The economics of food velocity in a Despotism

[absimiliard]

Okay, so we've all realized that rush-building during your early-game Despotism is a good thing. We've even gone so far as to believe that it's a very powerful thing. But no one yet, that I've read has tried to quantify this tactic. I will tackle it, but I'll need some help since it's not quite all straight in my head.

First I will establish some assumptions. A point of population, when used to rush is worth 28-40 shields in my experiments, I will venture an average of 35 shields therefore as the value of that point of population. There is a cost to rushing however, the cost is the amount of lost resources the pop would have built during the time you take to rebuild that point of pop.

That opportunity cost (economics term here) varies dependant on how long it takes to build your point of pop. For a city with two food to spare, the norm, that time is 10 turns. During those 10 turns we can reasonably assume the point of pop would yield 20 food, 10 shields, and 10 trade, this will obviously vary widely but an average isn't unreasonable I think. So for 40 mixed resources you are netting 35 shields. In and of itself this isn't that impressive.

It gets better as your food-velocity, the speed with which a given city grows, gets higher. If you have a velocity of 4 food/turn you are only looking at a 5 turn growth rate. Your exchange rate then is much better, 35 shields for a loss of 20 mixed resources. A velocity of 5 food/turn brings your loss down to 16 mixed resources. Now you're really cooking with gas!

My conclusion is that it's only worth pop-rushing if you make 3 extra food/turn or more or are in an emergency situation. At 3/turn you're losing 28 resources to get 35, that's a good trade, whereas at 2/turn you're losing 40 resources for your 35 which I find less appealing.

Now on to transfer mechanics.

Pop can be transferred by means of Workers or Settlers. Settlers obviously carry larger chunks of pop than Workers do, but cost proportionately more. The math has Workers costing 10 and Settlers costing 15 per point of pop. For a 35 shield return on that pop we get efficiencies of 70% and 60% respectively. (That's a rough figure, 71% & 58% are more accurate). Clearly population transfer is best done with Workers, not Settlers. But when is it worth it to transfer that pop to build something, that's the important question.

Using Workers adds 10 resources to your opportunity cost when you pop-rush. So a 2/turn food situation now costs 50 resources instead of 40, clearly a poor bargain for 35 shields. 3/turn is better, now we're talking 38 lost for 35 gained. I might use population transfer for rushing in this circumstance if I really needed to, like to build a Temple to expand my borders.

4/turn and 5/turn is where this changes though. At 4/turn you're actually making resources by transferring that pop to another city where it can be used to rush, you're not making much, only 5 shields, but it's still a positive figure. 5 food/turn is even more compelling, I cost in expenditure & opportunity cost only 26 resources but I can gain 35 by pop-rushing. That's cooking with gas!

My conclusions are as follows. At a food velocity of 2, 2 extra food/turn, pop-rushing is feasible but not practical, use it only for essentials. At a food velocity of 3 become efficient at pop-rushing in that city and should do so as much as you can given the value of shields early in the game. At a velocity of 4 or 5 you become efficient as a source of export, in one of these cities you should build just Workers and use them to pop-rush in other cities.

Now I need your help. I'm pretty sure I've missed some factors, but I'm not sure what. As it stands I'm pretty pleased that my thoughts give us a good yardstick to guage pop-rushing by, but I'm afraid of those missing variables.

So . . . . if you can think of how to better express this relationship, please speak up. I'm convinced pop-rushing is an essential early-game tactic and I'm certain it can be quantified. I'm just not absolutely sure I've gotten it done right.

[mharmless]

To help you with your math, the first person killed in pop rushing is worth 40 sheilds. Second and all beyond (up to eight at least) are worth 20 each.

The rush cost of an item is doubled if it has no work into it yet.

Finaly, in the early game your cities are going to be capped at 6 pop points (for the most part), and it will be a long time before you unlock the 12 point cap. Once you get to 12, your city will collect food untill it would grow the next turn, and then halt there. Thus if you rushbuild an item at that point you will replace the worker immediately the next turn and suffer only one turns production loss for 40 sheilds of production value (roughly).

