Optimum Early Growth Strategy

This article is intended to determine the optimum strategy for maximizing production in the first 40 turns of the game. My intention is to quantify the advantages of chopping down forest and to compare different tactical paths in the early game. Tactics to be discussed include the relative advantages of growing your initial city, building workers, improvements, founding your second city, chop-rushing, and queue shuffling. I chose a 40 turn window because in this time it is possible to have two solid cities, with workers improving both, and to be in position to develop a third city if you desire. Over longer periods the mix of tiles, external threats, and other priorities (such as road building and military development) complicate the situation. I’ll contend that the following general conclusions apply for normal speed games:

  1. Building worker/worker/settler is optimal for early growth.
  2. If you can either build a mine or farm a special resource before chopping you end up equal to straight chopping at turn 40. This implies that you do not need to research Bronze Working first (but do need to have it completed by turn 20).
  3. Limited chopping (3 trees) is a key to getting your initial cities set up.
  4. Growing your city to size 2 before building a worker carries a significant production penalty.
  5. Queue switching will be discussed in a followup post, as will the develop-one-big-city first approach.

Commerce is omitted here, but I contend that is actually reasonable, since significant commerce usually requires worker improvements and thus typically takes off later than this period. As you will see below, any commerce advantage from early growth would have to be balanced against the rather substantial production disadvantage.

I’ll begin with some basics. A size one city has 3 free production and each additional population point (PP) can generate 3 more production (if there are forests or flood plains) before improvements. Each PP uses 2F. Before improvements, this means that

A size 1 city has 4 production
Growing a city by one PP adds 1 production

Chopping trees yields 30P (at normal) and takes 4 turns including travel time.
Costs for a warrior, worker, and settler are 15, 60, and 100 respectively. I’ll discuss epic speed separately, but tree-chopping is even more favored there (45 yield for a forest, workers and settlers are 75 and 125 respectively).

Farms and mines improve basic production, and building them takes a minimum of 5 turns including travel time.
Wheat and corn (with agriculture) and copper (with BW) add 3 production.
Mines add 2 production, as do deer camps (but the base is low on tundra and build times are longer). However, mines clear forests, so the maximum production from a mined tile without a special resource is 4 (gain of +1 over a forest or flood plain).
Normal farms add 1 production – but only on base 2 production sites or flood plains. Creating a farm on a flood plain also takes longer. For this reason I’ll only include the +1P (floodplain+farm and grass/hills+mine) and +3P cases for improvements.

You can already see from the above that starting a second city adds much more production than growing the first city, and that the best improvements are almost as valuable in the short run as founding a second city. Normal improvements increase total production modestly, but only on certain tiles.

No growth cases: in this model the first city build is a worker, usually coupled with researching bronze working. On turn 15 the first worker appears. I then compared the following strategies, all ending with 2 workers, and one settler. I also compared the lucky +3 production improvements and the more typical +1 production improvements. Here are the cases:

  1. Chop worker 2, both workers chop settler, improve
  2. Chop settler, chop worker2, improve
  3. Improve city(+3), chop worker 2, chop settler
  4. Improve city (+1), chop worker 2, chop settler
  5. Improve city (+3), settler with no chop, worker 2 with no chop.
  6. Improve city (+1), settler with no chop, worker 2 with no chop.

Here are the results. Worker turns is the number of turns that you would have workers available to do things by turn 40 other than chop settlers/workers and build the first improvement:

Case A: Worker2 T23, Settler T27, Imp T32, 21 worker turns, 8 overflow
(12 x 4P + 120 from 4 trees = 168)
Case B: Settler T25, Worker2 T31, Imp T36, 13 worker turns, 24 overflow
(16 x 4P + 120 from 4 trees = 184)
Case C: Imp T20, Worker2 T24, Settler T28, 24 worker turns, 6 overflow
(5 x 4P + 8 x 7P + 90 from 3 trees = 166)
Case D: Imp T20, Worker2 T24, Settler T30, 24 worker turns
(5 x 4P + 10 x 5P + 90 from 3 trees = 160)
Case E: Imp T20, Settler T32, Worker2 T40, 15 worker turns
(5 x 4P + 20 x 7P = 160)
Case F: Imp T20, Settler T36, Worker2 T48, 7 worker turns
(5 x 4P + 28 x 5P = 160)

Now, to put these all onto a common metric:

The earliest completion of all workers and settlers is T27. After this point the main city can grow. Later starts are penalized 10P per turn of delay (4P in direct cost and 2P in delayed production from population points 2,3,4 each). Beyond that point the happiness and health limits can be relevant.

The earliest settler is T25. Later starting cities are penalized 10P per turn of delay for the same reason.

