I think ST cleared up the ratings. Free air rating in much higher, and is typically what we use in theater/entertainment. Ratings for overhead lines are even higher. I have a 600A service coming from the transformer on 1/0 aluminum, but it splits into (3) 2/0 cables before entering the conduit on the building. I'm not vouching for these specs, its just what the power company put in, but you can see that the more space and heat dissipated, allows for a significantly higher rating. This is conversely the same reason we de-rate socapex cables by 50% compared to individual conductors. All of that aside, I have never had an issue using 4/0 for a 400a service or 2/0 for a 200a in Canada, though you should check with the local AHJ. Really most of the difficulty is from boarder patrol holding tour buses at the boarder just to screw with them.
Even those who are qualified may not remember the exact ratings of a particular cable. That is why I posted the commonly used sizes for a given power service. Off the top of my head I might not remember what the maximum rating is for #2, however I know it is more than 100, and less than 200 amps. So when I find a ball room with 100A disconnects, I know to use #2, just as I would choose 2/0 for a 200 amp. These same rules of thumb are used all over the industry. 3/8" steel for 1-ton points, 1/2" for 2-ton. I know this to be true in most common uses, but I cannot tell you the exact rating of the steel unless I look it up. When you start to go outside of typical application then it is prudent to do exact math, but for most things, just using accepted standards will do the trick, otherwise you would have to have an impressive reservoir of numbers and equations in your head.
