Maximizing Production After the Opening

[ohioastronomy]

In this thread I discussed optimizing production at the beginning of the game. To briefly summarize, the optimal production sequence is worker/worker/settler, with one worker left at the capital and a worker/settler pair sent out to the second city. Using workers to chop 4 trees yields a significant production advantage over not doing so. You can do slightly better by improving one good tile before chopping, costing you 3 trees (or one less than pure chopping). See junior7’s comments on page 4 of the thread, quantifying which nations benefit from improving specials before chopping trees for the initial worker/settler pair.

In a typical game, once you have founded your second city there is a distinct stage in the game when you can expand your civilization to some degree. The size of your cities will be capped by health and happiness, and the number of your cities will be capped by maintenance and geography. Both will be strongly impacted by the difficulty level, and the map you choose will also play a role. This phase typically could end when you unlock the advanced resources and buildings that raise the happiness/health limits (for city size), and when you get Code of Laws and Courthouses (or build up sufficient commerce) to make further city expansion feasible. The focus of this article is addressing the question of the fastest way to build your cities up to a modest initial size of 5 with the strongest production mix.

I’ll say from the beginning that there are a number of game situations where reaching the theoretical maximum may not be your main goal. The tactics discussed here, however, are fairly general, and there are preferred sequences that will make a real difference in your early game. The basic thesis is as follows:

In almost all cases you will maximize production and commerce if you send out worker/settler pairs, build improvements before roads, and make your first improvement in a new city a food resource that you work until you hit the happiness limit. You can either chop workers and settlers or use a city with a large food surplus as a settler farm. Here is a more detailed summary, to be followed with analysis:

1. There are two viable models for producing settlers and workers once you have workers: chopping trees and building a settler/worker farm with a large food surplus.

2. When founding a new city you should have a plan for what tiles it will be working when it is at your limit, and you should plan which tiles you work to grow to that limit. These two things will frequently not be the same. You will also need to factor in whether you can grow your cultural boundaries to work tiles 2 spaces from your city. Either being a creative civ, building Stonehenge, or getting a religion should be a priority. Since getting a religion and spreading it can be a production sinkhole, and Stonehenge can be chopped quickly, this makes Stonehenge a valuable early production investment for non-creative civs.
3. A city with a food surplus of 4 or more can grow as quickly as a single worker can improve tiles. In most cases, this means that cities with a food special have a production advantage, and improving that special resource first will maximize your production. If you have two or more food specials, the extra growth from developing both will not increase overall production much unless your goal is a settler farm.

4. You should budget about 25 worker turns for 5 improvements, or 5 worker turns per improvement at normal speed. Fully connecting a city with roads and adding roads to specials will add another 16 worker turns. Rivers can reduce or eliminate this overhead. Sending worker/settler pairs is therefore far more efficient than founding cities and building a worker. You may be forced to send a settler alone to a contested site, but you will take a production hit without also sending a worker.

5. In the early game you are better off for production if you improve first and build roads later. Connecting food resources should be a low priority in the early stages; connecting luxury resources is more important, and general resources may be the most important. If your strategy requires hooking up general resources rapidly (copper, horses, etc.) you’re better off adding extra workers for roads.

6. Granaries are only important for early production if you have cities with a severely limited ability to generate food surpluses (2 or less). They do matter a lot for later growth. If you need them, chop them in cities with limited hammers and use production for them in production sites.

 

[ohioastronomy]

Basic assumptions:

Production (P) refers to the sum of food (F) and hammers (H). A city gets 3 free production (2F, 1H), and each additional person consumes 2F and can work a tile (or be a specialist). I won’t consider specialists at this level because they normally become significant for larger cities with the relevant wonders or buildings). A floodplains or forest tile has 3P, which is the maximum before improvements. Improved tiles can have as much as 6P (irrigated wheat, corn; copper, pigs, etc.). Mines and floodplains farms have 4P. A basic size 1 city therefore has 4P (3 free + 3 from first tile – 2 food consumed). Every person added working an unimproved tile adds 1P; improved tiles can add up to 4P. Commerce is more complex and will be treated separately. Forests yield 30P and take 4 turns; workers cost 60; settlers cost 100.

In order to quantify production, you have to assign a value to founding cities, worker turns, and improvements. I’ll consider a limit of 5 (prince) before happiness/health stop growth. If you’re running at lower difficulty levels the values discussed below increase because the cities get larger; conversely, they drop for higher difficulty levels. The easiest way to visualize this is to compare two situations where everything but one factor is held constant. This amounts to picking a final target for a city (which tiles it will eventually work) and looking at the fastest way to get there. For example, imagine that I develop the same city site in exactly the same way, but I delay the founding of the city by 1 turn. I’d lose 4P (from the missing turn), and I’d grow to sizes 2,3,4,5 (or whatever the pop limit is) one turn later. This gives a minimum cost of 8P for every turn that I delay founding a city. Assuming that I can at least work two +1P tiles before I hit the limit, I therefore assign a value of 10P per turn that founding a city is delayed.

