Wrong. What happens is that you have a
25% boost to the
hammers you put on the worker. Even if you are getting a worker on purely hammer basis ( like a plains hill forest , that gives exactly 4 hammers or via chopping ), this means that you get 1 hammer free for ever 4 invested. That in my books is 20% faster , not 25%
And obviously , if you start putting food in the middle things get increasingly less shiny
I didn't really follow the math, here.
25%
boost means +1
per 4
earned, that's correct.
You equate this to a 20% speed increase, but that doesn't make sense.
4 * 1.2 = 4.8
4 * 1.25 = 5
Seems like it's a 25% bonus, as stated. That being said, your point regarding the value of
vs
is valid, in that you need to optimize your production to get at least the base 4
required for the bonus to take effect, which means either an ordinary 1
capital with the initial citizen working a forested-plains-hill, or a plains-hill 2
capital working any 2
tile. I play on Marathon, and an expansive leader can cut the initial worker production from 30 to 24 turns by managing production as stated. You can get as low as 20 turns if you have a plains-hill capital and a forested-plains-hill to work, which exponentially boosts the rate of improvement by bringing the second worker out earlier, and getting the first settler chopped much earlier.
I play a co-op game with a partner, mostly, and our starting builds are typically Worker-Worker-Settler. In the above optimal case I can have my settler started so early that the limiting factor for finishing production becomes the tech-rate to Bronze Working, but even then my settler is finished ahead of schedule.
For the sake of simplicity, we'll assume reasonable starts with irrigated corn for both players. Lacking a +6
site in one or both cities further increases the value of the expansive build.
Maths:
Global Techs - Mining (15) -> Bronze Working (28)
Expansive Case:
20 turns for first worker, begin building a farm (16).
Farm up on turn 36, (second worker is 80/100).
Second worker out on turn 39 (only one turn is saved by switching to the farm), begin settler.
Two workers sit tight for four turns, although you could build a road or start another improvement project.
Bronze Working finished on turn 43, workers chop first forest on turn 49, settler is 114/300.
Workers chop second forest on turn 54, settler is now 210/300.
Workers chop third forest on turn 60, settler is out at 306/300 with 6 overflow.
Non-Expansive Case:
30 turns for first worker, begin building farm (16).
Farm up on turn 46 (second worker is 48/100), worker begins chopping (Bronze Working finished three turns ago).
Second worker out on turn 52 with 44 overflow (8 turns are saved by improving the farm and chopping), begin settler.
Two workers chop second forest on turn 58, settler is now 140/300.
Two workers chop third forest on turn 64, settler is now 236/300.
At this point there are two choices. The settler has 11 turns left, so you could chop it again to get it five turns early, or let it finish.
Option A:
Two workers chop fourth forest on turn 70, settler is out at 332/300 with 32 overflow.
Option B:
Two workers begin alternate project on turn 59.
Settler is out on turn 75.
I was even thinking worker 1st, mining the pigs hill, and teching bronze-working straight away and chopping might be best. 