Every worker turn that is available after the base tasks above are completed is worth 7.5P (chopping trees; could also be improving for future growth, but that is tile-dependent).
Production overflow is credited to each case as available.

Case A: +145.5 (4 trees)
Case B: +81.5 (4 trees)
Case C: +146 (3 trees)
Case D: +100 (3 trees)
Case E: -87.5 ( 0 trees)
Case F: -307.5 (0 trees)

There is also a difference in the improved city production after the workers and settlers are produced. This is significant for cases A, B, C, E (where there is a good special available).

These cases get stronger production released after turns 32, 36, 28, 40. When this effect is accounted for, Case C (improve a +3P special before chopping) saves a tree and gets the highest yield. Cases A and C are thus very close).

Chopping is strongly favored, and building a second worker before a settler is favored. Improving a special resource is a wash with chopping first, and building a 4 production tile before chopping is disfavored. You don’t need to clearcut for a solid start.

What about growing first? If you have the right tiles available you can grow to size 2 and put out a warrior by turn 10. How does this compare with building a worker first? We’ll focus on Case A above (worker/worker/settler), as it doesn’t rely on a handy wheat or corn. In this case:

Size 2 turn 10, worker 1 T22, worker 2 T28, Settler T34, Imp T37, 10 worker turns, 20 overflow. In all the other cases we assumed the city would start growing on turn 27, while in this case 10 turns of early growth went to the city+unit and it is free to grow again after turn 34. As a result, I give this case 30 extra production for a growth head start (it gets 10 turns of growth by turn 34 while the other cities get 7), and add 24 for the extra production in turns 11 through 34. In effect, the worker-first cities catch up in size while the grow-first city is catching up in workers and settlers. This setup has a rating of +36, e.g. significantly worse than the build-worker first case. In terms of the land grab, it also postpones founding the second city by a potentially crucial 9 turns.

An early delay in building workers (without growing to size 2) costs 25 production/turn: a one turn delay in founding a city and two lost worker turns chopping trees. I hope this is useful; comments/questions most welcome.

Queue swapping is an interesting tactic to combine early growth and tree-chopping. It starts the same as the worker-first strategy, producing a worker on turn 15. On turns 16, 17, 18 the city grows and builds a warrior. On turn 19 the city switches to a worker, with 34 production (4 basic plus 30 from chopping a forest). The second worker appears on turn 23, both chop on turn 27, and one chops on turn 31 while the other produces an improvement on turn 32 (6 overflow). Relative to case A, the founding of the second city is delayed 4 turns, and 4 turns of worker action are lost; this is a 70 production penalty. However, the main city has had 12 extra turns of growth (a 120 production edge.) As a result, queue swapping is a net +193.5 on the original scale, but does burn 5 forests. There is some opportunity cost in losing resources that could be used later (for wonders, barracks, granaries, etc.)

There is also a trick to use only the chopped timber for settlers and workers (extreme queue swapping). Essentially, you set production to settler on the turn the chop is due, manually make the worker chop, and then set production back to warrior. This is more competitive at epic speed, but is an expensive idea on normal speed: settlers cost 100 and forests yield 30, so you would have to chop 6 forests (with 20 overflow) by turn 31 to get out the settler. Relative to normal queue swapping, this method loses 4 worker turns (30 penalty) and gains 4 turns of growth (40 benefit) with 14 extra overflow. The overall net is +217.5, so it scores highest on an absolute scale. If you subtract the opportunity cost of the forests used, however, the relative rankings are different:

No queue swapping +63.5
Normal queue swapping +43.5
Aggressive queue swapping +37.5

Whether you use this technique or not therefore depends in part on how many forests you can use and what else you might do with them.

An alternate approach is to build a large city first and then use the enhanced production to churn out units later. An additional advantage is that such a city produces more early commerce. However, this strategy is significantly weaker in production (and, over the long term, not as strong in commerce as it might appear) because of the power of chopping and improvements. Assume the most favorable case for growth, namely 5 good food resources or flood plains on a river. In this case the capital will grow to size 2,3,4,5 after 8, 14, 19, and 24 turns respectively. By occasionally swapping in some grass/hills/forest it is possible to build 2 warriors and grow to the prince capital happiness limit (5) in 25 turns. The larger city will have 8 production, and if you follow up with worker/worker/settler then you can have worker1(33 turns), worker2(37 turns), and settler (42 turns). There is a commerce edge until the initially smaller capital catches up in size (108), and a production edge (95), assuming the growth pattern is the same. However, there is a 16 turn delay in founding city 2 and you need 9 worker turns past turn 40 to finish the initial builds. The net effect is -132.5 on the original scale, or almost 300 production behind emphasizing settlers and workers early. If anything, this understates the disadvantage of growing onto unimproved tiles. A size 1 city working an improved wheat has almost the same production (7) as a size 5 city working 5 unimproved tiles (8). By the time the big city has produced its first settler, you could have had two medium cities (size 2-3) working improved tiles and could have even founded a third city with supporting worker. Even the commerce edge (roughly one good tech) has to be kept in perspective; a single gold mine has a much bigger long-term yield.

