Optimum Early Growth Strategy

[Brighteye]

People often talk about saving their forests for later chops, but this is pointless. The forest gives you the same amount of hammers each time. If you have a production bonus that is applied to the forest it's also applied to your city's production, so you're cutting the amount of time that your city gets the bonus and not getting anything extra from the forest.
The only reason to save forests if you know you're going to cut them is if you're going to be behind or level in tech. and you need some extra speed on a wonder once the tech. has been discovered: in any other situation you could be building whatever it is however many turns earlier by chopping early.
So, imagine you chop a settler, and then a library, and 50 turns later you build some units because you see a barbarian threat. If you saved the library forests the library would take longer, so saving those forests doesn't get you the units more quickly; it just enables you to respond to the threat quickly if you hadn't anticipated it.
In fact, saving your forests loses you turns because as your city's production increases the number of turns that the forest stops you having to use decreases, so that a forest's effect is greatest early on. This is the whole point of forest chopping.
So saving forests for later chopping is only useful for wonder races, and even then you're sacrificing some of their benefit by saving them.

 

[carn]

People often talk about saving their forests for later chops, but this is pointless. The forest gives you the same amount of hammers each time. If you have a production bonus that is applied to the forest it's also applied to your city's production, so you're cutting the amount of time that your city gets the bonus and not getting anything extra from the forest.
The only reason to save forests if you know you're going to cut them is if you're going to be behind or level in tech. and you need some extra speed on a wonder once the tech. has been discovered: in any other situation you could be building whatever it is however many turns earlier by chopping early.
So, imagine you chop a settler, and then a library, and 50 turns later you build some units because you see a barbarian threat. If you saved the library forests the library would take longer, so saving those forests doesn't get you the units more quickly; it just enables you to respond to the threat quickly if you hadn't anticipated it.
In fact, saving your forests loses you turns because as your city's production increases the number of turns that the forest stops you having to use decreases, so that a forest's effect is greatest early on. This is the whole point of forest chopping.
So saving forests for later chopping is only useful for wonder races, and even then you're sacrificing some of their benefit by saving them.

I agree with most of what you say, but you forget, that not chopping forest is a choice if there is a very good alternativ for the worker to improve instead.

ohioastronomy's analysis for example shows, that after 40 turns improving a +3 resource prior chopping ends up with ~+145 and 3 forest chopped while chopping first gives ~+157 and 4 forest chopped. Assuming that the safed forest is chopped soon afterwards, the first +3 improvement strategy is better than chopping immiediately.

Stone/marble/copper/iron/happy/health can be better to improve than chopping, if not many roads have to be built and the resource is needed. Then the added production of special resource + effect from resource + safed forest can outweigh earlier chopping.

But if workers got nothing useful to do chopping is always recomended.

Carn

Edit to add: A further benefit of having the worker building some productive or usefull resource enabling improvement is, that non chopped forest have a chance to grow new forests. But i think this only adds a little in the long run, but could make a difference for a close contest, like sheep vs chop.

 

[carn]

ohioastronomy is it much work to check whether for civs, that start without mining, but with agriculture and/or hunting and with pig/cow and hunting/agri resource and without mining reource in city radius, its better to go animal husbandry first and improve/grow to the special resources while mining+copper is researched?
Could this be advantagous to research mining+copper, as then the worker is without useful things to do?

Carn

 

[MyOtherName]

First off, the long term is the only term of importance, because that's when the end of the game happens. It doesn't matter if your first 40 turns are better if you fall behind at the 100 turn mark!

Surely y'all are referring to the principle that 30 hammers now is better than 30 hammers later. But that's not what we're really comparing! As Carn said, the choice is between 30 hammers now, improvements later vs improvements now, 30 hammers later.

As a concrete example, let's suppose that you quickly chop three more forests than I do, with the net effect that you get your second city 8 turns before I do. However, we're playing emporer, and we have no happiness resources. So, it plateaus at 3 happiness, making, say, 8 hammers per turn. Overall, your city will have produced 64 hammers more than my city.