[absimiliard]

Thanks. That doubling of cost & the lower value of extra pop used in rushing must have been what was making getting an exact figure difficult for me. I think that working with an average figure is acceptable though, I never get the full 40 from my rushes, normally I pull in like 35 though it does vary a bit from time to time.

I had forgotten the cap on pop. That would imply that rushing is economical for every instance where you would have a city sitting still in pop-growth. I suspect you're still better not doing much rushing at under 2 food/turn though, so if a size 4 city had no more 2 food squares to work I'd rush it then, before my food velocity dropped. But that's just a hunch.

The largest factor I've missed though is the presence of a Granary. Having a granary nearly doubles your food velocity, you have the same amount of excess food per turn but only need to go half as far. In fact I'd go so far as to venture a hunch that rushing is always the right idea with a granary a velocity of 2+.

[David Weldon]

I would argue that the opportunity cost is even less than presented. The reason is that you are not capped only at 6 in the early game, at emperor and deity you are often practically capped at 2 or 3, depending on how many MPs you wish to waste sitting around in your cities. At levels where you can have larger populations more easily, I don't rush-build things very much but at higher levels I find it very important.

The biggest missing factor in your math is that the first thing that should be rushed is a granary. This halves all of the opportunity costs you discuss, as well as greatly accelerating the point at which you hit the natural population cap (due to happiness or lack of aquaducts).

In my experience on difficult levels, if I ever rush anything from a city then my max population is 1, even with a temple and multiple luxuries. The opression unhappiness is a large factor when you're rush building every two turns thanks to some irrigated cows or wheat. This means that I can't grow my cities to two unless I have MPs or I immediately rush another military unit. I bet you can guess which I normally choose...

The opression unhappiness eventually wears off, but I normally don't worry about growth until I've conquered or subjugated at least two civs.

[Dale]

Pity ya can't pop-rush the pyramids. Then you'd become some sort of Power Pop-rush Empire.

[pchang]

In addition, the resource trade off doesn't include the benefit of getting the shields NOW instead of waiting X number of turns for them to build up slowly. TO do this properly, you would have to include some sort of net present value calculation.

[absimiliard]

Hey pchang. I think that my analysis is only valid over a short run of turns. Over that time period the depreciation will not be too much. We should be able to ignore it, or if need be account for it by introducing a variable.

Mr. Weldon's comments are more damaging. He is correct that I am not accounting for granaries adequately in my math. I think the solution is to redefine quite a few things.

First I define an average value for a square, call it A. Food is F, shields are S, and commerce is C. A = F + S +C. This is a little simple, but equally valuing the resource types can be dealt with later. (I think a typical square is like 2F + 1S + 1C, though it's easy enough to get higher-value squares as well) This value, A, can also be simplified to the sum of the values in shields by claiming that food, shields, and commerce are all equally valuable. The example square then has a value of 4S.

We'll switch to growth (G) instead of velocity. Using time as turns (T) and a unit of population (P) grown, we get G = T / P. Growth is defined as Turns per unit of Population grown. It's odd to see time on top of a fraction, anyone who can elegantly get it into the denominator where it belongs gets kudos.

O = G * A. If your opportunity cost is under your gain of 40S, the value of a unit of population in a rush, then you should rush, hypothetically. So if (G * A) < 40S you should rush. For a typical value square you thus rush if (4S * G) < 40S, or G<10. This says you can hypothetically gain value from rushing if you can grow a unit of pop in under 10 turns. Given some inevitable loss in your shields from rushing I'd say you're more practically looking at 35S in returns making a rush at 8 turns practical.

Given that a special can make a city have a G of like 2 to 4 the effects on the game are spectacular. A city with a G of 2 nets a gain in shields (G) equal to say 35 minus the opportunity cost. 35S - (G * A) = 35S - (2 * 4S) = 35S - 8S = 27S. So every two turns a G2 city that rushes gains like 27 shields in production value relative to itself not rushing.

That goes somewhere too. Let me think about it.

