NobodyImportant said:
I think I understand this, but I wonder whether your conclusions still hold when we complicate the analysis to include commerce.
Consider my current game as a case study. I'm playing as the Americans on Noble level at Normal speed, with Washington as the leader. Washington (the city) is in a lovely spot, on a plains hill by a river bend. Playable resources include Wheat, Gold, Ivory and three flood plains squares. It's 3480BC, and I've just completed my first worker.
As I understand it, your strategy would have me start a Settler next, while my worker irrigates the Wheat and then chops forest to speed production. That seems like it would be effective. But my intuition tells me that I should push out a Warrior and wait until my city grows to size 2, in order to get a bloke working the gold mine before I start Settlers. It'll take 7 turns to grow the city, but the gold square will be worth a whopping 9 commerce and 3 production once the mine is built.
Once again, I think I understand your point about the importance of making Settlers early, but I wonder if it's worth the opportunity cost of missing that gold square in this case. I'd be interested to hear your thoughts on the matter.
In this case, chop-rushing actually has the nice benefit of accelerating early commerce as well as production, with a modest change to the cycle. Here is how it would work:
If you wait until the city grows to size 2, you usually have to work some tile other than the gold mine for the population to have excess food. Before the worker improves a tile, this growth will be slow - 3 food/turn on an unimproved wheat. You therefore have to wait 8 turns on normal before you have a spare person to work the gold mine, plus the lag time to build a worker who can build the mine.
In the worker-worker-settler setup, your first action is to build a worker and improve the gold mine. Once it is improved, have the city work the gold mine and pump out early commerce. You don't get growth anyway when you're building workers and settlers, so you might as well pick a tile with nice commerce. Then you chop a second worker. Have the second worker chop for a settler and then improve the wheat. (Improving the wheat first doesn't help, because your city can only use one tile at size 1, and you want that tile to be the gold mine). Now you have an improved gold and wheat and you set the city to grow, working the wheat tile. Since you're now at +6 food, growth will be quick (4 turns). More details:
Work the wheat turns 1-15 (make worker) and turns 16-20 (building gold mine). Worker1 chops on turns 24, 28. Worker2 appears on turn 24 and chops turn 28. Settler appears turn 31, wheat is improved on turn 33.
Work the gold turns 21-33, then work the wheat turns 34-37, followed by wheat+gold. You get 13 turns of high commerce out of the first 37. The mathematic maximum if you never grew and only worked a developed gold mine is 17. Everything is a bit faster with extra production from a starting hills/plain, but the principle is the same.
If you improve the wheat first, followed by the gold, grow to 2:
Work wheat turns 1-25 (1-15 for worker, 16-20 to farm wheat, 21-25 to mine gold). Growth to size 2 will occur on Turn 24. Turns 25+ you work gold and wheat. Worker1 chops turns 29, 33. Worker2 appears turn 29, chops turn 33. Settler appears turn 34. By turn 37 you've had 12 turns of high commerce, one fewer than the other approach. You've also delayed your new city by three turns (but gained one turn of growth on your home city), for another small net negative.
In either case you have the ingredients for a very, very solid start.