Overall, the net effect of your early chopping is to convert three forests into 64 hammers. I still have the opportunity to convert my three forests into 90 hammers! As long as I do so in a reasonable timeframe, I come out ahead.

 

[Wreck]

3 chops is 90 shields. Unless your city has 11 surplus shields + food, chopping a settler will speed the second city more than 8 turns. Most early game cities have four net production: the center center gives 2F+1P, and the one pop works a tile with net production 3, eating 2 food. This city will take 25 turns to make a settler; chopping, you do it in 12. So the time saved is 13 turns.

If the second city grows to developing 8P/turn, then chopping nets you 104 hammers, for a cost of 90. So it's positive even viewed with no time-cost for resources.

In reality, there is time-value for resources, and what you get from speed doesn't arbitrarity stop after 13 turns of advantage. Instead, you buy a city earlier, which gets new resources earlier and builds stuff earlier, which increases your happiness limit and commerce output earlier, which keeps feeding back into the economy.

What rate of growth do people actually achieve in CivIV? If we take the starting position in terms of its unit values, you start with 115P in "capital", and invest it as best you are allowed, producing a stream of just 2P/turn, initially. 4P/turn if we allow food==hammer. 600 turns later, you've "compounded" that initial stream into say 20 cities, each producing 50P/turn or more. Net of 1000P/turn. So, we've achieved a multiplier of 250 times our initial outlay. Per turn, the growth rate achieved here is thus .92% - less than 1%/turn! Still, 13 turns here means achieving a 12.7% increase in your economy, on average.

 

[MyOtherName]

3 chops is 90 shields. Unless your city has 11 surplus shields + food, chopping a settler will speed the second city more than 8 turns. Most early game cities have four net production: the center center gives 2F+1P, and the one pop works a tile with net production 3, eating 2 food. This city will take 25 turns to make a settler; chopping, you do it in 12. So the time saved is 13 turns.

You're comparing an unimproved city with chopping to an unimproved city without chopping. The point is that's the wrong comparison!

If I'm not chopping right from the start, that usually means I have a 5 or 6 production tile, and maybe a second 4 production tile. A pop 1 city with an improved cow produces a settler in 15 turns, and only 10 turns if I opt to make a single chop! You can't shave 13 turns off of that via chopping.

In reality, there is time-value for resources, and what you get from speed doesn't arbitrarity stop after 13 turns of advantage. Instead, you buy a city earlier, which gets new resources earlier and builds stuff earlier, which increases your happiness limit and commerce output earlier, which keeps feeding back into the economy.

You're right -- it doesn't arbitrarily stop; it stops because you hit a plateau.

In reality, if you build a city 13 turns before me, it will always have at most a 13 turn advantage over mine. The compounding effect you describe is explained by the fact that as the city grows, each city-turn becomes more valuable. If our cities could grow indefinitely, then your advantage keeps growing and growing.

Actually, that turn advantage shrinks over time, because you generally will not have new options 13 turns before I get those options. E.G. we both might start building markets right when we get currency -- I'm not going to wait 13 more turns just because my city was built later!

Or even better, I might use my leftover trees to chop rush a growth-improving building! So, even though you might have gotten your city up and running 13 turns earlier, I could potentially catch up or even surpass your city because I built my granary and marketplace before you did!


However, our cities don't grow indefinitely. They might hit a harsh 3 happiness cap, which puts growth to a halt. We might build all the buildings faster than we can research techs to make new buildings available. In this case, your 13 turn advantage is entirely reduced to however many extra units you can make in your extra 13 turns at the plateau and whatever extra commerce it produced. Then, our cities become exactly equal.


As a practical example of a reason this matters...

I've recently been playing a lot of Emporer opening games to refine my strategy, and I've had several opportunities to grab 6-8 cities without AI interference... but in such circumstances, I simply run out of trees to fuel my expansion somewhere around 3-4 cities, since there simply aren't enough trees to build all the workers I need, all the warrior escorts necessary, and stonehenge (more tree-efficient than obelisks)... not to mention that I might need barracks and real military units before I'm done expanding!