[i]As a brief aside, may I note that I've been rushing brutally and have found that it leaves me horribly poor and ignorant. I'm gonna try a more mixed game next, some rushing cities, others not.

[Easy Rhino]

abs, I just want to say I'm really impressed with this topic.

Uses all the concepts that I never learned in ECON

ER

[Grim Legacy]

Some more thoughts:

1) The population gets unhappy from rush jobs. In a size 3 city, you need 2 MP already. Rush a job and you may end up with a size 2 city needing 2 MP... as soon as it grows to 3 again you have a disorder. If you need an entertainer to compensate, you'll lose the revenue of a laborer.
So you'll need a temple to help and to make them forget sooner in addition to a granary (without a granary, the food revenue of a Despotism city is typically only 2 unless special tiles are near).

2) When you have a granary and temple already, you might consider Monarchy instead of looking to get Rush benefits: under Monarchy food production balloons, yielding a very tangible benefit over rushing even worthy city improvements like libraries -as these offer limited gains in a small despotism city. In addition to the extra food and thus laborers, you get extra happiness from a 3rd MP as well. One more laborer.

3) Taking into account the pop cap, a factor that is often overlooked is the possibility to re-allocate production tiles: switch the grassland laborer to forest or mined hills (+roads of course) and you'll receive a nice production bonus, maybe even a trade bonus if you have gold or dyes etc near (these special resources typically appear in low-food squares that can be used in the situation I described).

[absimiliard]

Thanks ER, I appreciate the compliment.

Grim, I'll try to fit the unhappiness factor into my equations. I'm aware of it's existence as a population cap to be sure. My practical limit in a rushing city is 4 pop, that's being dealt with by 2 MP & 1 Temple. A luxury can help out here of course, but 4 is a viable limit since it allows a rush of a Settler unit.

Perhaps the proper approach is to view a long-term opportunity cost, O(lt), as being different from a short-term opportunity cost, O(st). In the short-term unhappiness isn't much of an issue, since I'll deal with it by rushing my pop down to the point of happy again. In the long-term however you're quite correct that I'm losing the use of a pop-unit for 20 turns. (Until the city calms down again)

That invokes a cost of either 20A or the cost of an MP. I value an MP at 5S + 20C in this circumstance. (the cost of production plus the cost of upkeep) Clearly the MP is better, cost-wise, than 20A. Thus Unhappiness (U) as a factor is valued at 5S + 20C, or 25S for simplicity's sake. (someone really needs to figure out a decent conversion ratio for F, S, & C.)

So O(lt) = G * A + U. Or for a normal value of A, O(lt) = 4S *G + 25S. Plugging in our value of 40S for a rushed pop and doing a bit of math gets us a hypothetically profitable long-term rush when G < 3.75. So even in the long-term rushing can still be profitable, it's just much harder. This is also a purely theoretical break-point, lots of inefficiencies can get into the equation.

If you can't use an MP to keep your pop happy then O(lt) is even worse. Then O(lt) = G * A + 20A. Basic assumptions in place yield O(lt) = G * 4S + 80S. Since a rush yields 40S, a long-term rush without MPs to quiet people will never be profitable. Can't be since O(lt) will never be under 40S. If my math's right, that's brutal.

Regarding your third point, I fully agree. If I'm in a non-rushing city and am bouncing on a pop-cap, either hard (aqueduct) or soft (unhappiness), then I firmly believe in reallocating if I'm not focussing on pop-growth. The trick is knowing when & where to rush, not just rushing blindly everything in sight, like I did when I first started trying this technique.

Grim's second point is actually the most easily addressed. All this is pre-Monarchy or Republic. I'm of the opinion that this tactic is mostly useful in the earliest of early games. By the time I'm getting close to one of the better governments my cities are fully developed & just need pop. At that point I'm looking more at the long-term and am view O(lt) as more important in my judgements than O(st)

[Aeson]

One thing no one has mentioned in this thread, is how pop rushing affects highly corrupt cities. In those cities its trade off is practically nil, as no matter how large the city gets, they will only be able to produce food. A completely corrupt city should always be pop rushed at the level where it is producing the most excess food. If a city has three 3+ food spaces it can use, then it should be pop rushed whenever it hits a pop of 4. This doesn't account for civil disorder, which would limit the max pop differently depending on luxuries available and difficulty level. All that said, I usually keep each city that is being pop rushed down to 1, as its just easier to spot which cities need to be rushed each turn.

