mnf said:
This has always been a problem for me---city growth vs specialists. Suppose the city is at size 4, and happiness cap is at 7. You're working all resources and there are some plains and a few grassland tiles around. You're growing at 3 food surplus. Would you assign a specialist and let the city grow slowly at 1 food surplus? What if the city has 5 food surplus? Wouldn't you, then, want it to grow quickly to the population cap first, and only then assign specialists?
I will normally grow the city to max happy, then rehire the specialists.
The model in my head: Suppose we have a grassland city with pastured cows (+2F) and pigs (+4F), and no other food bonuses. At size 6, this city can support 4 specialists, so lets start there.
Now, with no extra food lying around, we have to build our own. That means farms (+1F assuming we havn't discovered biology yet), and we need two of them to support the fifth specialist. So we need to grow 3 sizes in all; let's assume a full granary, so the growth requires 16, then 17, then 18 surplus food (51 total). Each specialist turn you give up is +3 food.
OK. So if you surrender a single specialist for 6 turns, that will grow you one size (with 2 left over). You can then rehire the specialists, and grow at +1 for 15 turns, then at +2 for 9 turns. 30 turns total.
Compare that against firing all four specialists. You'll be at +12 F for two turns, then at +13 F for one turn, then at +14 food for one turn. You've spent 10 extra specialist turns growing to size 9, and as a result you have the new specialist 26 turns sooner than you would have. Assuming the marginal cost of a specialist is constant, the second case shows a profit.
In practice, we don't normally jump from 6 happy to 9 happy. So what should we do in the mean time? In essence, each surplus food is 1/3 of a specialist turn, so parking on a farm for slow growth is contributes to your goal, right up to the point where you cross the happy cap. At that point, you can switch to a neutral tile(s), either on their own or micromanaged in pairs.
But this is the area where the pure specialist economy begins to lose some of its oomph. You are essentially investing 3 population to produce one specialist, where you could instead invest that same population in 3 cottages, using the same tiles. Without some additional vigorish somewhere, that math is difficult to sustain.