Clearcutting might get me to 4 cities the fastest, but during most of these turns, I would have a hollow shell of an empire that desperately needs improvement.

However, if I improve tiles, then start cutting, much of those first 4 cities will be built on the merits of the tiles themselves. Those tiles will continue to fuel further expansion, as well as all the trees I've not yet cut down. I'm tentatively convinced that improving tiles before chopping will surely get me to 6-8 cities quicker.

(And this ignores how essential it is during such a long growth phase to build commerce-generating improvements, and to hook up happiness and strategic resources)

 

[ohioastronomy]

You're comparing an unimproved city with chopping to an unimproved city without chopping. The point is that's the wrong comparison!

If I'm not chopping right from the start, that usually means I have a 5 or 6 production tile, and maybe a second 4 production tile. A pop 1 city with an improved cow produces a settler in 15 turns, and only 10 turns if I opt to make a single chop! You can't shave 13 turns off of that via chopping.



You're right -- it doesn't arbitrarily stop; it stops because you hit a plateau.

In reality, if you build a city 13 turns before me, it will always have at most a 13 turn advantage over mine. The compounding effect you describe is explained by the fact that as the city grows, each city-turn becomes more valuable. If our cities could grow indefinitely, then your advantage keeps growing and growing.

Actually, that turn advantage shrinks over time, because you generally will not have new options 13 turns before I get those options. E.G. we both might start building markets right when we get currency -- I'm not going to wait 13 more turns just because my city was built later!

Or even better, I might use my leftover trees to chop rush a growth-improving building! So, even though you might have gotten your city up and running 13 turns earlier, I could potentially catch up or even surpass your city because I built my granary and marketplace before you did!


However, our cities don't grow indefinitely. They might hit a harsh 3 happiness cap, which puts growth to a halt. We might build all the buildings faster than we can research techs to make new buildings available. In this case, your 13 turn advantage is entirely reduced to however many extra units you can make in your extra 13 turns at the plateau and whatever extra commerce it produced. Then, our cities become exactly equal.


As a practical example of a reason this matters...

I've recently been playing a lot of Emporer opening games to refine my strategy, and I've had several opportunities to grab 6-8 cities without AI interference... but in such circumstances, I simply run out of trees to fuel my expansion somewhere around 3-4 cities, since there simply aren't enough trees to build all the workers I need, all the warrior escorts necessary, and stonehenge (more tree-efficient than obelisks)... not to mention that I might need barracks and real military units before I'm done expanding!

Clearcutting might get me to 4 cities the fastest, but during most of these turns, I would have a hollow shell of an empire that desperately needs improvement.

However, if I improve tiles, then start cutting, much of those first 4 cities will be built on the merits of the tiles themselves. Those tiles will continue to fuel further expansion, as well as all the trees I've not yet cut down. I'm tentatively convinced that improving tiles before chopping will surely get me to 6-8 cities quicker.

(And this ignores how essential it is during such a long growth phase to build commerce-generating improvements, and to hook up happiness and strategic resources)

I have to confess to being puzzled, since I did exactly the comparisons that you're talking about. Remember that I was only talking about making the first settler, not something that you have to do for every single subsequent city.
This is important - once you have workers, there are other ways to get settlers and workers out besides chopping trees. But you don't at the start, which is why they are so handy. The start also definitely lends itself to quantitative analysis. I do agree that there are alternatives to chopping once you have some workers and a second city.

I compared growing to size 2 and then going for workers, going to size 5, and building a worker at size 1 and then improving without cutting trees. In every case, you are unconditionally better off investing your trees in the first two workers and settler. The reason why the first builds are special is that you need workers to make growth useful, and your city is stalled until you're done with workers and settlers.

