Question re: new commerce cities

[GKrause]

Something to consider is that if you're at the stage of the game where 15s are easy to obtain on your caps, then you presumably have or will soon have access to watermills and decent workshops (through CS, guilds, and possibly chemistry). CS especially brings up the point that you might not be in slavery anymore. So in addition to balancing pure population growth to get maximum worked tiles vs. time for cottages to mature, where does production fall? Surely if you want to be a great commerce city, you're going to want the science and/or gold multiplying buildings (and especially a granary which you might not be able to whip) in order to maximize your yield for the commerce.

So it would seem to me that with a good food resource, you still may want to not only workshop and/or watermill some tiles, but also farm one or two tiles as well to make up for the potential cut out of the surplus that workshops will incur, taking into consideration Replacable Parts, chemistry, and potentially guilds if not already known) bonuses to production that will come into play down the line.

 

[KrikkitTwo]

One other point is Developing the commerce city, if you are running US then cottages alone is OK, otherwise slavery with farms is probably the ideal before cottaging.

(after all a Riverside Cottage + Library + University= Riverside Hamlet

 

[spoooq]

The final per turn is exactly the same in both cases, so whoever has the most accumulated commerce at the point when both totals turn parallel wins. Also, by that time, all cottages will have experienced their complete and equal lower-income growth period, so that is irrelevant. Only the number of full town-turns accumulated by the end of all cottage-growth can affect the result. If the city-slickers gain more gold in the early days than the farmers can catch up in the period between the farmers hitting max pop and the city-slickers hitting max pop, they win. This is not a particularly useful observation, but maybe it will help someone come up with an algorithm.

 

[Maestro_Innit]

I can't wait for a definitive ansdwer -= I've often pondered this one myself

 

[spoooq]

I think the answer will have to be in terms of "how many food resources does it take to beat cottages?". My guess is somewhere between zero and infinity (where infinity is equal to or greater than 21). Infinity may not be enough, but I would guess the real answer is less.

 

[VoiceOfUnreason]

What assumptions do you want to make about other population related concerns (example: trade routes)?

 

[Bleys]

I think its a case of how advanced you are. If you have CS, you can build a single riverside farm, then add a chained farm or two (not every tile is by a river, right?), and cottage over the rest of the riverside tiles. I do this often with new commerce Jungle cities. In fact, if possible, I try to chain in a farm from a nearby city instead, leaving all the riverside tiles for immediate cottaging.

I have even started farming over Calendar resources in some cases. I have a game going with Willem, where I only had 2 AH food sources, a couple FPs, and 2 non-jungle, riverside Dye tiles. I didnt want to farm the FPs, then have to cottage over them later, since it was still the beginning of the game and thats a LOT of worker turns, so I farmed the dye tiles first, while I was researching to Pottery, to fuel growth (they function like oasis's, 3 food, 3 commerce, with a FIN leader). This allowed me to put off AH for a while, since there was no real hurry to pasture Plains cows or Grass Hill Pigs.

 

[Artichoker]

this is what I was looking for. so, basically, ideally you would want to grow to 15 asap and then swap the farms out for cottages immediately.

the situation that prompted this thread was that I founded this kind of city mid-game. i had a bunch of spare workers at the time and i wasn't sure if it would be better to farm then switch or just grow slowly (most of my other cities were size 15+ at this point and i wanted the new city to join them asap).

thanks all!

I also like the concept of fast city growth...but the one factor that is not considered here is the development of those Cottages into Hamlets, Villages, and Towns.

I'd say go for a compromise and realize that you won't have infinite workers. So the goal would be to minimize the worker turns spent changing farms to cottages, while still allowing fast growth.

You could achieve this goal by building a few cottages at the very beginning, but build farms as well to speed up the growth. The advantage is that after many turns, those cottages will evolve into higher-commerce tiles.

