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City maintenance costs - the numbers

Discussion in 'Civ4 - Strategy & Tips' started by Pedro78, Mar 26, 2017.

  1. Pedro78

    Pedro78 King

    Joined:
    Oct 20, 2016
    Messages:
    965
    I was searching around the forums for a detailed sheet about city maintenance costs, didn't find any (is there any?). So I made a bit of maths myself.

    Everything here will be about cities placed on the same continent as the Palace.
    All the numbers are for standard size / deity difficulty.
    Of course, everything here is counted pre-inflation.

    To convert for other sizes/difficulties, I came across this awesome resource : https://forums.civfanatics.com/resources/civ4-bts-reference-en-standard-version-pdf.6570/
    Not sure if the person who did this is still active on the forums, but this is really clean work.

    The total maintenance cost of a city is "Number of cities" + "Distance from Palace" + "Colonial expanses" + "Corporation expanses". I will talk about the first two.

    Number of cities maintenance costs

    A simple formula :
    Depending on the size of the city, and your actual number of cities, this cost does not follow a completely linear pattern.

    A good formula that will give you the "number of cities" maintenance cost of a given city, with a precision of under 0.5GPT is : "number of cities cost" = (0.6 + 0.033*(city pop - 1))*(number of cities)/2

    The correct formula :

    B = base "number of cities" function.
    p = city population
    n = actual number of cities
    N = "number of cities cost"

    "B" is the "number of cities" cost of a given city, in a 2-city empire.

    Here are the B(p) value :
    upload_2017-3-26_23-10-31.png

    The correct formula is : N = B(p)*n/2

    As the B function isn't completely linear, the first formula is only using an approximation of B, which is enough to calculate your "number of cities" cost at a precision smaller than 0.5GPT.

    The "number of cities" cost cap is 8GPT, so if the formulas above result in costs superior to 8GPT, the "number of cities" cost of the given city will be 8GPT.

    "Distance from Palace" maintenance cost

    The "base" "distance from Palace" cost, i.e. for a 1-pop-city, is not calculated upon how many movement points it takes to move from the Palace to the city. There are rings around the capital (or the Versailles/Forbidden Palace city) that determine how much the base distance cost will be. Let me take an example :

    If you found your second city 3W1N, or 3W2S of your Capital, the "distance", i.e. the number of turns it takes for your warrior to move from your capital to your second city spot (without roads ofc :D), is the same. But the second settlement option will result in a higher "distance from Palace" cost, because it is in the fourth ring and not in the third.

    Third ring is the settleable area from the second border pop. Fourth ring is defined by the thid border pop, and so on. The distance costs do of course keep increasing when you settle out of the "Legendary-culture area", they are defined by rings built on the same pattern as border pops. I attached a BTS save where I manually draw the 14 first rings.

    The base distance cost (D) of a city is : d = (ring number)*0.29

    The distance cost, contrary to the "number of cities" cost, has a linear evolution. The total "distance from Palace" expanses of a city (D) are : D = (7 + p)*d/8

    Hope this helps :)
     

    Attached Files:

    Last edited: Mar 26, 2017
    Anysense and fractals like this.

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