I have long struggled to figure out the number of workers which would be appropriate to build in Civ4 in order to improve my land in an expeditious manner. Though I don't believe this equation is perfect, I welcome any improvements (perhaps we can make a Wiki of this) to seek the ideal worker formula together.
Some thoughts....
A good number of cities on a huge map might be 30-40, not including any vassals. If each city has 8 in the inner ring, and 12 in the outer ring which they can access, this brings us to 20 workable tiles per city, assuming no overlap, mountains, coastal tiles, desert, or other unworkable tiles. This turns into 600-800 tiles to be worked across the ideal finished state empire.
Next we must account for jungle to be cleared and forests to be chopped. On marathon, chopping a square of jungle takes 12 turns, while forests take 9 turns. To clear 600 tiles of jungle is 7,200 worker-turns, 800 tiles is 9,600, while with forests that would equal 5,400 worker-turns, while 800 tiles is 7,200 worker-turns. This is a situation I have never seen or heard of before, but it gives us an extreme example of how many workers we need to improve our situation quickly.
Under marathon settings, a mine takes 12 turns, a farm 15 turns, and a cottage 12 turns. I will use the first letter of each improvement to determine the range of worker-turns each improvement combination (jungle-clearing+cottage, etc.) will take based on the number of cities. I did not include camps, plantations or other improvements since the number of turns they take (12-15) falls inside this range and are thus redundant.
JC+M=(14,400 - 19,200) (30-40 cities)
JC+F=(16,200 - 21,600)
JC+C= (14,400 - 19,200)
FC+M=(12,612 - 16,800)
FC+F=(14,400 - 19,200)
FC+C=(12,612 - 16,800)
So we see anywhere from a range of 12,612 - 19,200 worker-turns in order to improve every single tile, not including roads and railroads. A road and railroad will take 12 turns each, which creates a range of (600*12)=7,200 - 9,600=(800*12) turns added.
9,600+21,600=31,200 worker-turns to improve every single tile to its utmost, assuming the most adverse conditions possible.
Now how many workers do we need to fully improve this in a timely manner? I have heard the rule of thumb that you should build all of your cottages before the year 0 in a standard game so that they are given the maximum opportunity to produce - especially by the time you get to PP and FS.
To create a table, this is the number of turns it will take to improve every single jungle tile to its utmost (21,600 on 40 cities) assuming we only need to waste two turns to send a worker to the tile, and we only send one worker to work on each tile to avoid that waste, but that we need to improve the tile and then come back later to build a road, so as not to slow our economy. That is an easy, set number - 1,600 worker-turns used on moving to the tile without any improvement - just movement itself. So now we are add that 1,600 to 21,600 to reach 23,200 worker-turns to improve all jungle tiles to farmland on all 20 workable tiles on an all jungle map.
I have put forth the most extreme assumptions, which will never appear on a standard map, but this is not a problem, since it means we will only improve our land more quickly.
So how many turns will it take to improve every single tile, assuming we start with 40 cities with 1 border pop (another contrived assumption, but it will help us, so let's go with it).
23,200/1=23,200
23,200/2=11,600
23,200/5=4,460
23,200/10=2,320
23,200/15=1,547
23,200/20=1,160
23,200/25=928
23,200/30=774
23,200/35=663
23,200/40=580
23,200/45=516
23,200/50=464
23,200/55=422
23,200/60=387
23,200/75=310
23,200/100=232
So hypothetically if we were to start off with 40 cities at 1 border pop so that we have 20 tiles per city that can be worked, this could be fully improved by 100 workers in 232 turns, but 50 workers in 464 turns, or 30 workers in 774 turns.
This of course does not account for how quickly we should produce the workers, however.
In the early game with a non-expansive, non-industrious leader (assuming no bonuses toward the worker production in general) we need 120 hammers/excess food to produce one worker. If start off every new city before acquiring 50 workers with a Worker>Granary>Forge/Barracks/Market queue, depending on its specialty, and every jungle city with more or less the same except two workers, We should aim to build about 15-30 workers in our earliest cities to gain this worker advantage earlier.
This is just a rough outline, let me know your thoughts and any variable I missed!