In this comparison (worker, build best improvement, then use normal production for another worker and a settler) you have a 5 turn delay in the settler and an 18 turn delay in the second worker. (Yes, you save turns spent chopping trees - but after the first improvement nothing you can do affects your production in the near term). Your primary city gets to start growing on turn 28 if you chop 4 trees, while your initial city growth is delayed until turn 41 if you don't. If you do everything else the same, this means delayed improvements, delayed growth, and a delayed start. Of course, you could have the second city stall out while it builds a worker - but that is just moving the production loss to another city where it will take longer. You can quantify these things, and they do matter for the very first city.

More to the point,building more than one improvement doesn't help you until your city grows to use the new improvements...you'd get a much better yield from having workers building improvements just before the cities can use them e.g. one improvement each around two size 1 cities is more productive than 2 improvements around one size 1 city.
Connecting health/happy improvements only helps you when your cities are big enough for them to matter; connecting cities and general resources is more useful but time-intensive.

For subsequent settlers and workers, a size 2 city with two good specials (e.g. corn and pigs) can put out workers and settlers faster than the best lumberjacks. Note also that forest depreciate as the game progresses because cities have more production. A unimproved starting capital has, at most, 4 hammers (5 on a plains/hills). A fully improved size 5 city, before forges, can have 16 hammers (plains/hill city, 4 grass/hill/mines, cow). A forest is 7.5 turns of maximal production at the start and less than 2 later.
They do have real uses (especially wonders), and they are very valuable around hammer-poor cities to get out essential commerce/science buildings in a sane time. But your capital usually isn't hammer-poor, and other cities can fill that role.

 

[MyOtherName]

I have to confess to being puzzled, since I did exactly the comparisons that you're talking about.

Sorry, that was my response to Wreck, not to you.

 

[Vatec]

More to the point,building more than one improvement doesn't help you until your city grows to use the new improvements...you'd get a much better yield from having workers building improvements just before the cities can use them e.g. one improvement each around two size 1 cities is more productive than 2 improvements around one size 1 city.
Connecting health/happy improvements only helps you when your cities are big enough for them to matter; connecting cities and general resources is more useful but time-intensive.

This is true, but only to a point. There -is- some strategic value to having more improvements than citizens to work them: flexibility. A size 3 city with 3 fish and 3 mines has a lot more options than a comparable city that only improved 3 of those 6 plots. You can maximize growth, maximize production while starving, or mix the two to taste.

Does this flexibility outweigh the efficiency achieved by "just in time" improvement? That's hard to say.

On a related note, I frequently keep my first two workers together in order to chop or improve at double speed. I generally play on the Marathon setting, though. At faster speeds, a solo worker might be fast enough.

 

[DaviddesJ]

Most early game cities have four net production: the center center gives 2F+1P, and the one pop works a tile with net production 3, eating 2 food. This city will take 25 turns to make a settler; chopping, you do it in 12. So the time saved is 13 turns.

Most early-game cities of mine have a lot more production than that. The citizen isn't working an unimproved tile; it's working a pig/pasture, or a corn/farm, or a deer/camp/forest, etc. Your logic is circular, because it's based on the assumption that you rush to bronze working first, rather than researching technologies that give useful improvements first (or even starting with them!).

I do, nevertheless, agree that rushing to bronze working and chop rushing is very effective. That's too bad. I avoid playing that way, even though it does work.

 

[ohioastronomy]

Most early-game cities of mine have a lot more production than that. The citizen isn't working an unimproved tile; it's working a pig/pasture, or a corn/farm, or a deer/camp/forest, etc. Your logic is circular, because it's based on the assumption that you rush to bronze working first, rather than researching technologies that give useful improvements first (or even starting with them!).

I do, nevertheless, agree that rushing to bronze working and chop rushing is very effective. That's too bad. I avoid playing that way, even though it does work.