City growth can also be quantified; I compare the results for holding everything else fixed but examining the production consequences of different growth rates. Finally, worker turns also have high value. The simplest method is to assume that workers in the early game can just chop trees, yielding an average of 7.5P/turn at normal speed (30H, 3 turns to chop, one turn to move into a forest; India can do better). However, even if you just look at improvements, worker turns are valuable. If I have the same set of improvements in a city, but delay getting a worker started on them by one move, then my city will get to use each of the improvements one turn later. Assuming that I can work two specials (+3P, +2P), and two floodplain/farms or mines (+1P), I get a penalty of +7P for that lost worker turn. I can also accelerate founding a new city (+10P), and my city will grow faster if it is working food resources, so this is a pretty conservative estimate.

 

[ohioastronomy]

Building workers and settlers.

From the first article, once you have a worker you can use 4 forests to chop a worker and settler in 12 turns (12 x 4P + 4 x 30P = 168; 8 overflow). One simple expansion method is therefore to assume that the first 12 turns of a new city are devoted to sending off a worker and settler to the next city site, relying on older cities to make military units and improve/grow. This is easy, but you may not have that many forests available. You also may have other goals (wonders), or you might need the hammers for steady production. Is there an alternative?

A.You can reduce the number of trees and gain in net production if you improve a +2P or +3P tile before chopping trees. If you improve the best tiles (+3P) you will get normal production (4P) for turns 1-5 and enhanced production (7P) after. This implies that in 13 turns you can chop 3 trees and have a worker/settler pair (5x4 + 8x7 + 90 = 166; 6 overflow). You delay the settler 1 turn (10P penalty), but you gain on worker turns (22.5P) and production (12P). (After turn 12 your city with chopx4 still has to spend 5 turns on an improvement, and you only have 2 surplus worker turns; the improve-first city got to enjoy 4 turns of improved production devoted to other things, and if it is a food special the improve-first city has a growth head start). For a +2P tile your settler/worker pair will take 14 turns and 3 trees (5x4 + 9x6 +90 = 164; 4 overflow). You have the same worker turns as the +3 improve case (+22.5P) but a higher penalty for delaying the settler (-20P) and a smaller production benefit (+8P). If all that you can do is build a normal mine or floodplains farm, you have a penalty for improving first and then chopping.

B.You can improve a city to generate a large food surplus, and then have it churn out settlers and workers without using trees. A city working 2 good special food resources can put out worker/settler pairs in 15 turns without cutting trees; you get extra growth/production at other cities at the cost of stretching out your early expansion. In this approach, you grow your city to a target size and then switch it to making worker/settler pairs. A larger settler farm will have higher long-term production but a bigger delay in sending out the first colony.

This approach does not work well if you leave the city at size 1. You have 4P for the first 5 turns and 7P every turn thereafter. This means a 25 turn delay for the first colony (5x4 + 20x7 = 160) and a new colony every 23 turns thereafter. The delay penalty is substantial. The picture changes if you have more than one resource to work. If you have a size 2 city working 2 6P tiles, you have 11P that can be used for workers and settlers; you can have as much as 15P from a size 3 city, etc. In this case you devote your city to growth; 22F are required to reach size 2 at normal speed. For a size 2 target you have 5 turns of 3F/1H (hammers wasted, unfortunately) and grow after 7 turns (5x3 + 2x6 = 27, 5 excess). You then switch to worker/settler, and the second improvement comes on line after 10 turns. The first worker/settler pair can be sent out 16 turns later (3x7 + 13x11 = 164; 4 overflow), which is an 11 turn delay over straight chopping, and subsequent colonies can be sent out in 15 turns (15x11=165; 5 overflow). You gain 12 turns of growth/production in all new cities, so the net effect comparable to chopping with a longer delay between cities. You don’t need trees to do this, and you also don’t need a worker improving the settler farm city. More to the point, 11P is pretty respectable for an early city, especially at size 2, so I’d view the “lost growth” in the settler farm city as a smaller production hit than the “lost growth” you’d have in subsequent cities while they were generating settlers and workers. I’d recommend this route if it is possible for your starting position and you aren’t concerned about losing a good city site to one of the AIs.

If you have enough specials, you could grow to size 3 after 10 turns (5 carryover + 7x3=26, 2 left over) and have the third improvement up on turn 15. In this case the first worker/settler pair leaves 12 turns after you switch from growth to settlers (5x12 + 7x15=165, 5 overflow), or 10 turns later than straight chopping. Subsequent colonies can be sent out in a speedy 11 turns (11x15=165, 5 overflow), and you have an edge over chopping. It is very rare to have such an ideal city, however.

 

[ohioastronomy]

Two city models: In order to illustrate the power of the approach I’m advocating I’ll look at two representative early city cases. These correspond to a production city (maximizing hammers) and a commerce city (cottages). I’ll start with the cottage city, since the advantages of building a farm first for a production city are obvious (it can’t grow without a food surplus!).