 

[VirusMonster]

I could work out the math on this problem, but I don't think it'll be much help without other game variables such as presence of universal suffrage, freespeech, biology, overexpansion, etc.... It is very hard to make overgeneralizations for a question like this.

Intuitively, it makes most sense to work only farms until you grow size 6-8, and only start working more cottages gradually after. Why? Because at size 8, you will start reaching the health and happiness caps and must slowdown city growth. You should not work the cottages early on, because every turn you are wasting valuabe health and happiness cap.

In reality, the happiness and health caps do not jump to 15 instantly. They get there gradually. So what makes most sense, imho, is work only farms until your city size reaches 50% of the health and happiness cap. Then, start assigning the citizens above the 50% happiness and health cap to cottages. It should give you the optimal commerce&growth scenario.

 

[vicawoo]

The math is harder than it sounds, because growth is discrete and that recursively affects food and commerce.

 

[Artichoker]

I could work out the math on this problem, but I don't think it'll be much help without other game variables such as presence of universal suffrage, freespeech, biology, overexpansion, etc.... It is very hard to make overgeneralizations for a question like this.

Intuitively, it makes most sense to work only farms until you grow size 6-8, and only start working more cottages gradually after. Why? Because at size 8, you will start reaching the health and happiness caps and must slowdown city growth. You should not work the cottages early on, because every turn you are wasting valuabe health and happiness cap.

In reality, the happiness and health caps do not jump to 15 instantly. They get there gradually. So what makes most sense, imho, is work only farms until your city size reaches 50% of the health and happiness cap. Then, start assigning the citizens above the 50% happiness and health cap to cottages. It should give you the optimal commerce&growth scenario.

Not even 1 or 2 cottages at the very beginning? How about a city size of 4 with a cottage?

You mention the value of the health and happiness cap, but what is the main purpose of this? At size 8, you are working 1 Food Resource and 7 Farms (with +1 commerce from River). That's a total of 8 Commerce (including the city tile).

Suppose you had instead 1 Food Resource, 6 Farms, and 1 Cottage. That Cottage will be a Hamlet by then, producing 3 Commerce per turn. So, by having the early Cottage, you will have 10 Commerce (including the city tile).

Or, at size 8, 1 Food Resource, 5 Farms, and 2 Cottages. That will be 12 Commerce per turn, which is 50% more than working 7 Farms.


Here's an idea (I'm not claiming this to be mathematically correct or anything of that sort):

size
1 1 Rice
2 1 Rice, 1 Farm
3 1 Rice, 2 Farms
4 1 Rice, 2 Farms, 1 Cottage
5 1 Rice, 3 Farms, 1 Cottage
6 1 Rice, 4 Farms, 1 Cottage
7 1 Rice, 4 Farms, 2 Cottages
8 1 Rice, 5 Farms, 2 Cottages
9 1 Rice, 6 Farms, 2 Cottages
10 1 Rice, 6 Farms, 3 Cottages
11 1 Rice, 6 Farms, 4 Cottages
12 1 Rice, 5 Farms, 6 Cottages
13 1 Rice, 4 Farms, 8 Cottages
14 1 Rice, 2 Farms, 11 Cottages
15 1 Rice, 14 Cottages

Basically, the idea is to have at least twice as many Farms as Cottages for city sizes 1 to 10.

After city size 10, growth slows down from happiness and health caps. Beginning at city size 12, start to convert the Farms to Cottages.

You will still want to keep at least the Rice at the very end, so you can run specialists.

 

[VirusMonster]

Not even 1 or 2 cottages at the very beginning? How about a city size of 4 with a cottage?

You mention the value of the health and happiness cap, but what is the main purpose of this? At size 8, you are working 1 Food Resource and 7 Farms (with +1 commerce from River). That's a total of 8 Commerce (including the city tile).

Suppose you had instead 1 Food Resource, 6 Farms, and 1 Cottage. That Cottage will be a Hamlet by then, producing 3 Commerce per turn. So, by having the early Cottage, you will have 10 Commerce (including the city tile).

