KrikkitTwo
Immortal
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- Apr 3, 2004
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Waiting for the Unit Maintenance
You were assuming normal speed, normal size or smaller, prince+ difficulty for your first formula for pb, right?
Yes, I wasn't aware that the culture costs changed with map sizes and such until somebody pointed it out to me, but you can find the analysis with variables a little further down and the rest of the culture part is done with the variable version.
Will expanding increase or decrease policy speed?
This is the question Paeanblack and I discussed in said thread. To analyse this, we have to calculate the number of turns to the next policy and see how it's affected by going from n->n+1.
When we do the city number increase, both p and c change. Let p and c be the policy cost and culture yield before founding the new city and p' and c' be the respective numbers after the founding.
p' = pb (1 + pm n) = p + pm pb
c' = (n + 1) cT + cC = c + cT
Then calculate t' and check when it gets smaller than t (this would signify an increased policy speed)
t' = p'/c' = (1 + pm n) / (cT n + cT + cC) < (1 + pm n - pm)) / (cT n + cC)
(1 + pm n) (cT n + cC) < (1 + pm n) (cT n + cC) + (1 + pm n) cT - pm (cT n + cT + cC)
pm cT n + pm cT + pm cC < cT + pm n cT
pm (cT + cC) < cT
rC := cC/cT < 1/pm - 1 = (1 - pm)/pm
Interesting...
This is a pretty counterintuitive result. It means that, if you're getting zero culture from city states, then ANY increase in cities will reduce your time between policies, as long as cT is fixed. For example, even if all of your cities produce only 1 culture, adding a city will decrease your time, as long as the new city produces at least one culture and you're getting no culture from CSes.
[That's because cT is always positive, and pm is always greater than 0 and less than 1, so 1/pm > 1.]
Desired Pace
5 10 15 20 25 30
Policy Nr Base Cost
1 25 2 1 0.7 0.5 0.4 0.3
2 45 3 1.5 1 0.8 0.6 0.5
3 95 5 2.5 1.7 1.3 1 0.8
4 160 10 5 3.3 2.5 2 1.7
5 245 15 7.5 [B]5[/B] 3.8 3 2.5
6 350 21 10.5 7 5.3 4.2 3.5
7 465 28 14 9.3 7 5.6 4.7
8 600 36 18 12 [B]9[/B] 7.2 6
9 745 45 22.5 15 11.3 9 7.5
10 905 55 27.5 18.3 13.8 11 9.2
11 1080 65 32.5 21.7 16.3 13 10.8
12 1265 76 38 25.3 19 15.2 12.7
13 1460 88 44 29.3 22 17.6 14.7
14 1670 100 50 33.3 25 20 16.7
15 1890 114 57 38 28.5 22.8 19
16 2125 128 64 42.7 32 25.6 21.3
17 2370 142 71 47.3 35.5 28.4 23.7
18 2625 157 78.5 52.3 39.3 31.4 26.2
19 2890 173 86.5 57.7 43.3 34.6 28.8
20 3165 189 94.5 63 47.3 37.8 31.5
So dt/dn < 0 when cC/cT < 1/pm - 1, the same condition that alpaca found. I feel like the fact that we find the same condition using different methods means it's right, assuming the original functions are right.
Thanks a ton for the update. Reading that I think it seems reasonable to say that early granaries are somewhat viable for games where having cities with strong early production/income/early GS matters more than lategame city growth (but you do still want some city development through turns 50-150, say) - though it's also an option to skip granaries and focus on working more food tiles if you want to put the production into immediate military. Would you agree with that assessment?
(Misc. note: I guess they're bad in the capital whatever if you have at least one maritime state.)
Again - thanks for your time.
I'm glad you like it but you're giving me more credit than I deserve: I copied most of the basic formulas from other people and merely checked that they were correct. As I stated, the culture analysis was a kind of a joint work with Paeanblack in a Songhai-related thread where I wanted to argue that the Mud Pyramid Mosque is awesome. It doesn't directly relate to ICS, I had the idea of trying an ICS strategy in the demo, although back then I planned to base it on the Egyptian Burial Tomb.
Your table does not directly pertain to new cities, by the way, but to any city in your empire. To not slow your policy speed over time you have to increase the amount of culture your empire generates, obviously. It shows some of the deficiencies of my approach, however, because building the city up to high standards takes quite a lot of time.
SP Pace: 5 10 15 20 25 30
Policy: 1 2 1 0.7 0.5 0.4 0.3
2 3 1.5 1 0.8 0.6 0.5
3 5 2.5 1.7 1.3 1 0.8
4 10 5 3.3 [B][U]2.5[/U][/B] 2 1.7
Please do clarify, Napoleon with his +2 culture per city accompanied with +1 culture per city from Representation will see no hit in policy gain speed from the moment the cities are founded?
Well, let's dig in the table and find out
Napoleon's Representation cities generate 3gpt. Representation implies you already have at least 3 policies down (Liberty-Citizenship-representation) so you're at policy nr 4.
Code:SP Pace: 5 10 15 20 25 30 Policy: 1 2 1 0.7 0.5 0.4 0.3 2 3 1.5 1 0.8 0.6 0.5 3 5 2.5 1.7 1.3 1 0.8 4 10 5 3.3 [B][U]2.5[/U][/B] 2 1.7
Let's assume you have only Paris and want to expand. Paris has a monument so we're generating 1 (Palace) + 2 (UA) + 2 (Monument) = 5 cpt.
Our next policy costs 160 culture, so that's a pace of 18. To keep up with that you'd need to get 2.5 cpt in the new city to keep the pace. It might in fact even speed you up, as 3 is pretty close to a pace of 16-17 (Pace 15 value is 3.3 )
So yea, as I grudgingly mentioned before, France comes out good in this
I'd say you can expand very aggresivelly with France, and not be SPless. Add a monument and you'll be at 5cpt which will support bearable progress even upto the 7th SP; which is Theocracy (In ICS at least it should be: last game I went from -1 to +11 Happy from Theocracy alone)
(I'm actually at work, so I can't readily verify wether or not Representation also adds 1 culture to the capital, so I assumed it didn't - as per the logic it shouldn't "gains +1cpt for every city connected to the capital". Unless a capital can be connected to itself... )
Base 5 10 15 20 25 30
Policy: 1 25 2 1 0.7 0.5 0.4 0.3 Liberty
2 45 3 1.5 1 0.8 0.6 0.5 Citizenship
3 95 5 2.5 1.7 1.3 1 0.8 Meritocracy
4 160 10 5 3.3 2.5 2 1.7 Representation
5 245 15 7.5 5 3.8 3 2.5 Piety
6 350 21 10.5 7 5.3 4.2 3.5 Organised Religion
7 465 28 14 9.3 7 5.6 4.7 Theocracy
8 600 36 18 12 9 7.2 6 Order
9 745 45 22.5 15 11.3 9 7.5 Building upkeep one
10 905 55 27.5 18.3 13.8 11 9.2 Planned economy