Forge - return on investment - warning: math

[Roxlimn]

Creepy Old Man:

I checked your algebra and it seems to be more or less consistent. Have to check the manipulations later on and do some checking against standard speed.

By your estimate here, it will only take about 100 turns for a moderately good production site (20 base hammers) on epic speed to trounce what it could have done without Forges in terms of both gold and hammers. In other words, after 100 turns, the Forge is just pure profit.

Prior to those 100 turns, the Forge speeds production on units - particularly for new units that may not have been previously available prior to a new tech coming online.

For instance, if you had Metal Casting and complete the Forge before Steel comes online, and you have a 20 base hammer site, the non-Forge city will take 13 turns to make a new Longsword after you research the tech, whereas a Forge city will only take 10. In order to have the gold from upkeep from a possible Forge to allow you the ability to rush buy one Longsword, you will need to have had the Forge for 370 turns prior to the rush-buy.

Essentially, this indicates that if you want Longswords in 10 turns rather than 13, it makes sense to build the Forge and pay the upkeep - the upkeep will almost never allow you to rush-buy even one extra Longsword within the time alloted where Longswords will actually still be relevant.

And yes, I am aware that Longswords is only a placeholder. Units become more expensive as time and tech advance, not cheaper. This means that the break-point to allow the rush-buy of one unit between Forge and non-Forge cities only gets bigger the more tech you have. Since the breakpoint of even Longswordsman is 370 turns, my projection is that this will never actually happen in-game.

 

[ShuShu62]

Ok, my intuition told me that forges are a waste of time. So I did the math to decide when they're actually good.

So, consider two situations: either a particular city builds military units continuously, or it builds a forge first, and then military. The question is, how long until the city with the forge has produced more than the city without?

I'll assume the cities are producing longswords for the convenience of actual numbers.

Numbers:
forge cost 225 resources
forge maintenance 2 gpt
forge bonus 15%
longsword cost 225 resources
longsword rush 740 gold.
(Those are epic pace.)

T = how many turns are devoted to construction
P = production value of the city.
N = number of longswords produced.

Without the forge:
N = T*P/225 + 2*T/740
(the second term is the number of longswords that can be rush-built with the maintenance that was not paid since there is no forge)

Building a forge first:
N = (T*P-225)*1.15/225

Equate the two, and do some algebra:

T = 259 / (0.15*P-0.608)

is the number of turns elapsed before the city that builds the forge first builds more longswords than the one that doesn't build a forge.

So, chart this vs P (production of the city):

If the city production is 4 or less, then the forge never pays off - the maintenance cost exceeds the cost of rush buying the units.

City production:     Turns to pay off
<5                       never
5                         1824
6                         887
10                       291
14                       174
18                       124
22                       97
26                       79
30                       67
35                       56
40                       48

So we see that you need a pretty good city to get your money back in less than a hundred years. Furthermore, you have to build 9 or 10 longswords to get any advantage. In my opinion, (a) any city with a high enough production to benefit from a forge should be building wonders instead and (b) you might not even need enough units to make it worthwhile.

Conclusion: Never build forges.

I am confused by the conclusion. Are you claiming that cities never reach a production of 20, or that epic games don't last 100 turns past the construction of the forge? I read your logic in favor of early construction of a forge.

Especially if you run the analysis with: you have $740 to start with, should you buy the longsword or the forge to start with?