Question re: new commerce cities

[MyOtherName]

I'm pretty sure that the 7 extra cottage turns cannot explain the 43 commerce difference.

Reviewing my calculations, the suggestion that you don't work the rice at size 14 was based upon cottaging over the rice:

(G = amount of food needed to grow)
Working non-rice cottage = (G / 2) * -1 = -0.5 G cottage turns lost
Working farmed rice = (G / 5) * -2 = -0.4 G cottage turns lost
Working cottaged rice = (G / 3) * -1 = -0.333 G cottage turns lost

Since G = 72, the difference between non-rice cottage and farmed rice should be about 7.2: consistent with what you observed. You should get an extra 4.8 cottage turns beyond what you observed if you did cottage over the rice.

(The formula predicts what happens at size 11 is irrelevant, so the fact you didn't put any overflow into the granary at size 11, and didn't work any farms, should have no contribution to the observed difference)



The library is definitely useful. You will get a library just from the one hammer per turn from the city tile. If watermills are available, then you can "spend" a cottage turn working a watermill instead, to get one hammer. Each hammer makes the library appear one turn earlier. Making the library appear one turn earlier is worth several cottage-turns. Slavery is probably better than watermills. I predict the best strategy gets a library before any cottages are worked, although I haven't tried to reason out how best to do it.

 

[ParadigmShifter]

OK, I think, to sum this thread up, we have to quote Barbie

"Math is hard".

 

[namliaM]

Offcourse working a cottaged rice over a normal -non river- cottage will be better.
You get an extra commerce AND +1 food. It is only logical....

But, that is only "true" with the hard limit on 15 and 200. I would like the option to work the rice and run a scientist or even grow more/faster over getting some more commerce. BUT presuming hard cap on both size 15 and 200 turns, yes.... working a cottaged rice > Cottaged normal grass...

about the difference in commerce between your and my options...
Because you run no cottages untill size 11 and only run 1 cottage at size 11 (turn 52 - 55) and only at that size 12 work all cottages I get a jump on you. During the last turn of size 10 (turn 51) + the 4 turns at your size 11, I am allready running cottages.

By turn 56 you have put in 4 cottage turns, while my option is allready at 47 cottage turns. From that point on the total commerce switches up and down. I have cottages growing to towns earlier, while you are working more cottages. Also the 12th cottage grows earlier in your scenario vs mine, since you grow to size 12 turn 56 and I grow to size 12 only in turn 65.

This is the overall explenation for the difference of 43 commerce as at turn 56 the 43 is exactly the difference in our two "plans".

 

[MyOtherName]

Offcourse working a cottaged rice over a normal -non river- cottage will be better.
You get an extra commerce AND +1 food. It is only logical....

But, that is only "true" with the hard limit on 15 and 200. I would like the option to work the rice and run a scientist or even grow more/faster over getting some more commerce. BUT presuming hard cap on both size 15 and 200 turns, yes.... working a cottaged rice > Cottaged normal grass...

about the difference in commerce between your and my options...
Because you run no cottages untill size 11 and only run 1 cottage at size 11 (turn 52 - 55) and only at that size 12 work all cottages I get a jump on you. During the last turn of size 10 (turn 51) + the 4 turns at your size 11, I am allready running cottages.

By turn 56 you have put in 4 cottage turns, while my option is allready at 47 cottage turns. From that point on the total commerce switches up and down. I have cottages growing to towns earlier, while you are working more cottages. Also the 12th cottage grows earlier in your scenario vs mine, since you grow to size 12 turn 56 and I grow to size 12 only in turn 65.

This is the overall explenation for the difference of 43 commerce as at turn 56 the 43 is exactly the difference in our two "plans".

It doesn't matter how the cottage+ turns are arranged: spending 7 extra turns working towns is a 28 difference in commerce -- and the difference must actually be less, because yours all matured, while mine didn't.

You harvested:
225 cottage turns (= 225 commerce)
450 village turns (=900 commerce)
675 hamlet turns (=2025 commerce)
690 town turns (=2760 commerce)
-----------------------------------
2040 cottage+ turns for 5910 commerce from them

I harvested (using your estimate that one village had 8 turns left until town):
225 cottage turns (= 225 commerce)
450 village turns (=900 commerce)
667 hamlet turns (=2001 commerce)
691 town turns (=2764 commerce)
-----------------------------------
2033 cottage+ turns for 5890 commerce from them


If you insist on looking at it differentially -- then you cannot ignore the fact that my city grows to 12, 13, and 14 faster than yours.