Another thing, pop rushing can be worth 39 shields for each pop point if you are willing to switch production after each step up in the unit/improvement cost scale. Though if an improvement costs 60 shields, it's going to take 2 pop points either way. One benefit of using production steps is that on higher difficulty levels it alows you to actually build things that cost more than one point without having to worry about going into disorder by growing to size 3 or 4 or however large a population you would need to finish the unit or improvement. Instead you just keep knocking your pop back down to 1 at each step.

[rah]

I'm surprised everyone has overlooked one aspect of the long term benefits here.

Suppose you're rushing archers. What are those archers gonna do? TAKE OTHER CITIES. So you can spend those pop point on building settlers or TAKING AI cities. Depending on circumstances and territory will determine the best path. A few extra cities won early have a tremendous impact in long term benefit calculations. Especially if taking those cities helps you create the Vassel AIs that you can rape/milk for centuries using diplomacy. Done right, they will give you every tech and all the gold they have. That's worth a few pop point. Too much of the dimplomacy seems to be based on the size of you peni..... I mean army. So you better have a strong one.

It probably muddies the water enough that it will be hard to quantify. But please continue, because the discussion highlights the factors that you should be considering when you make that decision, even if it's all theory.


RAH

[absimiliard]

Corruption is actually easily dealt with. Basically it's just an alteration in the local value of A. If A = 2F + 1S + 1C ,then in a totally corrupt city you reset it to A = 2F. This doesn't change the equations, but it does effect the value of O(lt) and O(st). I think the effects on O(lt) are much higher since it includes a lot of A.

So here's an example city, now using 2S as the simplified value of A. (A nasty thing to do, but I'm too lazy to figure out complex math quite this early in the morning.) O(st) = G * 2S. This means short-term rushing is practical at values of G < 20. For O(lt) it's just as striking, if not moreso. O(lt) = G * 2S + 25S. This means long-term rushing, with an MP, is practical in a corrupt city if G < 7.5. Long-term rushing in a non-MP city remains impractical economically.

Excellent suggestion on step-rushing by the way. I hadn't thought of that yet. Very good idea indeed.

Rah, while I don't dispute that you're correct, 'cause I think you are, I'm not sure that's germane. I'm only talking about the point of profit in a rush economy. You're talking strategy based on the use of your rushed units. I'm totally trying to stay away from strategy because I don't think it's easily quantifiable. For my equations purposes it doesn't matter what you do with your profit they only exist to tell you if there is profit.

Not sure how I could change that. Perhaps strategy will always remain unquantifiable.

[rah]

Originally posted by absimiliard

Rah, while I don't dispute that you're correct, 'cause I think you are, I'm not sure that's germane. I'm only talking about the point of profit in a rush economy. You're talking strategy based on the use of your rushed units. I'm totally trying to stay away from strategy because I don't think it's easily quantifiable. For my equations purposes it doesn't matter what you do with your profit they only exist to tell you if there is profit.

Not sure how I could change that. Perhaps strategy will always remain unquantifiable.

That's the problem with all the QUANTIFICATION that is being done in this forum. Money Opportunity is critical in any economic equation concerning PROFIT. It's a big difference if you invest your money at a low interest rate or do a more high risk investment. (and personally I don't think SOME early conquest is that high risk). It can't be ignored.

I have seen the same problem with people quantifying civ characteristics or anything else. To look at long term benifits, leaving out conquest/diplomacy profits eliminates the most lucrative investment.

Having said that, please continue what you're doing. Even military inclined leaders need to know the cost of the conquest to determine if the cost/risk/reward ratio is worth it.





