You do need workers. In your first screenshot yesterday you had 6 unimproved tiles in your capital, you were working at least 3 of them. Even if you just wanted lumbermills on them, that would be 66 worker turns (16 for lumbermill+6 for RR on marathon speed x3tiles) that you are needing in your capital. Since Bureaucracy will have been the most powerful legal civic available for many hundreds of turns and it gives +50% hammers (and commerce) in you cap this is a lot of free production you are missing out on in your capital. So you are building your lumbermills far too slowly in your most important city. The quickest way to rectify this is is by chopping workers out. Lumbermills do not grow on trees.
FYI- National Park is a really bad idea in your Ironworks city. NP removes access to coal in the city it is in, coal gives +50% hammers in your IW city. The two do not go together.
You did not learn this tactic in MP as any human player would ignore your hill, capture the city, raze it and move on leaving your expensive upgraded unit sitting on its hill looking foolish. From what I know of how the civ4 AI operates it will not behave as you describe either, so this is all just wishful thinking on your part. If you are militarily inferior you have to not be in the war.
For someone who has talked so much about preserving your resources you are being extremely wasteful of them. You have are fighting against stacks of rifles and cavs with pikes and grenadiers, neither of which come close to being able to attack with winning odds. So you are losing. You are countering this by spending huge amounts of resources on MG which can only defend one tile, you are then defending your least valuable tiles. You have researched RR, MilSci and are doing your best to avoid researching economics. You could have gone rifling and assembly line and be shredding charlie with infantry. You wouldn't be able to put RR on your lumbermills but since you haven't even built these yet this does not matter.
Back to the original thread, you could also have just chopped everything, made it to state property and be running workshops.
Nope, in Madrid I'm working only 1 lumbermill, 1 mine, 1 deer, 1 cows, 1 lake, 9 towns. I'm not building Lumbermills there.
Many forests there are regrown. You all seem to ignore this, and it's part of the topic.
Are regrown, so I chop them 2 or 3 times.
I see a waste of hammers building many workers: you must not arrive at one point where your workers have nothing to do. Chop for worker, then chop again for another worker? Without Mathematics? Forests far away from the city? Less than 40 hammers per chop?
I prefer to wait for Mathematics, then wait for borders expansion. And also wait for Masonry to have Stone or Marble for a Wonder, then chop after having them connected. Also, chop for a Warrior or wait for Copper or Iron to be connected, so you chop for Axeman? Don't chop a forest waiting to chop for one Wonder?
There are so many reasons why not chopping at a given time.
National Park do work there with Factory (not Ironworks, but would be the same) and Industrial Park: I have Power from the Three Gorges Dam.
With Nat.Park you have the health to sustain the Ind.Park.
I'm killing AI stacks of Cavs and Rifles with Cannons, then Conquistadores and Grenadiers, plus anything else: I killed many Cavs with Elephants, and Riflemen with Swordsmen and Bows. 2* Grens can kill a 10 strenght Cav (weakened by cannons). And Conquistadores can kill weak Riflemen. I have a few MGs, one or two per tile-to-defend only.
I wanted to get Rifling
after Assembly Line, like I've done in other games. Now I dont need Riflemen if I build enough Cannons. And I'm winning by now, not losing - despite lower power.
State Property is something very late from Repl.Parts if you rush for it: you will have so many things to discover, about a 100 turns, 200 turns, to deal without State Property, you might die before reaching it.
When you will reach StateProp, you could get rid of some Lumbermill eventually: it's not something preventing it.