Cog to gold spending wise is 1:4, or less depending on what it is specifically. But, gold to cog income is 2:1. Which means when you factor in both income and expenses, you get 1:2.
I presume, those two ratios are:
- 1:4 is the purchase price of buildings
- 2:1 means "gold-producing choices yield twice as much as cog-producing choices"
in which case the 1:2 ratio you compute is means
For the purposes of building buildings, taking the cog-producing choices is twice as productive as taking the gold-producing choices.
Which is an important figure since it expresses the inefficiency of producing gold for the purposes of buying buildings, but that's not what the thread is discussing.
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I've been saying "value" -- maybe let me change the word to "utility", to reduce the potential for confusion with purchase prices.
The point of quantifying the relative utility of gold vs cogs is to guide you when you make choices, such as:
- You could buy a building with gold rather than produce it with cogs
- You could send envoys to gold giving CS's rather than cog giving CS's
- You could build cog-giving buildings rather than gold-giving buildings
- You could work a tile 2
1
3
or a 2
2
tile
or other more complicated things.
In the broadest strokes, any self-consistent way of making these choices can be described by assigning a utility to each yield, and noting that each choice maximizes utility.
One can use the converse: one can make self-consistent choices by trying to judge the utility of each yield, and then making the choices that maximize utility.
For example, if you assign utility so that 1 cog = 3 gold, that means:
- (all other things being equal) you would pick a trade route that produces 3 cogs instead of one that produces 8 gold, but you would prefer a route that produces 10 gold.
- You would never buy a building or unit, unless you're willing to spend 34% extra to have it now rather than in the future
There is a fair amount of fungability in yields, which means this broad stroke has a lot of applicability; gold is obvious, but for cogs:
- You can redistribute cog production via trade routes
- Most builds don't care which city they are built in, which lets you redistribute cog consumption
- You can focus cog-producing infrastructure in cities that will need to build more things
- Various forms of rushing (e.g. chops, gold spending) can be used to make up deficiencies in fungability
Yes, the assignment of utility will vary over time (e.g. you probably want the utility of 1 cog to be nearly that of 4 gold in the very beginning of the game, and decreasing over time). Yes, there may be times when you need to make local deviations from the general rule. The point of the heuristic is to set things at a broad level.