RAH

[absimiliard]

I think quantification in general is a good thing, kind of obvious since I'm goind it here, but I would agree that the quantification of the civ-traits is flawed. The analysis we've seen so far has failed to take into account inflation, which is why the early game low-value stuff like expansionist isn't total suck. The problem as I see it is that no one yet has a good value for inflation in Civ III.

I see my work as providing input for strategic decisions, not as deciding them. Heck, even a highly unprofitable rush may be great if the strategic or tactical situation requires it.

As an aside, I view early-game conquest as a fairly low-risk investment as well. I'm generally fairly sure I can take the AI so basically it comes down to are the units worth the cities gained, and that's a trivially easy question to answer "yes" to.

--------------------------------

I've been thinking about population transfer mechanics again. I'm an old Stars! player, and in Stars! your pop is really all that matters. It's all about the exponential growth curve. Civ III is looking fairly different though since I've been refining my economic equations.

Basically I thought early on that building a Worker in a high-food city and using it to rush something in another city might be profitable. To be sure there's some wastage in the 10S cost of the Worker, but I thought it might work in general.

I still think pop-transfer can be profitable if you are considering O(st). However in the long-term the high value of A makes up most of O(lt). This means that it's not the cost of the lost pop that's your main loss, it's the unhappiness, and that won't change even if the pop is from another city originally. So I think pop-transfer is only practical for short-term returns, or for corrupt cities where the value of A is low.

---------------------------------

As a final aside. I think I miscalculated the cost of an MP. I said 5S to build and 20C to support. That should be 10S + 20C. I think Warriors cost 10, and they're the cheapest MP I can think of. This should only slightly change the equations though. The actual math is left as an exercise for the student.

[Gatamelata]

Pop rushing is an interesting topic, to be certain. I was first seduced by its allure - the promise of fast and easy production at a time when my empire needed it the most. But it has a long term cost.

Take, as an example, a game I played recently as the Romans on Regent difficulty on a standard sized map. Rome was my first city on some nice grasslands, and typically had a food velocity of 2. Veii, my second city, encompassed two wheat tiles, one of which was flood plain. So it had a food velocity between 3 and 5. I used both Rome and Veii to rush build extensively. Veii was obviously my main source of rushed legions, since the pop growth was so high. I finally switched from Despotism to the Republic at 1 AD, interestingly enough.

Once my cities started growing, I noticed something horrible - Rome was somewhat hobbled, and Veii was stuck with one producer and three entertainers. Rome finally started growing again around 800 AD, but Veii didn't start growing until the 1600s, and its people remembered all of the oppression until the early 1800s.

This is not to say that it wasn't a valuable tool for me, and the trade-off was rather minor - those Legions conquered the Aztec empire and doubled the size of my territory. But the net effect was that my first and second cities were nearly useless for many turns after that, and their growth was stunted even after the period of uselessness ended. I'm still stunned by how long the Veiians remembered the rush building. Now, Veii produced quite a lot of legions and city improvements, but still.

At any rate, I have yet to find the perfect rush-building balance. And for some players, this trade off may be perfect - it certainly was advantageous to have the early super-production from Veii, but it did hurt not to have much production at all from it later. Incidentally, after Veii shedded its protestors in the 1800s, it boomed to primacy among my cities in short order, which gives a good indication of what it could have been in the interim if I hadn't been so eager to sacrifice population.

[absimiliard]

Hate to say it friend, but I think you need to build more MPs in those rushing cities. I've found that I can keep rushing city content up to pop 4 with 2 MPs and a Temple. For MPs I recommend Warriors, though if you rush them you might as well go with Spearmen.

Your example is a perfect display of the high cost of rushing in the long-term. Recall how high O(lt) can be if you can't use MPs to reduce the value of U (unhappiness) in the city in question. By rushing you lost 20 turns of productivity in Veii, in your example. Using MPs can cut that down somewhat, but O(lt) will always be fairly high.

The high value of O(lt) versus O(st) is why I think the tactic of rushing is mostly useful only in the early game and even then only in some of my cities. I'm still perfecting my strategy on it to try to balance the power of rush-building against the losses it incurs in the long-term.