I think it's useful to distinguish between what you do at the very start and what you do later. When you start with no worker, your city is very limited in production; that's why building a worker first is so useful. Your city is also stuck in neutral (for growth) until the first settler is produced; that is a big reason why chopping trees to accelerate the process works so well. You can only get the benefit of a single improved tile until your city grows, and you can't found new cities without stopping that process.

For later cities you can start with a worker, and that changes the calculus in interesting ways. A size 2 city working 2 food resources can have as much as 11P, which gets a worker/settler pair out the door only slightly slower than chopping 4 trees (16 turns vs 12). This doesn't require 4 trees per city, which isn't even always possible, and it's handy if you want to build wonders, barracks, libraries, granaries, etc. Since you're not burning 12 worker turns to get out the worker/settler, the production loss from delaying subsequent cities isn't that bad (although your settler farm city isn't growing, that isn't actually such a bad factor - you can prebuild the improvements that it will grow into, and with a big food surplus it'll grow quickly once you let it).

So worker/bronzeworking/chop,chop,chop is very advantageous at the very start, and it can be useful for later cities as well. But once you have workers, there are reasonable alternatives.

 

[DaviddesJ]

I think it's useful to distinguish between what you do at the very start and what you do later. When you start with no worker, your city is very limited in production; that's why building a worker first is so useful.

Well, of course. But this seems to ignore the question, which is comparing worker/bronze working/chop/chop/chop to worker/agriculture/farm/animal husbandry/pasture/bronze working.

As I said, I'm not questioning that the former does work quite well. I'm just saying that leaving the alternative out of your comparison and discussion entirely (as when you implicitly assume that a size-1 city only has net food+hammers of 4/turn) makes the discussion very incomplete.

 

[Wreck]

Unless you build your city on a plains/hill (which is quite worth spending time to do), or possibly a resource tile, you are very likely to have net F+P=4 for your city in the time before you build a worker. There are almost no tiles that the terrain generator creates that have F+P=4. The only exceptions would be tiles combining a forest with a resource, and there are only two of those I think I've seen: forest/deer, and forest/elephant. (In theory many resource tiles could be forested and thus get to F+P=4 unimproved, but I don't think the terrain generator will put forests on most resource tiles.)

So, your initial city is going to have net food+hammers of 4/turn usually, unless you find a plains/hill for it (or a resource), in which case, 5/turn. If you are really lucky, you can find a plains/hill next to a deer/forest and get 6/turn.

 

[DaviddesJ]

Unless you build your city on a plains/hill (which is quite worth spending time to do), or possibly a resource tile, you are very likely to have net F+P=4 for your city in the time before you build a worker.

Of course. But so what? Before you build a worker, you don't have any choice as to whether to chop or to improve tiles. The question is what happens after you build the worker, and that's when the comparison of improving tiles (thus making the city more productive) to chopping (generating production directly) becomes relevant. And that's why counting a 30-hammer chop as 7.5 turns of city production at 4/turn (post #45) is wrong and misleading---if you weren't chopping, you would be improving the tiles you are working, and your city would be generating more than 4/turn.

 

[ohioastronomy]

Well, of course. But this seems to ignore the question, which is comparing worker/bronze working/chop/chop/chop to worker/agriculture/farm/animal husbandry/pasture/bronze working.

As I said, I'm not questioning that the former does work quite well. I'm just saying that leaving the alternative out of your comparison and discussion entirely (as when you implicitly assume that a size-1 city only has net food+hammers of 4/turn) makes the discussion very incomplete.

I did look at that; it is the last two cases (best = +3P from improvement, worst = +1P from a mine or floodplain/farm). You lose a lot of early production potential. Ditto if you improve and grow to the limit first; you're postponing the founding of your second city. There are certainly a lot of ways to make up for a slower start, but not beelining for bronzeworking and chopping trees does mean that you're choosing a slower start. The other things you get can make that worth the tradeoff, and all that I'm doing here is quantifying what that tradeoff is.

 

[Wreck]

Yes I see what you are saying; certainly should be doing something productive with the worker. You are correct to criticize my assumptions in #45. However, the more general point I was hoping to make there - that time value is real - still applies.

