Hail
Satan's minion
emphasis is mine. well i disagree. you overvalue population in the sense, that pop has value in itself -> therefore you choose to wait 10-12 turns or whatever for the pop to grow only to have the pop work a tile that will just support itself. what's the point?(1) Tiles improved to increase food: For tiles are improved to increase food, there are many inflection points - i.e., a tile can be worth working initially, not worth working a few turns later, and worth working again a few turns after that.
Let me illustrate with a simple example: say you are working a grassland, which produces 2 . The next tile you plan to work is also a grassland. Once improved, the grassland will produce 3 . Also - at standard speed, it takes 6 turns to build a farm.
With those conditions, it makes sense to improve the grassland if you are 12 or greater turns away from the next population point.* (The last think you want to do is delay a population point, because the additional yield from the next tile is greater than the additional yield from the improvement). So if growth is 14 turns away, you want to improve the tile. If growth is 11 turns away, you're better off waiting until you obtain the next population level.
*(Because by not working the grassland, you are forgoing 12 food [2 per turn * 6 turns]. The improvement provides 1 per turn, so it takes 12 turns to "make up" for this deficit).
the force behind city growth is not food yield, but food surplus. from this point of view, improving a 2 is a no-brainer decision because the mentioned tile goes from 0 surplus to 1(!!).
simple example:
the terrain is nothing but grassland 2
food to size 2 = 20 (f2). food to size 3 = 30 (f3).
a size 1 city -> produces 4 food, eats 2 = 2 surplus.
therefore turns to get to size 3 -> 20 / 2 + 30 / 2 = 50 / 2 = 25 turns
turns to get to size 3 if choosing to farm a grassland tile from turn 1 -> 6(to build the farm) + 20 / 3 + 30 / 3 = 6 + 7 + 10 = 23 turns.
note:
IF f3 / 3 - f3 / 4 > 6 then the player will increase growth(e.g. decrease turns to grow), if upon reaching size 2 immediately starts on the second farm
conclusion:
improve ASAP. first to improve should be "workable" tiles with minimal yield(their opportunity cost is less). hmm... after a certain point diminishing returns will kick in, but the impact of improving/leaving as is will become marginal as well.
probably will be fun in the beginning while morphing into tedious MM late game(as is now with workers). this is not the macromanagement system i want.