namliaM
Deity
You have to make some kind of assumption... even at the "rule of thumb" Food = Happy you have to farm and cottage a lot... Both get the "best" out of the city and needs x number of worker turns.IMO those assumptions are so far from real-game that it's hard to say if the approach is truly better. Worker turns aren't infinite in any practical game scenario that matters. Food surplus = happy surplus is a pretty good "rule of thumb", generally.
In a city with a happy cap of 15, like in this sample both Dave and I advocate growing ASAP, this takes the first 34-ish turns so lets ignore the first 30 turns where we both farm the heck out of this baby whip the granary and grow grow grow.
After that the strats start to differ a little.
But first... lets start by admitting there was a little miscalculation in my spreadsheet. To calculate all this I turned the cottage growth up side down.
On turn 130 Cottage on turn 0 Turn 120 Hamlett etc... This while turn 130 itself never actually got counted. As this affects both calculations exactly the same (i.e. commerce for turn 130 not counted)
Now 1 picture paints a thousand words. See below graph.
Because Dave starts cottaging earlier than I do, he builds up a head start which at its worst/best is 45 commerce on turn 55. Because Dave starts working them earlier they mature earlier, thus you get the sea saw going forward and back a bit in total commerce.
Because at turn 45 I start working the cottages vs Dave's turn 35.
Turn 45 I work 7 vs Dave's 7
Turn 46 I work 13 vs Dave's 7
And from that point on I work either more or eventually at size 15 equal number of cottages.
Turn 76 is the last turn Dave is in a small advantage situation, after that I start to run away with the total commerce.
I am not a mathmatician, so I cannot put a formula to it... But for (atleast) this case the formula as stated by Dave Food surplus = Happy surplus is NOT the best solution