Or, at size 8, 1 Food Resource, 5 Farms, and 2 Cottages. That will be 12 Commerce per turn, which is 50% more than working 7 Farms.


Here's an idea (I'm not claiming this to be mathematically correct or anything of that sort):

size
1 1 Rice
2 1 Rice, 1 Farm
3 1 Rice, 2 Farms
4 1 Rice, 2 Farms, 1 Cottage
5 1 Rice, 3 Farms, 1 Cottage
6 1 Rice, 4 Farms, 1 Cottage
7 1 Rice, 4 Farms, 2 Cottages
8 1 Rice, 5 Farms, 2 Cottages
9 1 Rice, 6 Farms, 2 Cottages
10 1 Rice, 6 Farms, 3 Cottages
11 1 Rice, 6 Farms, 4 Cottages
12 1 Rice, 5 Farms, 6 Cottages
13 1 Rice, 4 Farms, 8 Cottages
14 1 Rice, 2 Farms, 11 Cottages
15 1 Rice, 14 Cottages

Basically, the idea is to have at least twice as many Farms as Cottages for city sizes 1 to 10.

After city size 10, growth slows down from happiness and health caps. Beginning at city size 12, start to convert the Farms to Cottages.

You will still want to keep at least the Rice at the very end, so you can run specialists.

There could be a golden ratio of farms to cottages that yield the maximum commerce in the long term, and this ratio could be 2:1 as you claim. To be honest, most of my games follow the scenario you explained

What I said at the last parapgrah of my previous post, ie assigning the excesss population above the 50% of the happiness and health cap to cottages, would end up assigning 2-3 cottages in the early game. It will result in a very similar 2:1 farms to cottage ratio you suggested. So we are thinking along the same lines. Then as your cities reach the happiness caps, they will still slowly switch from 2:1 farms to cottages ratio to a 1:1 ratio, and eventually to a 1:2 ratio and even lower ratios.

The main purpose of prioritizing farms over cottages at lower city sizes, as you can easily guess, is to have more citizens who work the cottages later. I am sure the early loss of commerce for not working all cottages will balance out later when more citizens start on working the cottages.

Also, Slavery is a very, very, very strong civic to build those infrastructure faster. With 4 surplus and a granary, a size 10 city can grow 2 population every 30 turns on Marathon speed: 126/(2 (granary effect) * 4 (food surplues) = roughly 1 population increase every 15 turns

The poprushing unhappiness penalty disappears every 30 turns on Marathon speed. Thus you can poprush for 2 population every 30 turns or just 1 and grow still by 1 population every 30 turns.

If you had 6 food surplus, then you could grow roughly 126/(2*6)=1 population unit every 10 turns. Then your cities would grow by 3 until the poprushing unhappiness penalty wears off. Then you can poprush again that expensive Courthouse (360 ), Market, Grocer, etc.. for 3 population On marathon, poprushing 1 unit results in 90 hammers.

I agree the math looks ugly, but I was planning to code this stuff out Once you have a sample code, you can generate as many test cases as you want and play with the variables. I won't do it, however, since I feel this debate is very intuitive.

 

[Gr8scott]

I think a simple metric that captures the gist of the problem would be:

Grow first and then cottage if:

(% extra surplus food from farm) * (pop growth remaining) > 1

This ignores trade routes, pop size costs, and early vs. late science, but I think it is in the spirit of what you are looking for (and it is helpful to realize that starting a cottage two turns early ultimately ends up being two town turns so cottage turns lost/gained equalize over long enough time spans).

Basically, a farm can help you grow a population point faster. Suppose after growing that population, you decided to go all cottage growth from that point forward, was it a good idea to grow first or not?