I suggested that the only difference in the net results was due to the fact I spent turn 14 suboptimally (what I called the 'optimal strategy' cottages over the rice; I forgot to recompute the optimal strategy at size 14 if we do not cottage over the rice -- the formula says to work the rice). I've redone my timeline for what I assert is an optimal strategy given the condition we do not cottage over the rice:

The relevant difference is that I now work (rice + cottages) for 14 turns at size 14, and then all cottages for 1 turn.

Size  Start  Food  Surplus  Cottages  Turns  Accumulated cottage turns
 1   0  0/33  5  0   7    0
 2   7  2/36  6  0   6    0
 3  13  2/39  7  0   6    0
 4  19  5/42  8  0   5    0
 5  24  3/45  9  0   5    0
 6  29  3/48 10  0   5    0
 7  34  5/51 11  0   5    0
 8  39  9/54 12  0   4    0
 9  43  3/57 13  0   5    0
10  48 11/60 14  0   4    0
11  52  7/63 14  1   4    0
12  56  0/66  5 11  14    4
13  70  4/69  5 12  13  158
14  83  0/72  5 13  14  314
14  97 70/72  2 14   1  496
15  98  X/XX  X 15 102  510
XX 200  X/XX  X 15 XXX 2040

Which works out to 2040 cottage turns, all matured into towns.

This jumps to 2045 cottage turns if you permit me to cottage over the rice at size 14.



I speculate that the difference in commerce is accounted by the extra turns you spend working the rice. In fact, if we treat the rice as giving 5 food and 1/4 of a cottage turn, then calculations give, at size 11:

G = food needed to grow
N = number of cottages worked

net loss = { G / (5 + (10 - N)) turns } at {15 - N - 0.25 loss per turn}
= G * (14.75 - N) / (15 - N) = G * (1 - 0.25 / (15 - N))

So minimizing loss means maximizing N -- and so this variation on costing the rice suggests that we do exactly what you did: working rice + all cottages at size 11 is optimal... rather than it being entirely irrelevant what you do as long as you work the rice.

Exercise: replace the river with an alternate source of fresh water (and civil service), such as an oasis next to the BFC. This still lets us farm; I expect that your optimizing will also find that what you do at size 11 is irrelevant.

 

[namliaM]

It doesn't matter how the cottage+ turns are arranged

Appearently it does... now lets see...
Turn 51 is where the intresting stuff starts happening....
You work no cottages, while I start with 7 cottages. (i.e. in turn 51 I make 7 extra commerce)
Then turn 52 I add 3 more cottages at size 11, while you run 1 cottage. I still make +9 commerce over you (+16).
Turn 53 +9 commerce (+25), turn 54 (+34), turn 55 (+43)
Turn 56 you grow to size 12 while I am stuck at size 11. You add a cottage, and run all cottages... so at this point you are up one over me (-1). You keep gaining 1 commerce for 9 turns untill turn 65 at wich point I too grow to 12. 43 - 9 = 34
For one turn we work both 11 cottages, and the rice. Then turn 65 I have 7 Hamletts + 7 commerce (41 total difference).
Turn 66 another 3 hamletts, while you get 1 (+9 commerce, 50 overall).
This continues on thru turn 69 where you grow another pop and add a cottage for one extra commerce for you. Total difference at this point 68 commerce.
Turn 70 you too grow to hammlets but in comparison to me you are working one more Hamlett (over a cottage) and one more cottage. So the difference drops by 2 commerce each turn.
Untill I to grow and my cottage matures to a hamlett.... etc etc etc...

This goes on and on, graphic displayed below shows how and when.

I think this math is sound....

then you cannot ignore the fact that my city grows to 12, 13, and 14 faster than yours.

No I cannot, but simularly you cannot ignore that my cottages grow to hamletts/Villages/towns 4 turns earlier than yours do...

The relevant difference is that I now work (rice + cottages) for 14 turns at size 14, and then all cottages for 1 turn.

When you work this out, you will find you come to a total of 2040 cottage turns and a total commerce of 7599 (yes I do count the river commerce and CC! No trade route(s) tho)
I total agree tho, 5910 commerce from the cottages/hamletts/villages/town alone...

While I am getting overall still 9 extra commerce....

This jumps to 2045 cottage turns if you permit me to cottage over the rice at size 14.

I think this doesnt matter as I am not using the cottaged rice either. I do think with a hard cap at 15 and 200 turns cottaging the rice at -some point- is optimum, more food = more commerce...
Tho it is a few commerce... 5 in your calcs... but still... it is more.