Do bear one thing in mind though. If you do many rushes in a city O(st) will be your cost for all but one of those rushes. Only the last rush incurs a cost of O(lt). So if you do rush a city, rush it for all it's worth. Don't stop rushing until you've built every improvement and unit you'll ever need in that city. Then rush a few more military units for your main army before switching over to a normal economy.

[Sauron07]

This has been by far the most interesting and thought provoking thread I have encountered in the strategy forum to date, nice work absimmilliard(and other contributors)!. I have a few thoughts after reading through your analysis.

First, I believe the opportunity cost of one population point is actually less than you calculated due to the food required to support each additional point of population. While the value of working a single tile does not change the value of food decreases over time as each additional pop point requires 2 food to support it. Your city tile always produces at least 2 food so the the first tile worked yields 100% of its production value(f + s+ c) back to the city. After that however each additional pop point requires 2 additional food in support. Therefore the opportunity cost of the second popis acutally f +s + c -2f, or 20s for an average tile, as you dont gain anything by that two food other than being able to support the production of an additional square.

Therefore I beleive rush building is worthwhile in more situations than you have determined. All you really lose by rushbuilding down from 2 pop to 1 pop is the shields and commerce produced by the second tile as the rate of growth does not change unless the food produced by the extra tile is greater than 2. Using your formula 0= G*A, A=4 for an average tile for the first pop. point, but is decreased to 2 for each pop. point after that(and those are the only ones we can rush with). If a rush is worth 40s than G can be as high as 20 and still make it worthwhile to rush if you're not able to add an above average tile with your second pop point. This also gives a higher opportunity cost value to forests and other high shield and or commerce squares.


Secondly, and related to the first point. The ultimate issue which must be decided as you correctly note is the relative value of food, shields and commerce. This depends on many, many factors but I think if we limit the analysis to the start of the game some useful info can be gained. Basicly food is only useful to grow your city and thereby increase production and/or rush build. In the rush build context under despotism 1 food = 2 shields if that food is contributing directly to population growth and is not being used to suppor the city(this assumes no granary). Otherwise 2 food is = to the production of the tile which it supports(on average 1s and 1c). The value of commerce is difficult to quantify under despotism as it cannot be used to purchase units or improvements, but serves to support maintenence costs for improvements, purchase luxuries, research science, and trade once other civs are encountered.

Lastly, and I havent had time this morning to think this through completely, but I believe that a 1 or 2 pop city requires 20 food to grow and for 3 and above 40 food is required(again without a granary). This will definately have an effect on the efficiency of rush building and changes G rather dramatically once pop 4 is reached.

Thanks again for giving me something fun to think about this morning at work!!!

[Velociryx]

Simply an outstanding thread, and it very much appeals to the economist in me! I'm lovin' it!

Some additional things for your consideration:

1) Cultural Impact - Rushing early and often (especially where Temples and Libraries are concerned--the two earliest culture producing builds), will net you culture points that last from the turn of completion to the end of the game, assuming the city is not taken from you. Thus, the price of a few unhappy citizens from lossa rushing more than pays for itself via the cultural gain alone, and, if the despotic rush is used to speed build OTHER cultural enhancements (cathedral, coleseum), the unhappiness factor should be nicely offset by the builds themselves.

2) Question - When adding a "transplant pop point" (worker/settler) from another city, does the transplanted citizen have any "memory" of the previous rush-attrocities, or no? If no, then this represents a quick and easy fix to the unhappiness side of the equation....simply populate with a few out-of-towners, such that they outnumber the natives....

3) As has been mentioned, speed building military units that lead directly to the capture of enemy towns....hard to quantify, but a HUGE advantage.

4) Corruption....a little dicey to figure out....but the ability to sacrifice population points is a thing that keeps despotism a viable form of government long after you discover Monarchy! Regardless of the shields lost to production, you can KEEP your fringe cities cranking out infrastructure and units simply by pop-rushing....in my mind's eye, that's the major selling point....as long as you have a decent food tile and a grainary, corruption is a non issue.