In both cases I’ll assume that you have a dedicated worker for a new city. The reason is simple: production in unimproved tiles is far inferior to production in improved tiles. A new city has a maximum of 4P, and a size 5 city without improvements has a maximum of 8P. Maximum production for a city of size (1,2,3,4,5) working improved tiles is (7P, 11P, 15P, 19P, 23P). Reaching your maximum production is therefore a well-posed mathematical problem: you want to choose a strategy that gets your city working 5 improved tiles in the shortest time.

Growing to size 5 requires a total of 100 food at normal speed (22+24+26+28). Building 5 improvements requires 25 turns, so you can grow into improved tiles (for a substantial production advantage) if you can maintain an average food surplus of 4 and have one worker per city. The same average food surplus is required at slower speeds because the food required for growth and the time for worker improvements both scale; improvements are slower at quick speed relative to growth.

Commerce city: Assume that your target for a commerce city is working 4 cottages and a plains/hill mine (to give you a few hammers). If you simply built the improvements and worked the cottages followed by the mine:

Size 2,3,4,5 on turns 11, 23, 36, 50
Cottages turns 4,8,12,16; Mine 21
Cottages worked turns 4, 11, 23, 36; Mine first worked 50

If you chopped a granary first and then had the same build order:

Size 2,3,4,5 turns 11, 18, 25, 32
Chop turns 4,8; Cottages turns 12, 16, 20, 24; Mine turn 29
Cottages worked turns 12, 16, 20, 25; Mine worked 32

If you improved a +3F tile, then 4 cottages, then a mine:
Size 2,3,4,5 turns 7, 11, 15, 20
Farm turn 5; Cottages turns 9, 13, 17, 21; Mine turn 26
Farm worked turn 5; Cottages worked turns 9, 13, 17, 21; switch farm to mine turn 26

Your first cottage is delayed, but the later ones and the mine are substantially accelerated. The net effect is a significant boost in commerce from building the farm first, then building the improvements you’ll actually work when the city is grown.

Use the first build strategy as the comparison point. If you value each turn that a cottage is worked as 4C (2 for founding, one each for earlier growth to hamlet, village, assuming a financial civ and cottages on a river): the net effect for chopping a granary is (-8 -5 +3 + 11) x 4C = +4C; you also get 18x4H= 72H from working the mine. (If you chose a 5th cottage, you’d gain 76C and no hammers). The net effect for building a farm first is (-5 -2 +6 +15)x4C = +56C and 24x4H = +96H for the mine. You gain substantial commerce and production from building a farm first, even if you eventually abandon it and work a different tile. You continue to be ahead with a farm with 4F or better.

A strong production city will have a special hammer tile (e.g. grassland copper mine) and a mix of mines on hills with a food source to support the miners. If you have a +6F tile available, the eventual mix might be base (2F 1H), wheat/corn farm (6F), copper mine (2F 4H), 3 plains/hill mine (4H) for a beefy 10F 17H. (Substitute 2 grass/hills mines for plains mines if you have a +4F farm, e.g. floodplains). For a build order of farm/copper/minex3 your production pattern would be

Size 2,3,4,5 turns 7, 11, 18, 30
Farm turn 5, copper turn 10, mines turns 15,20,25
Farm worked T1(improved T5), copper worked T10, mines worked T15, 20, 30

If you built the copper mine first, your net production would be almost the same; you lose if you do not build the farm second, and you lose if your first build has less than 2F.
Note that every turn you delay in building the first 4 improvements (for example, road building) translates directly into a production cost. This cost is highest for the first 2 builds.

 

[ohioastronomy]

Other notes

Although game speed and difficulty don’t directly affect the overall conclusions, the differences in technology development do have important consequences. The research pace is slower for harder games, and it is also slower for longer games. What this means in a practical sense is that some theoretically useful tiles can be irrelevant for early city growth in long/hard games; it may be 150+ turns before you can actually use cows or pigs in an emperor/marathon game. Obtaining early commerce may therefore be important. Especially at marathon, you may find that an early investment in “general” worker technologies (farms, mines, roads) will have a much greater payoff than spending many turns on masonry to work a single stone quarry.

Also, do not underestimate the impact of cultural growth. Many of your best city sites have their most useful early tiles 2 spaces away from the city, and you can’t use them until your new cities can generate culture. I either run creative civs or emphasize Stonehenge early for this reason.

If a new city site has a lot of jungles, you should double the worker requirements if you have ironworking. If you don’t have ironworking, a city with a lot of jungles will probably be a net production loss early on; found it only if it is essential for strategic reasons.

Finally, gold mines are a bit of a special case. They provide crucial early commerce, but without a food source they stop city growth (0F, 2H-3H). In this case, you will need to develop a farm and switch to working that farm for a few turns to permit later city growth at some point. Because your city will have a small food surplus, an early granary will be a useful investment.