A wall of text with some thoughts on city stagnation and the value of trading posts in Civ 5 G&K.
I want to dig into at least the first level of city stagnation mechanics in Civ 5. Like previous Civ games, Civ 5 doesn't do a great job of visually separating the difference between "base resources" and "finished goods". Tile based "hammers" get turned into "production" by going through the production multipliers. Tile based gold goes through the gold multipliers to get turned into more gold? Yeah. A little awkward. However, the distinction is pretty important when trying to figure out simple concepts such as What is the production value of tile based gold?. Ok. Rant finished.
Because of the crazy growth in the cost of additional citizens, at some point it is clearly optimal to stagnate cities. At the very minimum any food put towards a pop growth 20 turns away is completely useless if I expect to win 17 turns from now. However, in many situations we can shift excess food into hammer, gold, or beakers at very efficient conversion rates by a combination of tile shifting, improvement swapping or specialist hires. All are roughly 1:1 conversions. This means that the optimal stagnation time is pretty far removed from the game end. While it is not easy to calculate exactly when this optimal stagnation point is, lets attempt a rough approximation.
For my Boudicca game I won a conquest victory on turn 214. The last ~15 turns of any conquest is pretty much a death parade to the last city, which means that anything useful that a city could make was finished around turn 200. Under perfect conditions a newly grown late game conquest citizen will be put onto a 4 hammer mine. The new citizen is also worth about 0.75-1 base beakers and 1 GPT. The beakers are useless after Dynamite (~ t 190), but hammers are useful to ~ t 200. Gold is useful a little longer because we can rush buy a unit close to the front, or use the money for upgrades, or to rush buy a + happy building to keep our empire from collapse. This means a (admittedly simplistic) view of when to stagnate is when future citizen production potential is less that the food required to grow it. This is an underestimate of the value of stagnation since Civ 5 has a very high discount rate; hammers now >> equivalent hammers later. In all my games so far I am happy cap constrained as well which means that part of the "cost" of growing a new citizen is the hammer cost of building + happy building to support it + the maintenance cost of that building. The latter nearly offsets the trade route income generated by having + 1 pop in the first place. In this size 16 city I would need roughly 150 food (with Aqueduct carryover) + 60 hammers (for the marginal cost of +1 happy from buildings). That's a lot for a new citizen to pay back. 50 turns! So stagnating like this, around t170 (45 turns to the end) may already be too late. I could be convinced to stagnate at t190 - 50 = t 140 or so, much earlier than I thought.
![[Image: stag2.png]](http://i275.photobucket.com/albums/jj294/olodune/Boudicca%20Civ%205/stag2.png)
Rush buying, and the value of trade posts
At first glance trade posts are pretty miserable improvements in Civ 5 even with Economics (+1 gold) and Free Thought (+1 beaker). This is because the steady state conversion from gold to hammers is only 5:1. If we think about grassland trading posts as 2food/0.4hammer/1beaker converting from 2food/2gold/1beaker then they are a very weak tile! in many cases we could be working a 4 food farm + 4 hammer mine instead! However it is not that simple, since we ignore the effect of multipliers (minimal usually), targeted production, and exponential compounding.
Targeted production
One of the reasons gold -> hammers is more valuable is that it allows us to instantaneously swap productive tiles between cities. Rushbuying a final Library to open the National College gives a much bigger hammer equivalent than 4:1. A NC 15 turns earlier could be worth ~230 beakers (size 10 capital, bought in a size 2 city) which is worth 100 hammers? 180 hammers? Certainly total conversion is better than 2:1 since that earlier research will get us other good stuff more quickly, which brings up the next point.
Exponential Compounding.
Consider the following, totally artificial setup. We have 1 city with 25 base hammers. It can build as many non-unique factories as possible, and our "winning goal" is to produce as many surplus hammers as possible from the city over the next 100 turns. A factory is assumed to add +4 base hammers + an additive 10% multiplier.
Case 1: slowbuilding all factories. At 25 base hammers it takes 15 turns to slow build our 360 hammer factory. The factory adds 4 base production and a 10% (additive) multiplier so the marginal effect is a 6.9 = 1.1*(25+4)-25 increase in hammers. So the next factory is built on turn 26 with a marginal hammer impact of 7.7, etc. We end up building our last factory, which will pay for itself, on turn 78. Totals: 13 factories; 4,026 surplus hammers at turn 100.