If you do have specific resources in your starting city, then going for the tech to improve them instead of bronze might make more sense. Indeed, in a sense bronze-working itself might be seen as a particular strategy, only appropriate when you have trees around. It's just that it's a lot more common to have trees in your city than it is to have wheat/corn (and next to water), or fish, or cows/pigs; and that the correct technological means to exploit these (or other combos with two resource tiles).

But let us assume your 6 unit tile - cows, say. Assume that a settler is desired for the second build, and assume you can have either bronze-working that early, or animal husbandry. Thus you can either chop the settler, or you can improve the cows (then do other things, perhaps, but not chop, because of lack of tech). We can see already a problem here - if you've improved the one tile you can work, and you can't chop yet, the worker is more or less idle. It may be making improvements that you'll use soon, but it is producing nothing immediately profitable.

Is it possible to get Animal Husbandry (cost: 100) and Bronze Working (cost: 120) with a size-1 city in the first ~30 turns? I don't know. I 'd guess so, for a civ which starts with Mining (cost: 50) and one of the prereqs for Animal Husbandry (Hunting (cost: 40) or Agriculture (cost: 50)). I'd think not otherwise, although obviously having a floodplain tile will be helpful.

Anyway, back to the question. With chopping, the settler is created using two chops (60P), plus the city's production during those 8 turns, which is 32P, plus two more turns (8P). Total time 10 turns, and the last two are not wasted for the worker. (If you get Animal Husbandry during the time building the settler, it can start on the pasture and almost be done. Or it can just keep chopping.)

With cows, the settler spends the first 3 turns making the pasture, then does other stuff (perhaps irrigation of other tiles). So the city gets 3 turns at 4 each, for 12. Then its net production rises to 7/turn, so it takes 13 more turns to finish the settler. Total time 16 turns.

Since it took 15 turns to build the worker, its idle time starts at turn ~19. If you can get Bronze Working after Animal Husbandry in that time, then you can do one chop during the settler build, reducing the time by 4 turns to 12 turns. This would be ideal, I'd think. China can probably do it, given a floodplain and a cows. I don't think it's generally doable.

In the more general case, you're looking at a tradeoff. The 6 turns you gain by chopping cost the two forests, plus a bit during the delay until you get the cows online.

What do 6 turns gain you? To start with, it gets the 2nd city 6 turns earlier. Then it gets what that city produces for six turns... and then everything gained early by that extra production, and so on. Basically your growth should be exponential early on, so the advantage remains until at least you stop growing horizontally. How much is this likely to be? Hard for me to calculate.

But do let me correct one misunderstanding of the game, posted previously by MyOtherName in #46: "In reality, if you build a city 13 turns before me, it will always have at most a 13 turn advantage over mine."

This statement is only true if there are no events which are symmetry breaking - that is, events which are possible 13 turns earlier (but not later), or events that are only possible later, but not earlier. Events which are possible earlier (but not later) tend to bias for an early lead, expanding it. Events which are possible later (but not earlier) will naturally shrink a lead.

Now, what sort of events do we have in Civ4 of either type? There is only one event of the second type; all events in the game are keyed to earlier prerequisites, not to absolute time. The fixed game-end is the one exception.

On the other hand, there are many sorts of symmetry-breakers of the other variety, that is, events that happen once and not again. The clearest example of these are world wonders: one civ gets them; the other civs do not. If you are six turns behind me, you may not get a wonder which I do get. (And the effect of that can compound.)

It is a general property of games, that having opponents and "property" (single-owned things) breaks time-symmetry of what is possible developmentally. This is one of the things that makes Civ addictive.

