Golden Ages started by Great People don't count as far as I can tell. Do all golden ages have to be from Happiness? What about from say Reformation or Rationalism, the cultural GAs?
Civilization – From Archaemennid to Safavid: What Golden Ages count towards the achievement
achievementscivilization-5
Related Solutions
Although bwarner's answer was helpful as always, no one verified beyond "I think so" that puppet cities are affected by each of the civilization wide effects, so I did some testing and:
Yes, puppet cities are affected normally by all civilization-wide effects.
I can't verify that there are no exceptions, but I verified at least one of each of the things I was concerned about...
The Testing
Civilization Special Trait
I loaded up France on easy, and went about conquering. Japan fell, giving me Kyoto to play with. As soon as I conquered the city and took it as a puppet, it was producing 2 culture. This matches perfectly with France's ability, so CHECK!
More Test Setup
Having acquired my victim, I setup the test: social policy ready, golden-age ready, and wonder ready all on the same turn! (Save file available upon request, whenever I get around to it after that.)
Before
Social Policy
I enacted Liberty->Republic, which gives +1 production/city. That matches, so CHECK!
Golden Age
I already had culture working for me, so I started the golden age by enacting the social policy Piety->Reformation. Clearly shows an increase in both gold and production, CHECK!
World Wonder
If you take a look at all of my cities from the same turn, you can see Orleans is about to finish the Sistine Chapel, which gives +33% culture/city. I went to the next turn, and without any growth or buildings completing, the after shows increased culture on Kyoto. (Lyon also started with 7 culture and ended with 9 as well, so the rounding definitely matches.) CHECK!
Everything checks out. I suppose puppets really are just normal cities that you don't control. I would still love to hear if anyone finds any exceptions!
The base number of turn for the Taj Mahal is 15 a turn Golden Age. The Chichen Itza world wonder will increase that number by 50% (= 22 turns).
Building the Taj Mahal as Darius resulted in a Golden Age of 33 turns (should only be 50% longer). Darius with Chichen Itza resulted in a 49 turn Golden Age.
The base value seems reasonably balanced to me, maybe a bit too powerful. With Chichen Itza it is very powerful, but Taj Mahal with Darius is just outright overpowered, or even broken.
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Best Answer
The achievement will only trigger on 'natural' golden ages which come from citizen happiness.
Any of the ages which you can trigger yourself, via social policy or great people don't count.
If you are trying to nail the badges, the best solution is to focus on happiness improvements, and grab Meritocracy and Organized Religion.