Hello everyone. This is not quite a simple yes or no question, but would require a bit of an explanation.
Q: What do happy, content, and happy citizens do? (and if possible, could you provide the technical math, not just general information).
The only thing I could find was that if more then half your city is unhappy, you go into revolt; happy citizens do something with helping corruption; and happy citizen's add to your score. Thanks.
I think you pretty much covered it.
The basic intention is a difficulty multiplier: as you increase the difficulty level, you get fewer and fewer citizens born content, with all additional citizens born unhappy. This makes it more challenging to keep your cities under control each turn. At Emperor+ (in C3C), only the 1st citizen is born content, so to keep additional citizens content in a newly founded town, you may need to do at least one of the following during the turn after growth, to avoid getting a riot on the next interturn:
- Station a military unit (A≥1 or D≥1) in the town (under governments allowing military-police)
- Get a Lux-resource(s) hooked
- Set the LUX%-slider high enough that some of the city's income can make people happy
- Build a Happiness-improvement (Temple, Market if ≥3Luxes, Colosseum, Cathedral, several GWonders)
- Harvest sufficient food that you can turn the new citizen into a (content) Specialist, ideally without impeding further town growth
This thread details the Demographics and score mechanics. Basically, happy citizens score 2 points at game-over, content citizens (and Specialists) score only 1 point (multiplied by the difficulty-factor). So raising your LUX% to 100% on the last turn before the game ends (e.g. before you kill the last AICiv's last city, or launch your Spaceship) to make everyone Happy/Content, is a way to boost your score a little bit, especially at higher difficulties.
And although you mentioned corruption, you didn't specifically mention 'We Love the [Ruler] Days', which is when the corruption-lowering effect actually kicks in. From
GingerAle's FAQ:
What is We Love the King Day (WLTKD)?
We Love the King Day symbolizes that the citizens in a certain city are happy, and thus, that city has lower waste (less shields lost to corruption). You can tell as city is in WLTKD because there will be what look like fireworks exploding over the city. The criteria for WLTKD are as follows: a city, which must have at least 6 citizens, cannot have any unhappy/resisting citizens, and at least half the citizens must be happy. The city cannot also be starving (less than 2 food produced per citizen). If all the above is met, your city will enter WLTKD! There is no limit on how many cities can celebrate this, and it lasts until the city doesn't meet the aforementioned requirements.
As I understand it, WLTKDs basically drop the current corruption/waste level in a city one grade lower than the level associated with your current gov-type (see
Theov's guide to C3C govs). So e.g. under Despotism a WLTKD-city will get 'Monarchic' corruption, under a Monarchy it will have 'Republican' corruption, and under a Republic it will have 'Democratic' corruption.