5) Faction choice. Religious factions can make MUCH better use of Despotism than anyone else, which is a hidden strength of the trait. Switch to Republic/Democracy to speed research, get a new facility to build (or 2-3), then switch to Despotism, build them all in 2-3 turns, regardless of corruption, then switch back to Dem...poof....instabuilds!

-=Vel=-

[Grim Legacy]

Glad to be of help.

[Out4Blood]

Another note: Despotism is a viable form of government all the way to the end game, not just early. Rush building using pop is just too powerful. And if you rely only on food production (i.e., you rush everything) then there is NO corruption. You don't even need to build wonders - you just used rushed troops to capture the AI wonder cities. I do this all the time. Games end quickly when you just rush military units and your goal is a conquest victory.

[zapperio]

I just can't bring myself to rush under despotism/communism unless in dire strait. I mean...the people will hate me! Working people to death makes me feel so icky. Gee, I should never have taken this job.

Zap

[absimiliard]

Hey Zap, maybe I should have titled this "How to be an Evil Overlord to Your People in Civ III"! *grin* I gotta agree that rushing is very powerful, I believe it is how the AI grows at such stupendous rates. I feel no qualms in doing the same myself.

Velocyrix, I think that where the population comes from is irrelevant to the happiness. My belief is that happiness is purely a city-based phenomenon. (doo do de doo do) I think as long as the pop is yours it's irrelevant which city it's from. Sorry for the muppet gag.

Everything else you state are excellent reasons to rush-build at a lower profit point or even at a loss. *shudder* The more I think about this, the more compelling the case for rushing becomes.

Sauron extends the case even further. By using your reduced value for A due to the cost in food of supporting that pop you change the point of profit quite a bit. If A = 2S instead of A = 4S then you effectively double where you rush or don't.

I think unfortunately we should probably do the relative values of the resources on another thread. They're pretty important, but they'll complicate the math for us and can always be substituted in later when we're sure of a correct formula relating food, shields, and commerce. Maybe I'll start a thread to discover that, unless someone else does so first. (please do) I think growth is 20 Food up to Pop6 by the way. The manual claims such, I've never bothered to confirm it, but I know it's still 20 at Pop4.

I would like to talk about U for a moment. I think it needs to be the cost in shields of producing an MP plus the cost per turn in commerce times the number of turns it needs to be supported. I'm going to say that Commerce requirement is 1C, deliberately ignoring any lost to science. In short term builds this will be for a turn or two at most, in the longest term it is 20 turns, the time to pacify a city from an earlier rush-build. I'm still very unsure on whether this is a good approximation, the theory needs work here. Anyone care to jump in? If not, I'll worry at it a bit later.

So what does all this do to the equations? Let me summarize. This all assumes no inefficiency in the 40S return on a rushed pop, so

P = 40S -- Rush one Pop and get 40 Shields

A = 2S -- The new approximate value from Sauron.

U = 10S + T * C -- Approximated as U = 30S

O(lt) = G * A + U -- Still true.
O(st) = G * A -- No value for U since you will re-use the same MP multiple times in a series of rushes.

Normal values for P > O(st) now coming as 40S > G * 2S make a rush profitable if G < 20, as Sauron pointed out.

P > O(lt) is now changing as well. 40S > G * A + U or 40S > G * 2S + 30S boil down to a profit point for rushing at G < 5. This is much lower than I'd suspected.

These lower points mean Velocyrix is even more right. Rush for culture early and hard. Rush for military to conquer your neighbors after that. Then rush for a way to keep corruption in check, Sauron's change to A makes this even more important.

I'll even have to try the switch from better Gov. to Despot for quick rushing. After all, it's worth it if G < 5, and it's easy to get a big city to G5 status or better under a Republic or Democracy. No MPs when you switch back do mean you'll eat the full cost of a pop needing to entertain unless you can cover it with luxuries or somesuch.