Case 2: pay 1080 gold for the 1st factory, then slow build the rest. We end up building our last factory, which will pay for itself, on turn 78. The base production of the city is now larger than 360 per turn, so I don't think it is realistic to build any additional factories after this point. Totals: 22 factories; 8,390 surplus hammers at turn 100.
So for a 1080 initial investment we are actually gaining more than 4,000 hammers by turn 100! Of course this is not very realistic; you can only build one factory per city. However you can build "other good stuff" with a similar impact, so at the very least it is an interesting thought experiment.
What does this mean? Two things: 1) factories are actually a very weak investment! I think I will only be building them in 1-2 cities where production per turn is more important than surplus hammers, such as wonder building or finishing up the final few pieces of a spaceship. 2) While I am not suggesting that 1 gold is actually worth anywhere near 4 hammers, I do think the above suggests that the eventual payoff (as long as a city has good stuff to build) is a lot better than 4 gold -> 1 hammer. I think it's closer to 2 gold -> 1 hammer as long as spent somewhat judiciously.
Other Arguments for the Value of Gold (and trading posts)
- Militaristic city states can provide extremely efficient gold -> hammer conversions under the right circumstance. In my game I was allied with Sidon which had a knowledge of Cossacks. With "United Front" in the Order SP maintaing an alliance with Sidon yields a marginal gold -> hammer ratio of nearly 1 gold -> 3 hammers! (250 gold for 20 IP, degrading at 0.75 per turn, in exchange for a 225 hammer cavalry every 8(?) turns. Yes, please.
- The intangible benefits of maintaining city state alliances are often large and hard to calculate, but the fact that it seems to be a good place to dump cash suggests that it is more efficient than rush buying.
- Golden ages are common in Civ 5. Golden ages boost Trading Posts more than just about anything else in the game. Since I seem to be in GA about 20->30% of the time that suggests the "real" gold output of a TP is ~2.25 (with Econ).
- Big Ben (-15% purchase cost), and (-25%) in the Commerce Tree + the Commerce Tree finisher make gold -> hammer conversions MUCH better. I'll have to play with this soon!
I want to dig into at least the first level of city stagnation mechanics in Civ 5. Like previous Civ games, Civ 5 doesn't do a great job of visually separating the difference between "base resources" and "finished goods". Tile based "hammers" get turned into "production" by going through the production multipliers. Tile based gold goes through the gold multipliers to get turned into more gold? Yeah. A little awkward. However, the distinction is pretty important when trying to figure out simple concepts such as What is the production value of tile based gold?. Ok. Rant finished.
Because of the crazy growth in the cost of additional citizens, at some point it is clearly optimal to stagnate cities. At the very minimum any food put towards a pop growth 20 turns away is completely useless if I expect to win 17 turns from now. However, in many situations we can shift excess food into hammer, gold, or beakers at very efficient conversion rates by a combination of tile shifting, improvement swapping or specialist hires. All are roughly 1:1 conversions. This means that the optimal stagnation time is pretty far removed from the game end. While it is not easy to calculate exactly when this optimal stagnation point is, lets attempt a rough approximation.
For my Boudicca game I won a conquest victory on turn 214. The last ~15 turns of any conquest is pretty much a death parade to the last city, which means that anything useful that a city could make was finished around turn 200. Under perfect conditions a newly grown late game conquest citizen will be put onto a 4 hammer mine. The new citizen is also worth about 0.75-1 base beakers and 1 GPT. The beakers are useless after Dynamite (~ t 190), but hammers are useful to ~ t 200. Gold is useful a little longer because we can rush buy a unit close to the front, or use the money for upgrades, or to rush buy a + happy building to keep our empire from collapse. This means a (admittedly simplistic) view of when to stagnate is when future citizen production potential is less that the food required to grow it. This is an underestimate of the value of stagnation since Civ 5 has a very high discount rate; hammers now >> equivalent hammers later. In all my games so far I am happy cap constrained as well which means that part of the "cost" of growing a new citizen is the hammer cost of building + happy building to support it + the maintenance cost of that building. The latter nearly offsets the trade route income generated by having + 1 pop in the first place. In this size 16 city I would need roughly 150 food (with Aqueduct carryover) + 60 hammers (for the marginal cost of +1 happy from buildings). That's a lot for a new citizen to pay back. 50 turns! So stagnating like this, around t170 (45 turns to the end) may already be too late. I could be convinced to stagnate at t190 - 50 = t 140 or so, much earlier than I thought.