If you let:

T_F = Turns to grow 1 pop with a farm
T_C = Turns to grow 1 pop with a cottage
N = Number of population growth left to go

Then you want to farm if:

(T_C - T_F) * N > T_F

T_C - T_F is how many turns faster you get the pop growth with the farm. Critically, you want to multiply this speed benefit by the total number of population growth left to go. This is because if you go full cottage growth from this point forward, not only will you get the first population point this many turns sooner, but you will get each additional population point that number of turns sooner. This will let you start working on each future cottage sooner as well.

The question is will this net out to more cottage turns or not. To figure that out, simply compare the number of cottage turns gained to the number of cottage turns lost to going farm first. Namely the first cottage is started later. With the farm first strategy, you only start the first cottage after a pop growth, so you lose T_F cottage turns on the first cottage, but you gain T_C - T_F turns on all other cottages. That is the main comparison.

An example:
Suppose your food surplus is 4 and you are pre biology. You can work a farm or a cottage and you need to add 10 pop worth of cottages to the city. Should you farm or cottage?

taking food from 4->5 is a 25% increase. 10 * 25% = 2.5 >1 ==> farm away.
Suppose you grow. Add a cottage or a farm?
Now you are at 5 surplus and and have 9 pop left to go.
5->6 gives a 20% increase and 9 cottages = 1.8 > 1 ==> add a farm

1/6 * 8 > 1 ==> farm
1/7 * 7 = 1 ==> toss up
1/8 * 6 < 1 ==> cottage

So in this example, this rule of thumb would have you work 3-4 farms before starting to add cottages. As you approached the desired size, you would also go back and cottage over farms that were no longer sufficiently helping your percent growth.

I think that is right anyway

GS

 

[VirusMonster]

I think a simple metric that captures the gist of the problem would be:

Grow first and then cottage if:

(% extra surplus food from farm) * (pop growth remaining) > 1

This ignores trade routes, pop size costs, and early vs. late science, but I think it is in the spirit of what you are looking for (and it is helpful to realize that starting a cottage two turns early ultimately ends up being two town turns so cottage turns lost/gained equalize over long enough time spans).

Basically, a farm can help you grow a population point faster. Suppose after growing that population, you decided to go all cottage growth from that point forward, was it a good idea to grow first or not?

If you let:

T_F = Turns to grow 1 pop with a farm
T_C = Turns to grow 1 pop with a cottage
N = Number of population growth left to go

Then you want to farm if:

(T_C - T_F) * N > T_F

T_C - T_F is how many turns faster you get the pop growth with the farm. Critically, you want to multiply this speed benefit by the total number of population growth left to go. This is because if you go full cottage growth from this point forward, not only will you get the first population point this many turns sooner, but you will get each additional population point that number of turns sooner. This will let you start working on each future cottage sooner as well.

The question is will this net out to more cottage turns or not. To figure that out, simply compare the number of cottage turns gained to the number of cottage turns lost to going farm first. Namely the first cottage is started later. With the farm first strategy, you only start the first cottage after a pop growth, so you lose T_F cottage turns on the first cottage, but you gain T_C - T_F turns on all other cottages. That is the main comparison.

An example:
Suppose your food surplus is 4 and you are pre biology. You can work a farm or a cottage and you need to add 10 pop worth of cottages to the city. Should you farm or cottage?

taking food from 4->5 is a 25% increase. 10 * 25% = 2.5 >1 ==> farm away.
Suppose you grow. Add a cottage or a farm?
Now you are at 5 surplus and and have 9 pop left to go.
5->6 gives a 20% increase and 9 cottages = 1.8 > 1 ==> add a farm

1/6 * 8 > 1 ==> farm
1/7 * 7 = 1 ==> toss up
1/8 * 6 < 1 ==> cottage

So in this example, this rule of thumb would have you work 3-4 farms before starting to add cottages. As you approached the desired size, you would also go back and cottage over farms that were no longer sufficiently helping your percent growth.

I think that is right anyway

GS

Beautifully explained! Bravo You simplified the problem at hand into a basic concept.

