Hard Population Cap

[DarkSchneider]

So it seems there is a hard population cap for your empire given the number of cities that you build, rather than something food based as in previous Civ games. There are only 15 luxury resources in the game total, and there is a linear realtionship between population and generated unhappiness. Each city can counteract at most 15 happiness via buildings.

So it appears that without social policies your upper population limit is:
75+9+13*Cities = 84 + 13 * Cities.

With social policies that improves to:
(75+11+16*Cities)/0.8 = 107.5 + 20 * Cities

Does this look right to people? Certainly this changes based on Civilization and leader traits, but for a generic civilization you're looking at cities of 20 and under.

 

[ShaqFu]

Interesting idea, although I'm not sure it's a hard cap, since cities continue to grow (albeit slowly) even in mild unhappiness. If there's a point with where growth totally freezes, that's your limit; otherwise, you can grow indefinitely, just at a glacial pace, until you run out of food. I'll admit to being hypervigiliant about happiness so far, so I haven't seen my empire if it's in severe rage.

 

[DarkSchneider]

Interesting idea, although I'm not sure it's a hard cap, since cities continue to grow (albeit slowly) even in mild unhappiness. If there's a point with where growth totally freezes, that's your limit; otherwise, you can grow indefinitely, just at a glacial pace, until you run out of food. I'll admit to being hypervigiliant about happiness so far, so I haven't seen my empire if it's in severe rage.

That's true, I should have added another 10 to the hard cap. But there's still a hard cap. I suppose the only way to get around it would be to conquer all the other cities while you were already at your hard cap limit.

 

[ShaqFu]

You'll also need to account for Cultural Diplomacy (7.5 happiness from gifted luxuries), Protectionism (+1 from luxuries - does this stack with CD?), and Planned Economy in your second formula.

 

[Martin Alvito]

You need to account for Wonders, Gandhi's ability in particular (big difference) and Planned as well. The function can be solved, but the math will get a touch ugly along the way.

 

[rune42]

^ To add to the above:

Humanism SP increases happiness by +1 per University.
Military Caste SP increases happiness by +1 per troop garrisoned in a city.
Legalism SP reduces unhappiness in your capital due to population by 33%.

Notre Dame = 5 Happiness
Eiffel Tower = 8 Happiness
Natural Wonders = 1 Happiness

There are 6 natural wonders to be found in a standard game. It doesn't matter if you're the first or last person to find one, you'll still get the bonus. +/- 1 natural wonder per map size.

 

[Pragmatic]

Why is it 13*Cities, and not 15*Cities? There's 15 unhappiness per city that can be counteracted by buildings (expensive buildings... at least one, I think, requiring resources in the city radius), right?

 

[rune42]

^ Every city adds -2 happiness by themselves.

 

[QuothTheRaven]

You can get unhappiness from number of cities down to 0 if you have both the Forbidden Palace and Planned Economy.

 

[strollen]

There are several UB that add +2 happiness Egypt,Persia maybe somebody else. I assume you counted the benefits of Freedom but that is limited by the number of specialist spots which I think is around a dozen or so.

 

[KrikkitTwo]

It's not a trully hard cap, you can still add population through conquest (they need to fix this)

 

[Anastomosis]

Also, the game crashes when you end your turn after getting your 70th city, so you have to figure that in...