I speculate that the difference in commerce is accounted by the extra turns you spend working the rice. In fact, if we treat the rice as giving 5 food and 1/4 of a cottage turn, then calculations give, at size 11:

G = food needed to grow
N = number of cottages worked

net loss = { G / (5 + (10 - N)) turns } at {15 - N - 0.25 loss per turn}
= G * (14.75 - N) / (15 - N) = G * (1 - 0.25 / (15 - N))

So minimizing loss means maximizing N -- and so this variation on costing the rice suggests that we do exactly what you did: working rice + all cottages at size 11 is optimal... rather than it being entirely irrelevant what you do as long as you work the rice.

Totaly losing me, to much formula... not enough facts...
All I get is that you now seem to agree with me that working cottages at size 11 is optimal?

I highly doubt if having a river or not will make much difference. Weather you are working a 3/0/1 farm or 3/0/0 or simularly a 2/0/2 cottage vs 2/0/1 cottages will offcourse make a difference in total commerce, but not for optimum strategy?? The +1 commerce is there no matter farm or cottage...

Some day soon I hope to publish my spreadsheet

 

[MyOtherName]

No I cannot, but simularly you cannot ignore that my cottages grow to hamletts/Villages/towns 4 turns earlier than yours do...

I didn't ignore it. I separated the cottage+ turns into cottage turns, hamlet turns, village turns, and town turns.

No matter how you worked them, if they all matured into towns, then for each of them, you spent 15 turns working it as a cottage, 30 turns working it as a hamlet, 45 turns working it as a village.

The same for me, except one of them I only spent 37 turns working it as a village. (Becuase you said it had 8 turns left to mature) I worked 8 fewer village turns, but 1 extra town turn, for a commerce difference of 20.

Tho it is a few commerce... 5 in your calcs... but still... it is more.

5 cottage+ turns, when everything is a town, is 20 commerce, not 5.

I highly doubt if having a river or not will make much difference. Weather you are working a 3/0/1 farm or 3/0/0 or simularly a 2/0/2 cottage vs 2/0/1 cottages will offcourse make a difference in total commerce, but not for optimum strategy?? The +1 commerce is there no matter farm or cottage...

The +1 commerce is not there when we're considering the difference between a farmed rice and an off-river cottage. I suppose you could achieve the same effect by simply moving the rice away from the river. (But put it next to the city tile, so you still get the fresh water bonus immediately)

 

[namliaM]

I didn't ignore it.

So tell me what is wrong with below math??

Appearently it does... now lets see...
Turn 51 is where the intresting stuff starts happening....
You work no cottages, while I start with 7 cottages. (i.e. in turn 51 I make 7 extra commerce)
Then turn 52 I add 3 more cottages at size 11, while you run 1 cottage. I still make +9 commerce over you (+16).
Turn 53 +9 commerce (+25), turn 54 (+34), turn 55 (+43)
Turn 56 you grow to size 12 while I am stuck at size 11. You add a cottage, and run all cottages... so at this point you are up one over me (-1). You keep gaining 1 commerce for 9 turns untill turn 65 at wich point I too grow to 12. 43 - 9 = 34
For one turn we work both 11 cottages, and the rice. Then turn 65 I have 7 Hamletts + 7 commerce (41 total difference).
Turn 66 another 3 hamletts, while you get 1 (+9 commerce, 50 overall).
This continues on thru turn 69 where you grow another pop and add a cottage for one extra commerce for you. Total difference at this point 68 commerce.
Turn 70 you too grow to hammlets but in comparison to me you are working one more Hamlett (over a cottage) and one more cottage. So the difference drops by 2 commerce each turn.
Untill I to grow and my cottage matures to a hamlett.... etc etc etc...

This goes on and on, graphic displayed below shows how and when.
<Graph removed>
I think this math is sound....

 

[jason77024]

OK, I think, to sum this thread up, we have to quote Barbie

"Math is hard".

A possible generalization for us mid-level* Civ players not currently under consideration for a Fields medal:

After the Machinery/Calendar improvements and before Railroad, your workers aren't doing as much (except for lumbermills, but even that is a good way off). Cottage over all your non-resource farms (other than irrigation), start with the big (double-digit) cities. Ignore the GP farm, and the military city/-ies of course, and leave 2-3 farms in cities with only one food special.

NB. Whether or not you in fact change civics from Slavery to Serfdom, I am guessing Firaxis put Serfdom there for a reason. (It's not just for building plantations, is it? Especially if you chopped the jungle in advance.) And it's not for railroads - Steam Power is for that.

