@Yin Cognito that's part of the double standard you're applying here. You could replace almost word for word "slavery" with "chopping" and conclude it's OP because in virtually every game people chop.
I'm not so sure. Forests are a
finite resource - no matter how much you want to chop rush something, once the forest around the city is gone, so is the "rush". Population, though, is
infinite - since you can whip then grow a city as many times as you like over the course of a game. Of course, there is random forest growth, maybe influenced by a forest preserve nearby, but these depend on luck and how much you advanced technologically. Also, food is generally the most abundant resource on a map, while the amount of forests depends on the map type, latitude, humidity, etc. Assuming you have both the population and the forest at hand, chopping also takes time (9 turns on Marathon, I believe is 3 turns on Normal), while whipping is done instantly - although counting the turns needed to have some hammers invested before you whip something might level things up and probably make the time argument invalid. But ok, let's say you have half of a good point here - noted. I completely agree with the rest of the paragraph though.
Even though unit cost isn't equally proportional with mara from my understanding [...]
Yes, the marathon unit cost is the
normal cost x 2, and
normal cost x 3 for settlers. Everything else is x 3 (buildings, techs, etc). Unit cost (and movement, for that matter) are indeed an advantage for Marathon, but I suspect it has to do with the fact that Marathon was supposed to be played in combo with Huge maps (which I do) where it makes sense to have slightly different multipliers or you'll never get to explore all the map or wage war effectively.
Also, I believe slavery is strongest on marathon. [...] I think slavery still inherently gets weaker the faster the game speed. It's a rush mechanic, so there's a bigger impact to taking units from 20 turns to build to 2 turns as opposed to going from 5 turns to 2 turns.
The thing is that you're also applying double standards here, because you're not comparing how many rush turns does
the same number of chops/whips buy you at different game speeds - which would analyze things based on the same starting criteria and not based on some random numbers thrown for the sake of proving a point. I'll try to prove why your approach was wrong in this case, hopefully I'm not wrong and you'll understand where I'm going with this (I'll just use the chop numbers as I'm more familiar with them and chopping is also a rush mechanic, as you correctly pointed out, plus, the numbers are roughly similar for Slavery - give or take)...
Let's assume a city has 20 H production. Now on Marathon, a Settler cost is 300 H, so normally it will be completed after 15 turns (not exactly the 20 turns you mentioned, but close). Taking the Settler from 15 turns to 2 turns on Marathon (assuming that we don't count the turns needed to chop the forests) would require 2.(8) chops, so "almost" 3 chops after Mathematics for 90 x 3 = 270 H, which added to the 2 x 20 = 40 H of the 2 "regular" turns would give 310 H, slightly over the 300 H total needed.
On Normal, a Settler cost is 100 H, so the same 20 H producing city would normally complete it in 5 turns. Taking the Settler from 5 turns to 2 turns (same assumptions as before) would require
just 2 chops after Mathematics for 30 x 2 = 60 H, which added to the 2 x 20 = 40 H regular turns' output give the required 100 H total needed.
So yeah, I know what you meant that there is indeed a bigger impact to taking units from 15 turns to build to 2 turns as opposed to going from 5 turns to 2 turns (in absolute terms) ... but
it also costs you more (in terms of chops/whips and such), as in the example above we chopped 3 forests on Marathon compared to 2 on Normal - and that's taking only 15 turns into account as opposed to your 20, for the sake of computing simplicity, not to mention not counting the turns or the worker movement if chopping is done sequentially (I think there's a similar additional turns' impact if we talk about slavery and the need to have some hammers invested before the whip). That's why when making such a comparison one should start from the same set of base assumptions and see where it takes him from there (e.g. how many rush turns would one "gain" at different game speeds if he would
chop/whip the same number of times in a city producing the same number of hammers, and see if the results don't follow the proportion between the game speed factors - 3 to 1, in this case, but can be 2 to 1 for the rest of the units).
On the rest of the paragraph (as well as your opinion on slavery impact on different speeds - bar the numbers involved in what I pointed out above), you're probably right, you certainly have the experience to have an entitled opinion on it. On the anarchy turns though, as far as I know Civ 4 considers all the relevant variables (i.e.
Anarchy Turns = (1 + Civics + [Cities × MapFactor / 100]) × SpeedFactor × 0.5), so the issue you encounted at Quick speed might come from rounding the number. Since you mentioned it, changing to Slavery for me on Marathon accounts for 2 turns of anarchy, not 1. I might be wrong, but I prefer to change civics as early as I can, because although the early turns are more important in the gameplay, you lose less Food/Production/Commerce and benefit the change for longer afterwards. Point is, that lost turn pays off eventually.