Regarding Puppets and Happiness for wide play:
According to my theoretical analysis and personal experience Puppets hurt you without Martial Law and merely become neutral with Martial Law.
I think annexing all Cities is much better if you follow a barbell-like strategy for building Public Works.
More details below.
1. Yields from Puppets
Let us assume for a second that a City only produces Gold, Science, and Culture and that each of these Yields has the same utility value of 1 (Gold, Science, and Culture output of a City are all equally useful).
Let us further assume that the net Gold utility of Gold is the combination of -2 utility from Building maintenance and +3 utility from Gold production (Building maintenance is equal to 2/3 of raw Gold production).
For a regular City we thus get a net utility of 1 + 1 + 3 - 2 = 3.
For a Puppet without Martial Law all positive utility is cut by 80%, resulting in the following net utility value: 0.2 + 0.2 + 0.6 - 2 = -1.
For a Puppet with Martial Law (60% cut) we get: 0.4 + 0.4 + 1.2 = 0.
Under these assumptions Puppets are actually draining your resources without Martial Law and even with Martial Law they do not give you a net benefit.
Some things that were not considered for this analysis:
- Food/Production: these only have localized effects and do not contribute to your empire as a whole. I therefore think they're irrelevant.
- Faith: If you have a low number of Cities Puppets are not worthwhile in the first place. If you have a large number of Cities (which you do later in the game) the utility of Faith is low when compared to other Yields. I thus think it can be neglected.
- Tourism: If you have a low number of Cities Puppets are not worthwhile in the first place. If you have a large number of Cities you get more Tourism from Annexation than from Puppets. You still get some Tourism from a Puppet though.
- Build order: Puppets can have really bad build orders which results in overall lower Yields compared to regular Cities.
- Military Utility: Both regular Cities and Puppets provide some military utility but this is hard to quantify. I would argue that regular Cities are a little better though.
2. Puppets vs. Regular Cities in Terms of Culture/Science
Regular Cities increase the amount of Science needed for Technologies/the amount of Culture needed for Policies.
We can expect there to be some number of Cities beyond which it is better to puppet a City than it is to annex it.
However, there are several factors that need to be considered here:
- City Yields compared to the Yields of the Cities that you already have: if a City produces almost no Yields making it a Puppet is a better option than if the City produces a lot of Yields.
- Map size: the increase in Science/Culture needed for Technologies/Policies per City depends on the size of the map. On a small map a Puppet is better than on a large map.
- Martial Law: The Policy Martial Law found in the Imperialism branch doubles the amount of Yields that you get from Puppets.
I calculated how good a City needs to be compared to the average of your Cities to make annexation and puppeting equally good.
I have visualized the results in the attached figure (
Edit: the original calculation contained a bug that slightly distorted the results; I have uploaded a new image).
The x axis represents the number of Cities including the new City.
The y axis represents how good a new City needs to be compared to your average City to make annexation a better option than puppeting.
A value of 1 means that the City is exactly equal to the average of your Cities, a value of 0.5 means it's half as good as the average of your Cities, etc.
As we can see the difference between map sizes and Policy decisions is very large.
Also note that I did not take yields from sources like killing Units or City States into account.
3. My Strategy for going Ultra-Wide
Each non-puppeted City that you own increases the Needs modifier in your Cities by 9% (independently of map size).
If no countermeasures are taken a large empire will therefore become increasingly unhappy as it gains Cities.
Public Works can reduce Unhappiness to some extent but I think it doesn't fulfill the purpose it was added for.
If I remember correctly its purpose was to be a last resort for unhappy Cities.
However, if you only start building it once Unhappiness starts to become a problem it is basically useless.
Cities that are unhappy typically have very large Need deficits so if you build Public Works in such a City the Happiness and the Needs reduction has literally no effect.
You need to build
a lot of Public Works to get any effect, but once you do you can quickly eliminate all Unhappiness from Needs.
Conversely, if you build Public Works in a City that is already pretty happy you get immediate benefits without the need for a large up-front investment.
This has led me to develop a barbell-like strategy for dealing with Unhappiness: instead of trying to make all of my Cities kind of happy I only try to keep some percentage of my Cities very happy while completely neglecting Happiness in all other Cities; as long as I have more total Happiness than I have total Unhappiness I do not suffer any penalties.
In practice this means delegating some Cities to build Buildings and Public Works while delegating other Cities to build Buildings and Units.
(In case it isn't obvious: you also need to build as many Factories as possible to get enough Production.)
With the above strategy I was able to control ~40 non-Puppet Cities while staying at ~60% Happiness.
Keep in mind that the above strategy needs a lot of long-term planning and experience to pull off well; when in doubt designate too many Cities to building Public Works rather than too few.
Alternatively just found TwoKay Foods to completely eliminate Unhappiness (but I don't know if that is intended).
4. Changes That I Think Would Improve Ultra-Wide Gameplay
I think one or more of the following changes would lead to improved gameplay for games where you control 20+ Cities:
- Reduce Building maintenance of Puppets: if the Building Maintenance of Puppets were reduced by the same amount that their yields are reduced they would no longer drain your Gold. The Unhappiness from Puppets doesn't seem like that much of a problem to me.
- Change the local Happiness from Public Works to empire-wide Happiness: currently a lot of the Happiness that you get from Public Works simply gets swallowed up by the deficits. If the Happiness was instead empire-wide the benefits you get from Public Works would be much smoother and it would be a better option when you're already in a bad situation in terms of Happiness.
- Change the local Needs reduction of Public Works to a global Needs reduction: with the current system you would need to build some amount of Public Works in every City for each new City that you annex/found. If Public Works were to instead provide a global needs reduction you would only need to build a roughly constant amount of public works for each new City that you annex/found. The cost increase per Public Works built could also be made global.
- To reduce snowballing if any of the above measures are taken: remove the synergy between Factories to reduce the amount of production available for wide strategies. If you have a lot of Cities you already have an advantage in terms of Production because you need to build fewer Units per City.
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