

[mackoti]

Oho, nice discutions around here.So from all this you see why i consider fdr a strong leader: you dont have to think so strong about if worth or not building someting.
1.Granary is a must easy here.
2.Forge well with ind 99% worth so cant go wrong.
3.CH 2-3 turns of natural prod an 1 whip always worth even the reduction is small so not a big headeche,CH is the only bulid which gave money at 100% science or 100% and espionage is not something to sneaze at.I am sure not a spoiler but in pb 13 i had already 18 ch when other which i had met didnt build at least one.Doing some math an average 3 gold saved for city(it was more) thats a near 60 gold turn without working tiles or something...
4.LH well if seafood build otherwise wait till ot tiles to work.
And with other builds remained is far more easy to decide:
The science ones if you want to get a science city from that one.Gold ones same or if you have enough resources to make a market worth.
You see very easy with Roosvelt.

And btw i build loads of wealth,but mostly later in game when i have forge Ch in place, becasue building wealth your science citties work most of the time at 100% so you can avoid gold multiplier and have a great return.

[suttree]

I disagree with suttree's claim here. If a point of commerce is taken to be worth 3/5 of a hammer, then spending hammers to build wealth to get tech is 3/5 efficient* and does not necessarily meet the baseline standard.

I was going to say something about this when Will mentioned the 3/5/8 valuation since it's something I've been thinking about recently. There are actually two questions here:

(1) What is the value of hammers vs. commerce?
(2) When is it better to build wealth vs. infrastructure?

Summary: I agree that (in valuing tiles) 1h=5/3c is a good approximation but I don't agree that in building wealth the player is turning 1h in to the equivalent of 3/5h.

Explanation:
1h=5/3c is a good approximation (in valuing tiles) exactly because hammers in any given city free up (by buiding necessary units perhaps) hammers for an investment where the commerce return is (on average) ~5/3 of the hammer cost. New cities, wonders, failgold,libraries, courthouses, markets - built in a reasonable order they tend to have a present value commerce return of (on average) between 1.5 and 2 times the hammer cost. So, incorporating the whip, I like 1f=8/5h=8/3c.

But this approximation doesn't apply to the question of when it is worth building wealth. I make the decision to build wealth exactly when I don't need units (I'm not freeing hammers that could be applied profitably elsewhere) and when I don't have profitable hammer investments in the city in question (it's growing and infrastructure is unprofitable). In the decision to build wealth,then, hammers can't be worth 5/3c because the conditions that motivated that approximation don't hold. The breakpoint is when the marginal return on building wealth matches the marginal return on building infrastructure. IE when the present value commerce return of infrastructure is equal to its hammer cost. There's no conversion here, 1h=1g until I gain access to profitable investments.

TL;DR
1h~=5/3c is an approximation. Sometimes it's worth more, sometimes less. When cities are small or when I don't need units 1h=1g is the lower bound. That's when I build wealth.

[SevenSpirits]

But this approximation doesn't apply to the question of when it is worth building wealth. I make the decision to build wealth exactly when I don't need units (I'm not freeing hammers that could be applied profitably elsewhere) and when I don't have profitable hammer investments in the city in question (it's growing and infrastructure is unprofitable).

Whaaaat? How can a valuation be useful if you only use it exactly when you're NOT comparing to anything else? I really don't understand what you're thinking here. And certainly, deciding whether to build wealth or not comes up even if you have other things you want to build.

In the decision to build wealth,then, hammers can't be worth 5/3c because the conditions that motivated that approximation don't hold.

I think a major motivation of the conversion rate between hammers and commerce is how easy it is to produce them; it's about as easy to produce 5c with marginal population as it is to produce 3h. (e.g. work a farm and a mine or two 2/0/2.5 tiles (which, arguably, is what cottages are worth)). So suppose I want X cpt and Y hpt to make use of all my best opportunities of both types on average; then I will try to be working tiles such that I get that instead of e.g. X + 15 commerce and Y - 9 hammers.

In terms of efficiency, building wealth is a red flag, because maybe you could have gotten better total yield by making more cottages and fewer mines, or whatever. But you do it if your builds are low efficiency or getting the boost to tech is high efficiency or both. (And actually, it comes up a lot that you do it to preserve overflow, too.)

TL;DR
1h~=5/3c is an approximation.

I agree, and it seems like we should agree on most of it, so I don't know where I misinterpreted your (or failed to interpret you completely).

[WilliamLP]

Oho, nice discutions around here.So from all this you see why i consider fdr a strong leader: you dont have to think so strong about if worth or not building someting.

It seems to be a good point for Organized. A lot of courthouse build decisions that are hard at 120 hammers are easy at 60. (Or 54 base hammers if you have a forge too.)

(It seems true for RBMod expansive as well: buildings that are normally on the borderline like markets and grocers easily become good builds at +100%... If you're not getting attacked so much that you don't have time to build any of it. )

And btw i build loads of wealth,but mostly later in game when i have forge Ch in place, becasue building wealth your science citties work most of the time at 100% so you can avoid gold multiplier and have a great return.

Yeah, it's a point I should keep in mind more, going back to some T-Hawk articles and Seven mentioning it in this thread. It can like building wealth doesn't get bonuses but it actually supports science cities, which do have nice multipliers, converting more commerce to beakers instead.

(It's not relevant for this game but I wonder if Exp in RBMod actually gets the inverse: grocers and markets are cheaper than libraries, and banks (+Wall Street) are good, so maybe it actually makes more sense sometimes to build research, in order to run the science slider lower for better gold multipliers.)