I suggest you to edit what you have just written here, because it was a difficult read oh maybe, it is because I don't have the Nobel prize in math

Extending on what you explained in this post, I want to consider the 15 farms or 15 cottages scenario.

Assuming the inital rice resource already gives +4 surplus, increasing this food surplus from 4 to 5 in a pre-biology scenario would mean a 25% output increase. This 25% surplus increase would in return allow our cities to grow %25 faster (I am excluding the fact that cities do get slightly harder to grow with each additional population unit, but for simplicity reasons bear with me) If the city can grow 25% faster, it can work all future cottages 25% sooner. So the investment of working the farm now, translates into working 14 cottages later 25% sooner.

Multiplying this output increase with 14 possible future cottages equals 3.5. Working the farm now has an effective value of working 3.5 cottages. Then, 3.5>1 so build the inital farm.

Why did I compare 3.5 to 1? Because if I build the cottage now instead of the farm, I will get no benefit for future cottages. I will however get a single cottage starting from now on, that is why 1.

Next, you want to go from 5 surplus to 6, a 20% increase. Multiplying with 13 possible future cottages equal 2.6, still greater than 1, so form build the 2nd farm.

Next, you want to go from 6 surplus to 7, a 16% increase. Multiplying with 12 possible future cottages equal to 1.92%. Still greater than 1 so build the 3rd farm.

Next, you want to extend the surplus from 7 to 8, a 14.2% increase. 14,2% * 11 = 1,56 > 1, so build the 4th farm.

Next, 8->9, 1.25%*10=1.25>1 so build the 5th farm.

Next, 9->10, 1.11%*9=1=1, so this is the turning point. After the 5th farm, the benefits of the additional +1 surplus balance out with the benefits of having the cottage mature earlier.

so, build the farm on the rice for the +4 surplus. Then, build and work 5 more farms until working cottages become more feasible at +9 surplus.

This discussion does not take into account the effects of Slavery, but nevertheless, it gives some general idea on how many initial farm must be worked before switching to cottage tiles for optimal commerce yields.

To include Slavery usage into this equations, take the sample game data that it takes 126 to grow from size 10 to 11 on marathon speed. With granary, you need 63 to grow. If you want to poprush 3 citizens every 30 turns on marathon speed right after the poprushing unhappiness penalty wears off, then you need a food surplus of roughly 7. According to our calculations even a food surplus of 9 is feasible to prefer a farm over a cottage tile, so the presence of Slavery usage should not affect much the farms/cottages ratio. Just make sure you are close to the happiness cap when you poprush and the city will grow back in no time with 9 surplus (9 surplus requires 6 citizens to work 5 farms and the initial rice after poprushing)

 

[DaveMcW]

Bah, too much math.

Just download this game and tell me how much gold you get by 1 AD.

 

[VirusMonster]

I am a math guy dude You can do the test yourself, farm until you get +9 food surplus, then start cottaging. Can you also post a BTS save?

 

[futurehermit]

So, is the conclusion farm until you have a solid food surplus going then cottage the rest then cottage over the farms once you hit the size 15 health/happy caps?

 

[spoooq]

I would have thought that if some farms are good, more farms are better. Farm everything, grow till max, then cottage everything. I would also like to have an exact answer, because I have a game with a Fin leader whose capital has 8 gems... do I cram in a couple farms or just mine?

 

[Diamondeye]

Thanks for the maths, it makes a lot of sense

I would have thought that if some farms are good, more farms are better. Farm everything, grow till max, then cottage everything. I would also like to have an exact answer, because I have a game with a Fin leader whose capital has 8 gems... do I cram in a couple farms or just mine?

Screeenie!

 

[Artichoker]

Beautifully explained! Bravo You simplified the problem at hand into a basic concept.

I suggest you to edit what you have just written here, because it was a difficult read oh maybe, it is because I don't have the Nobel prize in math

Extending on what you explained in this post, I want to consider the 15 farms or 15 cottages scenario.