[David Weldon]

When thinking about switching between governments late in the game in order to insta-build improvements, remember that this will likely only be used in fringe cities, as all your core cities are so productive (roads, mines, maybe railroads) that A is much higher than 2. The corruption in your fringe cities, however, makes A essentially 0.

Conlusion:
Switch to despotism, rush in all corrupt cities, knowing that any growth is better than no production or commerce from extra workers, then switch back.

Edit:
Don't forget O(st) of the two turns of anarchy caused by the switching. If your interior cities are very productive, this might greatly outweigh the benefits of adding improvements to extremely corrupt fringe cities.

[Gaius Marius]

Originally posted by absimiliard
I think quantification in general is a good thing, kind of obvious since I'm goind it here, but I would agree that the quantification of the civ-traits is flawed. The analysis we've seen so far has failed to take into account inflation, which is why the early game low-value stuff like expansionist isn't total suck. The problem as I see it is that no one yet has a good value for inflation in Civ III.

I think you mean the discount rate, which is adjusted for inflation (which should be nil in Civ III, since the gold value of shields is constant). The discount rate depends on the expected value of the investment over its planned course, etc.

This may be impossible to determine independent of the game situation and playing styles. Then again, that's very realistic.

Great analysis, though. I look forward to more.

[Gaius Marius]

stupid me. The gold value of shields isn't constant. There is a one-time 100% deflation with the discovery of Economics (there's an Econ joke there, if I wanted to find it),

Of course this only applies to shields - other things of value (shields when rushing, techs (in the estimation of the AI), etc. are constant.).

[Sauron07]

I knew I should have gone home and grabbed my manual at lunch You are probably correct about the pop. threshold for cities before you need 40 food to grow, I couldnt remember and went to the infocenter at another "fanatical" civ site(which shall remain nameless) and it said 4 was the threshold. Whatever it is, it will have an impact on the rate of growth and relative worth of rush building.

One question, I thought there was no upkeep costs for units under a despotic government? Could someone please post or pm the relative number of "free units" you receive under the respective governments if they have that info available? This would substantially alter the U value and make MP's a more viable option to deal with unhappiness from rushing.

Also, I find that in the very early game after temples and granaries are rushed there is small period of several turns where I have no other improvements available (other than barracks and walls which I do not build in every city)to rushbuild until mapmaking/literacy/code of laws are discovered, and units are my only option so I have MP's available for most cities anyway(Im playing on Prince BTW).

Im also glad to see that the strategy of switching governments and rush building units and/or improvements being discussed. I raised this as a potential strat in one of vel's other threads on rush building and referred to it as the DRAFT(Despotic Rapid Acquisition of Forces Tactic/Technique). I agree this can/will be a viable strat in certain circumstances(multiplayer anyone?), especially for religious civs who can minimize the anarchy time. Sorry if this drifted a bit off topic, I guess my mind just works that way.

[ken01]

For everyone thinking rush building isn't THE ONLY way to go, remember the point brought up earlier. The culture benefit is immediate from rushing a temple.

I've maintained MASSIVE culture leads by expanding quickly, conquering my continent, and rush building temples and libraries on the fringes of the empire.

From those border towns, my culture quickly expands. My temples bring in 4 culture points vs 2 very quickly.

In mid to late game, rush building is worthless. Instead of rush buidling, use your core cities to build bombers, then move those bombers to fringe cities with no production. Disband the bomber, add some cash, and you have your improvement.

[DaveV]

Originally posted by Sauron07
Could someone please post or pm the relative number of "free units" you receive under the respective governments if they have that info available?

From the civilopedia.txt file:

Government                    Town            City            Metro
Anarchy                        0               0               0
Despotism                      4               4               4
Monarchy                       2               4               8
Communism                      2               4               8
Republic                       0               0               0
Democracy                      0               0               0

[David Weldon]

I've started a thread on inflation so that future benefits and costs can be properly discounted, please check it out and add to it as much as you are able:

http://apolyton.net/forums/showthrea...threadid=35196

P.S. I'll go with Gaius semantically. Perhaps 'inflation' is the wrong term, but for most people I think it connotes the idea properly.