City happiness is an important factor of civ - whatever the settings are, you´ll always have to deal with keeping your cities happy. In teamer games that are restricted to one era, you will either run Hereditary Rule, basically giving you unlimited happiness at least till you move out for an attack or additionally use the culture slider. This text is not about how to most effectively avoid (too much) unhappiness especially when slaving, but about the concept of the happiness cap (aka "happy cap").Of course you can define a happy cap when running Hereditary Rule and/or using the culture slider - the interesting part though is the happy cap without those two. In teamer games you don´t necessarily want to grow your cities to bigger sizes and additionally running 10% or 20% culture doesn´t hurt you as much as in a long solo game like Ironman or ffa, where you will want Representation or Universal Suffrage eventually and where sacrificing research in order to increase the culture slider for happiness is not an option if you´re planning on doing well in the game.

The concept of the happy cap is most important in Ironman/ffa. There you basically have three phases:
  1. before Monarchy for Hereditary Rule
  2. from Monarchy on
  3. when switching from Hereditary Rule to Universal Suffrage (or Representation)

When planning how to plant your land, you need to be aware of how big you will be able to let your cities be when switching away from Hereditary Rule - this is where knowing the happy cap of your empire is key. It´s very difficult to win an Ironman or ffa with 5-7 opponents when not being able to leave Hereditary Rule. The lack of Universal Suffrage or Representation and the additional upkeep and production of police units hurts too much.

Let´s get into defining the happy cap and analyzing possible strategies resulting from it. Remember, a city with one unit in it has as a basis a happy cap of 5, a capital 6. That´s 4 (5 in cap) without the unit and one more with it - the unit having nothing to do with Hereditary Rule. A happy cap of 5 means the city can support population 5 without any citizens becoming unhappy (negative effects on happiness like Slavery taken aside).

Resources

You´re playing an Ironman or ffa game, you´ve expanded to three or four cities and explored most or all of your surrounding land. Now you can count the happiness resources that you´ll most likely be able to plant over the course of the game. How well you know what you will get depends on the map you´re playing and on your experience.

Regarding the switch away from Hereditary Rule once having researched Democracy all happiness resources are equally worth +1 happiness as a basis. Two exceptions being Ivory and Whale, which become obsolete eventually, Ivory with Industrialism and Whale with Combustion. You should count those separately. Ivory is very helpful in phase 1 before Monarchy, but won´t be available in phase 3 from a certain point on at which you´d still be glad to have it.

Looking at the basic effect on happiness there are three kinds of happiness resources:
  • pre-Monarchy: gold, silver, gems, ivory, fur
  • Monarchy: wine

  • post-Monarchy, requiring Calender: spices, sugar, dye, incense, silk

... and there is whale with Optics.

In phase 1 any of the pre-Monarchy happiness resources can increase your happy cap by 1, which can be very helpful.

Example: Let´s assume we are playing India and got gold, wine, spices and dye - once hooked that´s a permanent increase of the happy cap by 4, that being a happy cap of 9 in normal cities and 10 in the capital.

Buildings

The next step involves checking whether and if which of your happiness resources provides an additional happiness with which building:
  • Market: +1 from fur, silk, ivory (till Industrialism), Whale (till Combustion)

The market is an undesirable building due to its high cost and in most cities low effect (you are probably running 80%-100% science). Markets see play only in ffa/Ironman games and even there you´ll build them in only a few cities for the bonus on gold. If you´ve got Fur and Silk, the ratio of cost/effect becomes decent enough. If you´ve got only the two resources that become obsolete, it´s not. If you´ve got only either fur or silk, you should think twice before counting it for your overall happiness cap from the start since you have enough other, better stuff to build and rather want to avoid getting markets.
  • Theatre: +1 from dye

The theatre requires Drama, a technology you want to avoid completely or at least as long as possible. Sometimes your happiness cap will be so low that you will require Globe Theatre for your capital, having to research Drama and build theatres even if you don´t have dye. It´s of course a valid option to get Drama for theatres if you have dye and are in need of the happiness - but since theatres don´t do much else good in an average Ironman/ffa, you´d rather avoid building them and researching their prerequisite tech.
  • Forge: +1 from gems, gold, silver

The Forge is a basic building anyway. You will want to have it in every city. Gems, Gold and Silver are already great due to their availability pre-Monarchy in phase 1 - a forge increasing the happiness they provide makes them the clearly best happy res.
  • Colosseum: +1

As easy as that.
  • Temple: +1

Temples are better, because cheaper Colosseums, but they require a Religion. You might have gotten one early - or not. An experienced player can evaluate his chances on getting one or having to get one over the course of the game pretty well. As a rule of thumb, you will want a religion anyway in every game.