Assuming the inital rice resource already gives +4 surplus, increasing this food surplus from 4 to 5 in a pre-biology scenario would mean a 25% output increase. This 25% surplus increase would in return allow our cities to grow %25 faster (I am excluding the fact that cities do get slightly harder to grow with each additional population unit, but for simplicity reasons bear with me) If the city can grow 25% faster, it can work all future cottages 25% sooner. So the investment of working the farm now, translates into working 14 cottages later 25% sooner.

Multiplying this output increase with 14 possible future cottages equals 3.5. Working the farm now has an effective value of working 3.5 cottages. Then, 3.5>1 so build the inital farm.

Why did I compare 3.5 to 1? Because if I build the cottage now instead of the farm, I will get no benefit for future cottages. I will however get a single cottage starting from now on, that is why 1.

Next, you want to go from 5 surplus to 6, a 20% increase. Multiplying with 13 possible future cottages equal 2.6, still greater than 1, so form build the 2nd farm.

Next, you want to go from 6 surplus to 7, a 16% increase. Multiplying with 12 possible future cottages equal to 1.92%. Still greater than 1 so build the 3rd farm.

Next, you want to extend the surplus from 7 to 8, a 14.2% increase. 14,2% * 11 = 1,56 > 1, so build the 4th farm.

Next, 8->9, 1.25%*10=1.25>1 so build the 5th farm.

Next, 9->10, 1.11%*9=1=1, so this is the turning point. After the 5th farm, the benefits of the additional +1 surplus balance out with the benefits of having the cottage mature earlier.

so, build the farm on the rice for the +4 surplus. Then, build and work 5 more farms until working cottages become more feasible at +9 surplus.

This discussion does not take into account the effects of Slavery, but nevertheless, it gives some general idea on how many initial farm must be worked before switching to cottage tiles for optimal commerce yields.

To include Slavery usage into this equations, take the sample game data that it takes 126 to grow from size 10 to 11 on marathon speed. With granary, you need 63 to grow. If you want to poprush 3 citizens every 30 turns on marathon speed right after the poprushing unhappiness penalty wears off, then you need a food surplus of roughly 7. According to our calculations even a food surplus of 9 is feasible to prefer a farm over a cottage tile, so the presence of Slavery usage should not affect much the farms/cottages ratio. Just make sure you are close to the happiness cap when you poprush and the city will grow back in no time with 9 surplus (9 surplus requires 6 citizens working farms after poprushing)

This all makes sense, but the assumption was that pop growth requirements are constant throughout. What happens when you have variable pop growth requirements?

Let's take an exaggerated example. Suppose, for example, that pop 2->3 required 10 turns without the extra farm, and with a food surplus of +5.

And then suppose that pop 3->4 required 100 turns with the same food surplus.

If, at pop 2, a Cottage were built for the 2nd extra tile (in addition to the initial Food resource), it would be producing commerce for the 100 turns at which the city remained at pop 3. At pop 3, there would be 2 Cottages producing commerce for 100 turns.

Now, if the 2nd extra tile were a Farm instead, there would be just a Food resource + Farm for the 1st and 2nd extra tiles, and a Cottage for the 3rd extra tile. So, at pop 3, there would be just 1 Cottage producing commerce.
Granted, the additional +1 food surplus from the new farm would increase the food surplus from +5 to +6, but it would still take 5/6 of 100 turns, or 83 turns, to grow from pop 3 to pop 4. So, during those 83 turns, there's only 1 Cottage generating commerce, and for the remaining 17 turns, there are 2 Cottages generating commerce.

However, in the first case, the extra Cottage gets a head start in working towards becoming a Hamlet, and then a Village. Whereas in the second case, the extra commerce from the extra Cottage is coming from a newly-built Cottage that has barely started to mature. So the generation of commerce is less for that newly-built cottage.

Of course, this is an exaggerated example, but the increasing costs of pop growth with tend to highlight the effect of Cottage maturity as a reward for building early cottages.