You could get better results by building two workers and then using them to improve tiles while letting the city grow to the happiness limit, then building a settler. The exact results are more complicated to compute because they depend on what tiles are available. In my view, this actually confirms the idea that building a worker first is optimal for a variety of play styles.

Different game speeds can significantly change the benefits of different strategies. The key thing to understand is the different way that units and tech/forests/growth/production scale with speed. As you go from Quick-Normal-Epic-Marathon (Q-N-E-M) the costs for a unit scale as
Q 4/5 – N 1 – E 5/4 – M 2
(for example, the respective costs for a settler are 80, 100, 125, 200).

However, tech costs, city growth, improvement builds, and forests change more quickly with speed. They scale as
Q 2/3 – N 1 – E 3/2 – M 3
(for example, the respective yields for forests and the turns to clear including travel are
Q 20 (3) – N 30 (4) – E 45 (5) – M 90 (9)
This means that Stonehenge always can be gotten with 4 forest (2 with stone) at all speeds,
but the cost in forests for a settler is
Q=4 N=3.33 E=2.78 M=2.22
and the time to build a settler with the basic 4 production of a city is
Q=20 N=25 E=32 M=50

With an important exception for technology speed at high difficulty levels and marathon, you can therefore expect the following
relative trends. I’ll post details for other speeds if people are interested.

1) In quick games cities grow rapidly and the yield from tree-cutting is smaller. The rapid pace of technology also means that workers are more flexible – it is very likely that you can improve special resources immediately upon founding a new city. This makes improvements more powerful, and dramatically reduces the differential impact of chopping on early production. If you start with good special resources you can do better by improving the first one (after you have a worker) than you can by focusing on tree-cutting (an improved wheat has a higher return than a forest cut after 7 turns). Worker-worker-settler is still the preferred sequence, but clearcutters will quickly run out of forests. Building a big city before a settler still fares worse than building a worker first, since once the tiles are improved the capital will grow to the happiness/health limit almost immediately. Note that because cities grow very fast (as quickly as three turns per population), having extra workers in the early game will have a large impact on production; you’ll benefit from hooking up special resources to raise the health and happiness caps. Peaceful builders and tree-huggers will probably like this speed.

2) In epic games the technology speed is still fast enough that it doesn’t play the huge role that it will at marathon. Worker-worker-settler is strongly preferred to other build sequences. Trees provide so many hammers that queue swapping is extremely effective, and can be used to put out early warriors, etc. without a large production penalty. You may even want to do a reverse queue swap, putting a warrior in the build queue when you want to get it out quickly and then crediting the overflow to the worker or settler. Remember that the costs are not exact multiples of timber yields, so that you want 200 production going to your second worker+settler, not the 180 you’d get just from cutting four trees (so you will want to have 5 turns of native production applied to units, not growth, to avoid using up too many of your valuable forests.)

3) In principle you might expect marathon games to be a simple extension of the above trends, and a theoretical analysis supports that. But the glacial pace of research has interesting consequences – especially at high difficulty levels. When you found your first city and choose your first tech on a normal start, you’ll see something like the following for bronze working (BW) and a Worker(W) at Prince:
Quick BW=9,W=12 turns
Normal BW=13, W=15 turns
Epic BW=21, W=19 turns
Marathon BW=49, W=30 turns. At Marathon/Deity, it take 67 turns to get bronze working….
(If you have a special start tile the worker time will be less, and if you have commerce on your second tile the tech time will be less. You can usually shuffle the worked tile in that case so that the arrival of the first worker and getting BW happens at the same time on epic).

What this means is that unless you either prioritize commerce or are extremely careful you will have extended stretches where your workers, and cities, have absolutely nothing useful to do. It is entirely plausible that it will take you 150+ turns before you can actually use that pig next to your starting city, and even improvement build times are long (15 turns for farm, etc.) As a result, financial leaders have a significant production edge, and coastal production, specials with commerce, etc. will dramatically speed up city development.
Timber is useful for a lot of things, and you should think carefully about how you want to spend it. The AIs don’t tend to use it for wonders, for instance, and it does save a lot of time for buildings as well. Unless you can speed up the tech, there is no gain in starting with a worker until you can time their arrival to coincide with a useful task – you might as well spend the first 20 turns getting a warrior out, unless there is a lovely gold mine next door.

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