World size settings are suboptimal

[star mouse]

Ever wondered why you *always* have some highly corrupt cities? Ever wondered why you often seem to meet the AI very quickly? Ever had trouble doing research on a large map?

I have been examining world sizes with a small spreadsheet I have created (see attachment) and I have found that the numbers are not optimum.

First, some mathematics:

Given:

• X and Y are the dimensions of the world
• C is the number of civilizations

For a world with a size of X by Y, the total grid squares (G) in the game is:

(1) G = X * Y.

The total space per civ (S) is then:

(2) S = G / C.

For a world with 40% land, the land area (L) per civ is:

(3) L = 40% * S.

The average distance (D) between adjacent civilizations is:

(4) D = SquareRoot (S).

The average number of cities per civ (N) is (assuming 40% land and 1 city every 21 squares):

(5) N = L / 21.

Science rate (R) can be formulated as:

(6) R = N * 5.

A good value for minimum distance (M) can be derived by dividing average distance by 2:

(7) M = D / 2.

Now lets' run some calculations using a standard map size of 100 by 100 and 8 civs, and compare them with the standard CIV3MOD.BIC file:

(1) G = 100 * 100 = 10,000.
(2) S = 10,000 / 8 = 1,250.
(3) L = 40% * 1,250 = 500.
(4) D = SqRt (1,250) = 35.4.
(5) N = 500 / 21 = 23.8. (CIV3MOD = 16)
(6) R = 23.8 * 5 = 119.0. (CIV3MOD = 120)
(7) M = 35.4 / 2 = 17.7. (CIV3MOD = 12)

We can see at once that:

• The minimum distance between civs in the standard CIV3MOD file is somewhat closer than half the average distance (it's actually a third).
• The optimum number of cities from CIV3MOD is only 2/3 of the best value.
• The tech multiplier is fairly close, but that's because I based my multiplier of 5 on the actual value.

When we try each of the world sizes, these are the values we get for N, R and M:

Tiny: N = 17.1, R = 85.7, M = 15.0.
Small: N = 20.3, R = 101.6, M = 16.3.
Standard: N = 23.8, R = 119.0, M = 17.7.
Large: N = 31.1, R = 155.6, M = 20.2.
Huge: N = 38.6, R = 192.9, M = 22.5.

Here are the corresponding values from CIV3MOD:

Tiny: N = 12, R = 60, M = 6.
Small: N = 14, R = 90, M = 9.
Standard: N = 16, R = 120, M = 12.
Large: N = 24, R = 180, M = 18.
Huge: N = 32, R = 240, M = 24.

In each case, it can be seen that in the CIV3MOD file, the tech rate is simply 10 times the minimum distance between civs, but this is an error. It should instead be based on average number of cities per civ.

Here are what I think the values *should* be, based on my figures above:

Tiny: N = 18, R = 90, M = 15.
Small: N = 20, R = 100, M = 16.
Standard: N = 24, R = 120, M = 18.
Large: N = 32, R = 160, M = 20.
Huge: N = 40, R = 200, M = 24.

If these figures are used, you will have fewer corrupt cities if you're avarage-sized (but corruption will still be a problem if you get big), you will not meet AI civs as quickly on smaller maps, and science will be easier on larger maps but harder on smaller maps.

This will also assist the player who wants to create custom world sizes by providing good values for the settings. In the attached spreadsheet, there's two extra world sizes (miniscule and gigantic) that show how this might work.

[star mouse]

Some more comments:

* Corruption will be more of a problem for you if you select 60% oceans. This is because there's more land area for cities

* Corruption will also affect you if you play with less than the maximum number of civs or kill off some civs in the game

* I have tested the settings on a tiny world by creating a few maps in the editor. In each map I created, the civs were well spaced, so it would have been possible to expand for some time before encountering another civ, even on a tiny map. The four civs tended to have starting positions in the corners.

[OneInTen]

For a world of 100x100, there are actually 5,000 squares, not 10,000. That is, G = X * y / 2.

Open up the editor and check if you don't believe me.

[star mouse]

Originally posted by OneInTen
For a world of 100x100, there are actually 5,000 squares, not 10,000. That is, G = X * y / 2.

Looks like I'll have to take a look at that because it will obviously throw all the calculations off. You'd think a 100 x 100 map would have 10,000 squares, but no, isometric decides it's going to be tricky....

[star mouse]

When the calculations are re-run after dividing the land by two, number of cities drops, science drops and minimum distance doesn't change much.

You can also fudge the figures easily, so you can still use the figures I gave. Assuming one city per 21 tiles and science points to be 5 times the number of cities are fudges I used that can easily be changed as needed.

Another note: there seems to be a bug in map generation because I have often found civilizations placed closer together than the minimum distance, even with the old distances. In one game I had with the old figures, Paris and Berlin were only 6 squares apart on a large map, and another civ was also nearby.

[lockstep]

Originally posted by star mouse
When the calculations are re-run after dividing the land by two, number of cities drops, science drops and minimum distance doesn't change much.

You can also fudge the figures easily, so you can still use the figures I gave. Assuming one city per 21 tiles and science points to be 5 times the number of cities are fudges I used that can easily be changed as needed.

I suggest to calculate with 30% land, as this is the standard setting. Furthermore (and also on 'continent' maps), the majority of cities will have at least some sea tiles within their radius; from my own test games, one city per 15 land tiles seems to be a solid assumption.

As for the optimal number of cities ... IMO, one has to decide how many times bigger an empire should be allowed to grow compared to an average-sized one before corruption becomes rampant. Assuming a factor of 2, you'll get your original figures.