Expansion

[Thalassicus]

I discovered a mistake in the formulas I used to figure out expansion costs for cities. I'm going to update the expansion costs with the new formula in v137.6, and we can tweak things further from that baseline. This might be the reason for recent questions about cultural expansion and city growth. This does not affect gold expansion. (We can't see the formulas directly because they're in the game core only Firaxis has access to.)

I assumed changing "multipliers" from 1 to 2 basically "multiplies" costs by 2. I figured out they chose a different formula:

Assumed formula
constant + multiplier * (x ^ exponent)

Actual formula
constant + linear*x + 1*x^exponent
​

The linear coefficient is ambiguously labeled "multiplier," which is what threw me off. With the quadratic coefficient fixed at 1, it's actually impossible to "multiply" the formula by a value, which will make things harder to balance.

 

[Thalassicus]

Okay, nevermind. It appears all three forms of expansion c5food:) follow different formulas, despite having similarly-named variables. The post above apparently works only to food. I'm now working on figuring out the cultural formula. It would have made more sense if they were all the basic second degree polynomial...

I know nobody's probably interested in this stuff, but writing it out helps me wrap my head around the differences.

n: number of expansions, starting at 0
m: "multiplier"
b: "base"
x: "exponent"

= 0n^x + mn + b
= (mn)^x + 0n + b
= 1n^x + mn + b

There's no logical pattern to it.

 

[mitsho]

it would, but when was civ (5) ever simple or logical?

(I would have more substantial things to contribute, but it's really late here )

 

[Thalassicus]

Several people expressed a desire for faster cultural border expansion in very large cities (3rd ring and up). This is due to frustration with keeping AI settlers out of gaps between tall-empire cities. I was hesitant to buff the policy because its old position in the tree was easily accessible to wide/militaristic empires. To solve both these problems, in v140 I buffed it and moved it to the finisher, where it's less accessible.

This shows the total required to fill a ring or get # tiles with the expansion bonus (compared to not having the bonus):

 

[Zaldron]

Awesome, I look forward to trying this out!

 

[Seek]

The 137 numbers felt just right to me - with LE my capital filled out completely (fifth ring) before t200 and my out cities got all the good tiles in a timely manner (I don't think I bought one tile all game). I did have the Kremlin eventually, and was fairly focused on culture as well, so my view is probably slanted because of that.

In other words, I'm probably okay with this change, but I do feel strongly that cultural expansion not reach the levels of pre-v131.

 

[Thalassicus]

I think culture expansion was somewhat slower in v138 than v137, so the buff to the Tradition policy should bring it back to the values you're used to. Please give your thoughts once you have a chance to try v140. I'd be happy to adjust up or down.

What I've been doing is smoothing out the jumps in the first few levels ("diff" columns below). Going from 30 to 55 is a 55/30=83% increase, then it immediately drops to a 45% increase. Those early stages felt really weird to me. I also increased culture expansion costs overall compared to vanilla, since gold expansion costs are lower than vanilla. It's basically intended to shift some focus from to while keeping total expansion the same.

Culture


Food

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