But there are many other examples besides wonders; the game is in fact interesting in large part because it is a race to so many things, and you must balance them. At the outset, it's a race to goody huts. Second place gets no hut. Early, it's a race for uncontested settlement. If you are six turns delayed, you may miss out on a great city site, or even be unable to block off a region of turf by settling a choke-point. Techwise, the game has a race to religions. You don't get shrines and the benefits of them without winning one or more of these races. And it's a race to certain other techs, too, later in the game, such as Liberalism. Getting it second is not as good as getting it first. Also midgame, with continents, is the race to caravels and then galleons, to explore the world (with possible new huts), and then grab all the good islands. At the end of the game, it's a race to spaceships. Getting yours six turns early may not make a difference. But it might. If an AI opponent launched three turns in, it does. It makes the difference between winning and losing.

Of course, building a second settler six turns early does not translate into a six turn net advantage - the settler represents only a fraction of your net capital, not the totality. The advantage is much smaller (and possibly offset by the still-standing forests). However, assuming it is an advantage... it will last the entire game, so long as you play well. And it may even compound, completely depending on the nitty-gritty details of the who/what/where of the AIs.

 

[DaviddesJ]

I did look at that; it is the last two cases (best = +3P from improvement, worst = +1P from a mine or floodplain/farm).

Where? Not in post #47. You only compare chop-first to chop-never. That's rather a strawman. The real comparison is chop-first to improve-then-chop.

 

[DaviddesJ]

What do 6 turns gain you? To start with, it gets the 2nd city 6 turns earlier. Then it gets what that city produces for six turns... and then everything gained early by that extra production, and so on. Basically your growth should be exponential early on, so the advantage remains until at least you stop growing horizontally.

I think this is very, very wrong. Growth is not at all exponential. Much of your progress is driven by your research rate, and most of your research in the very early game comes from your palace, which you only ever get one of. So additional cities don't speed that at all. Furthermore, each additional city costs more in maintenance than the one before (plus you choose the most desirable locations first, so each subsequent city is also likely to be less favorably placed), so additional growth becomes less and less valuable. Building additional cities also increases your need for defenses. And so on.

In fact, I think early expansion is mostly counterproductive in terms of the effect on your overall production. OFten you would be better off expanding later. The main advantage of early expansion is that you can seize territory; if you don't expand at all, the AIs will grab the available space and then it's hard for you to expand later.

 

[Wreck]

Of course it is exponential.

Yes there is certainly a large initial effect of the palace, and the "drag" of maintenance cost of new cities. These are relatively large effects compared to the initial productivity of land. But they are constant (palace) or linear in the number of cities. (There's a thread around somewhere on the maintenance costs - they are bounded.)

On the other hand, so long as there is land, a sufficiently large city can fork off a new settler and double itself; and (ceteris paribus) the new city will be able to become just as large and productive as the parent. To pay for it you need to put down cottages (hence a worker), but you can do that. How long do you suppose the doubling time is? Perhaps 50 turns? (Much less if there are trees around to chop.)

Keep in mind that I am not only talking about horizontal expansion. I am talking about any and all ways you can invest and grow your economy, including tech, building units, etc. We have been talking about chopping out a settler, so, in that context clearly it is horizontal expansion that is assumed. However, you may be right, that it is better to invest in tech early and not expand. If so, then you are getting superior returns from tech. Therefore it must also be exponential, since it is superior to a known exponential (city spamming with cottages to pay for it).

 

[carn]

Is it possible to get Animal Husbandry (cost: 100) and Bronze Working (cost: 120) with a size-1 city in the first ~30 turns? I don't know. I 'd guess so, for a civ which starts with Mining (cost: 50) and one of the prereqs for Animal Husbandry (Hunting (cost: 40) or Agriculture (cost: 50)). I'd think not otherwise, although obviously having a floodplain tile will be helpful.

Anyway, back to the question. With chopping, the settler is created using two chops (60P), plus the city's production during those 8 turns, which is 32P, plus two more turns (8P). Total time 10 turns, and the last two are not wasted for the worker. (If you get Animal Husbandry during the time building the settler, it can start on the pasture and almost be done. Or it can just keep chopping.)