  • Special religious building (e.g. Confucian Academy): +1 from incense, +2 if the religion of the building is the state religion

This one is expensive, though gets more bearable if you´ve got the resource that doubles its production. Remember that you require a different resource depending on the religion you got. Without the resource it´s very tough to build this massively. What´s almost worse though is the requirement of Music. The same arguments as with Drama apply. What you can do though is researching it (and its prerequisites) once you´ve got Democracy in 1 turn per tech - still sucks since that might make you lose turns on the race for corporations which is the next big goal after having reached Democracy in most Ironman / ffa games.
  • Broadcast Tower: +1 for CHM leader; +1 with Hit Musicals, Hit Singles, Hit Movies

In a game with picked leader, you should basically never be Charismatic. If you get one of the "Hit" wonders, broadcast towers are a no-brainer where required. You cannot plan for that from the start.
  • Unique Buildings: +X

There are a couple of unique buildings that provide additional happiness (making their civs top picks in Ironman/ffa). If you´ve picked one of those, count that when determining your happy cap. Three main targets here being Ottomans, Maya and India with Greece being an option. Byzantine and America completing the list, but not being any real option.

Example: In our example the happiness from the gold will be doubled by forges. The wine could only receive a health bonus from an (undesirable) grocer. Same being true for spices. The dye would give us an additional happiness if we researched Drama and build theatres.

That´s one additional happiness from gold for sure and one potential from dye. Additionally you can count Colosseums, bringing us to a total happy cap of 11; 12 with Drama and theatres. Having religion already allows for increasing that by another two (1 for state religion and 1 for temples), arriving at 13 without theatres. Finally we are India, giving us another +2 from the Mausoleum making it a total of 15 without theatres.

Wonder
  • Globe Theatre: Researching Drama, building theatres and then Globe (requiring production and taking away one National Wonder slot) is a compromise you sometimes have to take if your happiness situation is that bad.

  • Notre Dame: Prioritizing the rather secondary Engineering in order to get Notre Dame for another +2 in all cities on the same continent (not for sea maps in ffa games!) can be a response to a bad happiness situation. It´s a costly endeavour though delaying something else for it, whether that be Civil Service, Education or even Liberalism.

  • Broadway, Rock'n'Roll, Hollywood: Those are not tough to understand. If you´ve arrived in the late(r) game and happiness is a serious issue (or soon will become one once you lose Ivory and/or Whale), aim for those if you have a chance.

Conclusion

You can derive your happiness cap pretty precise by knowing the resources you´ll be able to plant, adding a potential Unique Building that provides happiness and taking an educated guess at whether and if how many religions you´ll get. The first two also tell you how much you should prioritize getting a religion - which though in general is very good due to the various Religious Civics which can all be put to good use at one time or another.

For any empire and any strategy you will need at least a happy cap of around 9-10. That being the absolute minimum and only working for very specific strategies (like planting cities super close to each other, sharing tiles, not growing bigger then pop 9 or 10). Still even in those strategies you´ll get in trouble with your capital, which you will want to be as big as possible and work as many tiles as possible in any game. In such scenarios the mentioned Globe Theatre finds its use. In general you should aim at as much as you can get of course, but at least as much as you need to support all or most of the maximum population you can get your capital in order to work as any cottages as possible and beyond that a couple of specialists potentially as well.Determining the happy cap as early as possible is important in order to plan ahead accordingly. On the one hand you need to adjust the way you plant your cities on the other hand you can look for ways to increase the happy cap:
  • Got a religion? Can you get one or another one if you´ve got one already?
  • Any wonders available without hurting you in other goals too much? (e.g. going for engineering while having a chance at liberalism)
  • Any neighbour you could conquer or partly conquer in order to get more happiness resources? (be careful with the "partly conquer" in non always-war games)