mdy said:
At the rate we are growing we aren't going to have a choice about which cottages to work after the next few turns (and as I already pointed out the existing hamlet will have already have become a village before printing press whatever we do, so we may as well work the village). The only way this could ever become an issue is if we assigned an additional worker to the capital to build improvements faster than we are growing, and we don't have any spare workers.
IMO the choice which cottage/hamlet/whatever to work is to get as few commerce above the x*8 pack. Say we are making 33C, we should switch a village to a hamlet if possible. It has nothing to do with PP, it's just about avoiding losses to rounding. It would be nice if we found some workerturns to build 1-2 more cottages at delhi.
@shyuhe: Commerce/science/etc is calculated city by city. First there's the amount of raw commerce. Apply any multipliers (like buerocracy) on them. Then there's the slider. For an example, we're having 20% science, 10% culture and 70% wealth (like during a war) and the city is producing 100 modified commerce. This means the 100 commerce is converted into 20b, 10c and 70g. In this step, rounding (down) occurs. Then you add any raw beakers/gold/culture (like from specialists). Then the city's research/gold/culture-modifiers are applied. Again, rounding occurs. Please, anyone, correct me if I'm wrong here at some point.
Since we're in buero and thus have a commerce bonus, the game is rounding down twice. If we are avoiding ANY rounding loss, we are making a multiple of 8 commerce since +50% (buero) creates an integer (multiple of 12) which is dividable by 4 as we're having +75% on research atm. Again we're not losing anything to rounding.
Our current situation:
We're producing 63 beakers at 100% in Delhi when working the
village. We're making 24 base commerce:
Code:
TR Palace Corns City Tile Silver Village
3 + 8 + 2 + 1 + 6 + 4 = 24
With buero that's 36 modified commerce.
With 100% science slider that's 36 raw beakers.
With the 75% research bonus from academy and library this is
63 modified beakers.
Now assuming we're working the
hamlet:
We are making 23 base commerce
Code:
TR Palace Corns City Tile Silver Hamlet
3 + 8 + 2 + 1 + 6 + 3 = 23
With buero that's 34.5 modified commerce.
We already lose half a coin to rounding.
With 100% science slider that's 34 raw beakers (compared to the 36 with the village).
With the 75% research bonus from academy and library this is 59.5 beakers,
rounded down to 59.
Now let's assume we're making 25 base commerce, 1 more than we are making now, be that due to a better trade route or whatever:
25 * 1.5 = 37.5 -> 37 modified commerce
37 * 1.75 = 64.75 ->
64 modified beakers, gaining nothing from our multipliers we're not already gaining!!
Now, with 26 base commerce:
26 * 1.5 = 39 modified commerce, no loss to rounding as amount of base commerce is even
39 * 1.75 = 68.25 ->
68 modified beakers, with minimal loss to rounding.
... this could go on and on.
Point is, only if we're producing a multiple of 8 raw commerce are we not losing anything to rounding.
To make this MM more effective, low-commerce tiles should be prioritized during 0%-science as we're having research but no gold multipliers.
While I think most probably know this more or less, I am writing this all down to emphasize how much can be gained (or lost) with a little MM. Going through every city, every turn is given anyway, this is just one more thing to check on such a tour through the cities. Since we want every cottage to be a town one day, it is more efficient if we don't just work the first cottage until it's a town, then the next, and so on, but to keep this rounding and multiplier stuff in mind.
The distance cost alone was 7.7g.
But I thought beakers are first aggregated across the entire empire and then rounded? Or am I thinking of the wrong issue here? 
It gives us an early shot at a GE, as it's gonna get progressively harder to catch up with Two Fish. Your schedule of pre-1AD Educ gives us about 45t for those two GS. We could roughly run 1 scientist + some turns of another (depending on HG date) for the next 50t without popping the 600 gpp.
Makes sense. Then it could still be Roosevelt. He could have built the GW...