With cows, the settler spends the first 3 turns making the pasture, then does other stuff (perhaps irrigation of other tiles). So the city gets 3 turns at 4 each, for 12. Then its net production rises to 7/turn, so it takes 13 more turns to finish the settler. Total time 16 turns.

Since it took 15 turns to build the worker, its idle time starts at turn ~19. If you can get Bronze Working after Animal Husbandry in that time, then you can do one chop during the settler build, reducing the time by 4 turns to 12 turns. This would be ideal, I'd think. China can probably do it, given a floodplain and a cows. I don't think it's generally doable.

In the more general case, you're looking at a tradeoff. The 6 turns you gain by chopping cost the two forests, plus a bit during the delay until you get the cows online.

8(palace) + 1 city tile + 1 (cow on river) = 10 research(below emporer)
10 turns till husbandry, then 12 turns till BW.
worker produced turn 15, improves animals on 19, starts chopping on 25(after building farm/camp), chop on 28.
Production settler gets till improvement of cows: 12.
After first chopping: 12+9*7+30=105.
Settler built in turn 28, 3 turns after pure chopping, but with only 1 forest used and 1 additional tile improved(camp or farm). The saved forest ensures, that further settlers or wonders can be produced faster compared to pure chopping(though ).
In my eyes superior, i hope i'll find the time to test.
On emporer, non-organized, the -2 on research will improve the situation for chopping first, as cow first takes 28 turns till BW, so settler will be produced normally in turn 32.
Of course assumes either mining/agri or mining/hunting as start.

The case agri or hunting and not mining and cow:

chopping immiediately means researching mining + BW = 17 turns.
1st chop 20, second chop 24. settler build still on turn 25.
researching husbandry first, means BW researched on turn 27, settler therefore turn 30 with a good surplus for next unit. 5 turns behind, chopping first looks better, if only slightly.

same on emporer:

chopping immidiately means BW on turn 22, first chop on 25, second on 29, setller built in 29.
Husbandry first, means husbandry researched in turn 13, BW in turn 35, after settler is built in 32 without chopping. Here husbandry first is far better, because the first chopper will after founding his second city wait very long till husbandry is reasearched due to city upkeep and thereby is relying just on forest, while the other strat is nearly as fast for settler 1 and will be faster for settler 2 and 3, since chop first cannot in near time improve cow.

What do 6 turns gain you? To start with, it gets the 2nd city 6 turns earlier. Then it gets what that city produces for six turns... and then everything gained early by that extra production, and so on. Basically your growth should be exponential early on, so the advantage remains until at least you stop growing horizontally. How much is this likely to be? Hard for me to calculate.

But do let me correct one misunderstanding of the game, posted previously by MyOtherName in #46: "In reality, if you build a city 13 turns before me, it will always have at most a 13 turn advantage over mine."

This statement is only true if there are no events which are symmetry breaking - that is, events which are possible 13 turns earlier (but not later), or events that are only possible later, but not earlier. Events which are possible earlier (but not later) tend to bias for an early lead, expanding it. Events which are possible later (but not earlier) will naturally shrink a lead.

Now, what sort of events do we have in Civ4 of either type? There is only one event of the second type; all events in the game are keyed to earlier prerequisites, not to absolute time. The fixed game-end is the one exception.

On the other hand, there are many sorts of symmetry-breakers of the other variety, that is, events that happen once and not again. The clearest example of these are world wonders: one civ gets them; the other civs do not. If you are six turns behind me, you may not get a wonder which I do get. (And the effect of that can compound.)

But the wonder argument works in favor for the first husbandry, as number of workers and number of avaible forests determine, which wonders are built early and the husbandry first uses 1-2 less forest for 2-6 turns later first settler.
The extreme case is emporer above, agri/hunt, not mining and not organized, chop first is just 3 turns faster, but uses 2 forests more and will have to use further forests to get same expansion as husbandry first, so husbandry first is far more likely to get pyramids and that is far more important than setler 3 turns earlier.

Carn