Especially for part- or full-time wonder-mongers, this gets towns (or villages at least) in place in time for Astronomy, SciMeth, and Corporation. It's admittedly not quite in time for Liberalism, so maybe run Bureaucracy longer (how terrible is that?), but Printing Press and Democracy should be fine.

I am certain that this is not mathematically perfect, but if nothing else it's a good jumping-off point for those mediocre players (like myself) who tend to

(a) stay stuck in an SE and hit the research wall with Industrial techs (losing the Colossus, GLib, and GLH along the way); or
(b) get frustrated with the early CE, especially if we get jumped and have to whip archers from slow-growing size 3 cities.

Note for the math guys here: your calcs are indeed very cool, but some of us would prefer to overthink other aspects of the game. Seriously, this does piggyback off the many posts above, just in a way that hopefully the non-number-crunchers can benefit. So I hope you don't mind me putting your math in a non-math format. I have been playing SE games lately that have not ended in the usual "knights and spies FTW,"** and have been thinking about this transition economy question the last couple weeks - usually as my civ tries to grind out the path to Advanced Flight after losing the Great Lighthouse.

* not including you in "mid-level," PS

** I have nothing against late-game domination wins. My -computer-, on the other hand...

 

[sugerdady87]

The optimal strategy is always to grow your city fastest, no matter you need it for cottage or production, then specialize it. Many exceptions... and yes I didn't read past the first post of this thread.

 

[noto2]

The question is a silly one anyway. Why would you want to cottage every tile? For me, I'd farm the food resource, maybe build 1 more farm, build a few watermills, and cottage the rest. That way the city grows quickly, gets hammers quickly so it can build its own infrastructure (if not running slavery) and then gets commerce going.

 

[Skallagrimson]

Let's say you build a fresh new commerce city with say 1 food source (e.g, grassland cows/rice) with a river running through the bfc and the city is on the river. The rest of the tiles are grassland. It's a nice commerce city, but doesn't have an abundance of food driving its growth.

Let's say you have the health and happiness to grow easily to size 15 right away.

Would it be better to:

1) Cottage the 19 non-food tiles and grow slowly, adding and working cottages along the way?

2) Farm the river tiles and grow to size 15 asap then cottage over the farms?

3) Add a couple farms to help growth, but then add cottages?

Slow growth with max cottages? Fast growth while delaying cottages? Medium growth with a mix of farms and cottages?

In that theoretical commerce city I would put it through three phases:

a) Farm up initially for growth to near the caps. Whip moderately for infrastructure. Run specialists.
b) At Machinery, water wheel the river tiles for faster infrastructure builds (them universities ain't CHEAP!)
c) At Universal Sufferage, infrastructure should be laid down for the most part and towns become more powerful. Switch the w/wheels to cottages. Supplement with farms or windmills as needed to tweak up the food yield. Towns don't take long to mature, especially in that phase of the game.

In a sense it's a conversion from SE commerce, to semi-prod, to CE commerce, over the course of the game.

 

[noto2]

except that you want to work the cottages as early as possible or else they are useless late game. That's why I mix it up. First 2 citizens, work farms, next one works a mine, next works a cottage, next works a watermill, cottages after that, for example.

 

[UWHabs]

You also have to think if you have a few jump points. I haven't gone through the thread, but if you're doing this post-printing press, then you want to grow the cottages into villages to get the extra +1 commerce. And if running free speech, then again, you want to rush to get your towns up and running.

My gut feeling is that if you're working more than 2-3 farms more than the food resource (ie getting a net higher than +6-+8 a turn of food), you're not working enough cottages. Getting even 1 or 2 towns up early will help you long-term more than waiting until you've made it to size 15 and cottaging.

 

[futurehermit]

Funny to see an old thread of mine brought back from the great beyond

 

[Bleys]

except that you want to work the cottages as early as possible or else they are useless late game.

Its not too bad, they grow pretty quickly under Emancipation. Sure, its best to have a decent amount of established Towns as fast as you can, especially if you plan to convert to a full-blown CE later in the game, but I have often built a pile of newish cottages just after Constitution and had them up and running in a reasonable timeframe.

As for the OP, I play em half and half. A couple farms, a couple cottages, and work what I wish too, build what I need next. I usually whip new cities a couple times, so the cottages dont get worked so much early on, but eventually, they pop a coin, and eventually I let em grow ASAP, build a fast Granary, Courthouse, Library, and away we go.