I propose a calculation framework if you are interested to see. It’s inspired by your approach and it’s not that complicated in my opinion. Here’s the thing:
Dark age food factor calculation :
let x = FV in dark age
-
Invest into one vil to take gold
– cost : 50 food = 50x gold
– reward in N minutes : 21N gold -
Invest into one farm to take food
– cost : 60 wood and 1 villager work time for N minutes = (60+21N) gold
– reward in N minutes : 19N food = 19Nx gold
By definition of FV, both investments are equally profitable, thus the cost-reward ratio should be the same, thus
50x / 21N = (60+21N) / 19Nx
Let’s calculate x in function of N :
50x*19Nx = (60+21N)*21N
950x^2 = (60+21N)*21
we get the food ratio x = sqrt((60+21N)*21/950)
It fits your calculation when replacing N with 4, we get x = 1.78
I even plotted a graph of food-value in function of N (number of minutes before evaluation)
When N is little, the farm is just build / the vil is just born, the reward is similarly little thus the cost 60wood and 50food resp. should evaluate the same thus around 1.2
When N is great, the farm takes away a vils time which could have been used to take gold, and yields some food. It costs a lot but rewards with less food than gold (in pure number comparison)