Wow that math is really interesting, thanks a lot. That explains the weird feeling why all my borders were so small lately with Liberty. So actually Liberty gives you a small production bonus, the ability to do massive pillage - repairs, a free Great Person, a Golden Age that's difficult to use at that time and an early free settler. Because all the other benefits are not really that great.
The Great Person isn't free. Actually, before this last patch, even a Great Prophet from Liberty made your STEM people more expensive! It might even still work like that!
As far as I'm aware, after the patch, there -are- no free Great People ever. Every one of them moves the counter up, no matter you got it from Pisa, Piety finisher, Porcelain Tower or otherwise. Bak'tun's aren't free great people, right? Is the International Space Station giving you a free Engine-ientist, at least? I doubt it.
The only exception are the Faith People. They up their faith cost counter.
Perhaps it was evident to many or all of you here, but I know the following result is not obvious to some people who play. All these bonus great people are the equivalent of getting GPPs equal to the current threshold, at the city where the Person will appear. So, it is provably always a benefit (there must be -some- Great Person you prefer to all others at this moment), and it is provably more of a benefit when it happens later. More in nominal terms anyway; the value of the GPPs themselves might shrink.
I mention the first because some people say the Liberty person is a waste to trigger it early. Well, no, not unless you waste it on a person you don't want, which ironically is what a lot of people advocate when they mention Liberal Engineers. You would never deliberately obtain an Engineer over a Scientist by other means at that point, why are you taking an Engineer now?! The policy gives you a strictly good thing - GPPs. Take good ones.
And I mention the second because that -is- the sense in which Liberty GP is a waste, because it only gives you 100 GPPs then, instead of at least twice as much later. Notice finally that while the bonus great person makes the next person take longer to appear, that second person will not take longer to appear than it otherwise would have taken the -second- Great Person to appear after the first one if he appeared normally, counting from now. Indeed, that Person will appear 100 points sooner - or x*100 points sooner, whatever the Liberty bonus was. And all the ones after that. And this means any one bonus great person, even if not free, represents sooner accrual of all Great Persons of that type, and it's faster the later this bonus is.
Bonuses snowball, so you're not just gaining one GP, you're gaininng your game's entire lifetime of GPs ye so many cost points (=turns, since sources of GPPs are few) sooner, including possibly some GPs at the tail end you wouldn't have seem before game over.
So I'm not that pissed about
missing out on the "free" part of GPs, just at how wildly inaccurate and therefore inconsistently termed it is.
It's the Golden Age I wish was free.