My search for the best division has led me to this:
I have been redpilled on the effectiveness of flame tanks. They add static terrain modifiers like the rangers and pioneers while also contributing armor. From what I can tell armor doesn't reduce enemy damage against you much (it's scaled by how much your armor beats their piercing, which means only really tough divisions benefit), but any amount of armor advantage seems to still mean you deal +50% org damage to them, which is what really matters (your divisions are cheap, you just want to be able to push). Making medium flame tanks and maximizing their armor (keep 6.4 km/h to not slow down the cavalry) seems the best, armor comparable to heavy flame tanks, better terrain modifiers, less cost. My current flame tanks only cost 111 production which is actually less than engineers.
When stacking terrain bonuses like this cavalry actually becomes basically equivalent or better than special forces even on terrain the special forces are optimized for. Math looks like:
Special forces: 266 soft attack -25% on large river = 199 soft attack
Cavalry (using a 6 cav to compare with a 3/3 marine/mountaineer stack): 248 soft attack - 40% on large river + 28% cavalry bonuses (12% general 6% field marshal 10% cavalry advisor) = 190 soft attack. Both special forces and cavalry get infantry bonuses so they cancel out, cav just also gets cav bonuses. Math isn't exactly like this in reality but close enough.
So using cav has basically no drawback even in the worst terrains unless you're combining attacking into mountains and across large rivers (which... just don't do that). In return you don't have to worry about Special Forces limit and get 60% more movement speed. You don't need more than infantry movement speed to encircle AI but its definitely nice.
Downside is it takes until late 1940 to really do this unless you're a nation that can rush multiple techs. You need 1939 engi to unlock flamers, 1940 to unlock 2nd special forces doctrine, 2 1940 techs to start producing rocket artillery, and you really need the sup firepower doctrine's +50% support company soft attack to bring it all together. That's a lot of tech cutoffs and a lot of land XP. If you're gonna fight earlier you really need at least 1 line AT in something like a 6 cav/1 art build to make it combat effective but that lowers your movement speed and terrain modifiers.
Also you have no AA so this assumes you have air superiority. Which you should kind of have by late 1940s tbh. AI seems to really produce shit planes that get increasingly worse and overpriced compared to yours over time.
Now to find a fun nation to play late game to test this out with. Oh wait, it's hoi4, such a thing doesn't exist...