![[Image: stag2.png]](http://s275.photobucket.com/user/olodune/media/Boudicca%20Civ%205/stag2.png.html)
Rush buying, and the value of trade posts
At first glance trade posts are pretty miserable improvements in Civ 5 even with Economics (+1 gold) and Free Thought (+1 beaker). This is because the steady state conversion from gold to hammers is only 5:1. If we think about grassland trading posts as 2food/0.4hammer/1beaker converting from 2food/2gold/1beaker then they are a very weak tile! in many cases we could be working a 4 food farm + 4 hammer mine instead! However it is not that simple, since we ignore the effect of multipliers (minimal usually), targeted production, and exponential compounding.
Targeted production
One of the reasons gold -> hammers is more valuable is that it allows us to instantaneously swap productive tiles between cities. Rushbuying a final Library to open the National College gives a much bigger hammer equivalent than 4:1. A NC 15 turns earlier could be worth ~230 beakers (size 10 capital, bought in a size 2 city) which is worth 100 hammers? 180 hammers? Certainly total conversion is better than 2:1 since that earlier research will get us other good stuff more quickly, which brings up the next point.
Exponential Compounding.
Consider the following, totally artificial setup. We have 1 city with 25 base hammers. It can build as many non-unique factories as possible, and our "winning goal" is to produce as many surplus hammers as possible from the city over the next 100 turns. A factory is assumed to add +4 base hammers + an additive 10% multiplier.
Case 1: slowbuilding all factories. At 25 base hammers it takes 15 turns to slow build our 360 hammer factory. The factory adds 4 base production and a 10% (additive) multiplier so the marginal effect is a 6.9 = 1.1*(25+4)-25 increase in hammers. So the next factory is built on turn 26 with a marginal hammer impact of 7.7, etc. We end up building our last factory, which will pay for itself, on turn 78. Totals: 13 factories; 4,026 surplus hammers at turn 100.
Case 2: pay 1080 gold for the 1st factory, then slow build the rest. We end up building our last factory, which will pay for itself, on turn 78. The base production of the city is now larger than 360 per turn, so I don't think it is realistic to build any additional factories after this point. Totals: 22 factories; 8,390 surplus hammers at turn 100.
So for a 1080 initial investment we are actually gaining more than 4,000 hammers by turn 100! Of course this is not very realistic; you can only build one factory per city. However you can build "other good stuff" with a similar impact, so at the very least it is an interesting thought experiment.
What does this mean? Two things: 1) factories are actually a very weak investment! I think I will only be building them in 1-2 cities where production per turn is more important than surplus hammers, such as wonder building or finishing up the final few pieces of a spaceship. 2) While I am not suggesting that 1 gold is actually worth anywhere near 4 hammers, I do think the above suggests that the eventual payoff (as long as a city has good stuff to build) is a lot better than 4 gold -> 1 hammer. I think it's closer to 2 gold -> 1 hammer as long as spent somewhat judiciously.
Other Arguments for the Value of Gold (and trading posts)
- Militaristic city states can provide extremely efficient gold -> hammer conversions under the right circumstance. In my game I was allied with Sidon which had a knowledge of Cossacks. With "United Front" in the Order SP maintaing an alliance with Sidon yields a marginal gold -> hammer ratio of nearly 1 gold -> 3 hammers! (250 gold for 20 IP, degrading at 0.75 per turn, in exchange for a 225 hammer cavalry every 8(?) turns. Yes, please.
- The intangible benefits of maintaining city state alliances are often large and hard to calculate, but the fact that it seems to be a good place to dump cash suggests that it is more efficient than rush buying.
- Golden ages are common in Civ 5. Golden ages boost Trading Posts more than just about anything else in the game. Since I seem to be in GA about 20->30% of the time that suggests the "real" gold output of a TP is ~2.25 (with Econ).
- Big Ben (-15% purchase cost), and (-25%) in the Commerce Tree + the Commerce Tree finisher make gold -> hammer conversions MUCH better. I'll have to play with this soon!