Ulti_mecia
Chieftain
25 percent increase
The Number Crunching Thread
- Thread starter alpaca
- Start date
25 percent increase
That's not much and somewhat of a disappointment. Certainly will not change the numbers much.
alpaca
King of Ungulates
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Yeah it has little influence. The +25% increase is applied to excess food only so to fit it into the analysis, just multiply the whole food formula by 1.25. Hospitals work slightly differently but you can get a good approximation by simply halving g (it's not quite perfect because what you will actually keep when going to level n+1 is g(n)/2, not g(n+1)/2)
Yes, you're right - in my example, if you're getting just 1 culture per city and no city states, that's an abysmally slow speed, so I suppose it does make intuitive sense that any additional culture from a new city would help speed it up.
Ulti_mecia
Chieftain
Basically yes, if you invest (the correct amount can be found throughout this thread 
)
@ alpaca,
I was thinking the same thing about the WLTKD, but I wasn't sure anymore.
Can we assume the same goes for the Floating Gardens bonus then ?
)@ alpaca,
I was thinking the same thing about the WLTKD, but I wasn't sure anymore.
Can we assume the same goes for the Floating Gardens bonus then ?
Bibor
Doomsday Machine
To answer your original question Bibor: Short term you'll have very little impact in SP pace. However if you don't keep up with the increases per SP level, you'll eventually start lagging.
(Pretty hard to translate numbers in my head to something clear for other people to understand, thank god I'm not a teacher
You mean:
Napoleon only takes care of the "number of cities inflation" part of policy prices and you still need buildings to counter the "number of policies inflation".
Bibor
Doomsday Machine
Basically yes, if you invest (the correct amount can be found throughout this thread
@ alpaca,
I was thinking the same thing about the WLTKD, but I wasn't sure anymore.
Can we assume the same goes for the Floating Gardens bonus then ?
Floating gardens are amazing as long as you have a lake(s) around and pretty good as long as you want your city to actually grow. It also costs just 1 not 2 GPT, compared to the building it replaces. It's also ridiculous if you have a 4-5 hex lake that you can put your city near to.
However, I realised painfully that a Lighthouse does not improve lake food as it used to in CIV4.
Ulti_mecia
Chieftain
At least they added the extremely handy Seaports now.
As a small point in favor of the Lighthouse: it increases The Great Barrier Reef tiles with 1 food
Absolutely correct.
As a small point in favor of the Lighthouse: it increases The Great Barrier Reef tiles with 1 food
Absolutely correct.
alpaca
King of Ungulates
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Basically yes, if you invest (the correct amount can be found throughout this thread
@ alpaca,
I was thinking the same thing about the WLTKD, but I wasn't sure anymore.
Can we assume the same goes for the Floating Gardens bonus then ?
I don't know, I never played the Aztecs yet. However, if that is the case the floating gardens are very lame compared to a watermill because 15% of your growth will rarely even match a flat +2 food per turn (would require a food surplus > 13)
I noticed today that when you conquer a city, nT gets reset to 0. I have no idea what happens on re-conquest though.
Ulti_mecia
Chieftain
Wow, just noticed a huge oversight on my part: representation isn't "+1 culture to all cities connected to the capital"; but instead "+1 culture per city". This makes it slightly better than I thought as it applies both instantly and to the capital as well
"Assumptions are the mother of all-ups". I assumed it was, and therefore was wrong
"Assumptions are the mother of all
-ups". I assumed it was, and therefore was wrong
alpaca
King of Ungulates
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The same. Quite stupid if you ask me. I'm ok with the city keeping the tiles but afterwards the growth speed is fairly high. Of course, all cultural buildings are razed on conquest.
alpaca
King of Ungulates
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Unit Maintenance
Unit maintenance is calculated as follows:
c(t,n) = ((j n)//100 (1 + 2t m/1000))^(1 + 2t/(1000*d))
where n = number of units and t = number of turns. // denotes an integer division. j, m and d are constants from GlobalDefines.xml, j = INITIAL_GOLD_PER_UNIT_TIMES_100, m = UNIT_MAINTENANCE_GAME_MULTIPLIER, d = UNIT_MAINTENANCE_GAME_EXPONENT_DIVISOR
With the vanilla settings, the formula then is
c(t,n) = floor(floor(0.5 n) (1 + 16/1000 t))^(1 + 2/7000 t))
Since there's no easy "each unit in turn t will cost this much" here's a table you can use as a rough reference. The first row is the number of turns, the first column the number of units
Here's an equivalent table detailing the cost per unit
Edit: Small caveat, I still have to check if the game floors or rounds the values after calculating the function.
Edit2: Ok, the game floors so I updated the tables
Unit maintenance is calculated as follows:
c(t,n) = ((j n)//100 (1 + 2t m/1000))^(1 + 2t/(1000*d))
where n = number of units and t = number of turns. // denotes an integer division. j, m and d are constants from GlobalDefines.xml, j = INITIAL_GOLD_PER_UNIT_TIMES_100, m = UNIT_MAINTENANCE_GAME_MULTIPLIER, d = UNIT_MAINTENANCE_GAME_EXPONENT_DIVISOR
With the vanilla settings, the formula then is
c(t,n) = floor(floor(0.5 n) (1 + 16/1000 t))^(1 + 2/7000 t))
Since there's no easy "each unit in turn t will cost this much" here's a table you can use as a rough reference. The first row is the number of turns, the first column the number of units
Code:
Turns
Units 1 20 50 100 150 200 250 300 350 400
4 2 2 3 5 7 9 11 14 17 20
8 4 5 7 11 15 19 24 30 36 43
12 6 8 11 16 23 30 38 47 57 68
16 8 10 14 22 31 41 52 64 78 94
20 10 13 18 28 39 52 66 82 100 121
24 12 16 22 34 47 63 80 100 122 148
28 14 18 26 40 56 74 94 118 145 176
32 16 21 30 46 64 85 109 136 168 204
36 18 24 34 52 73 96 124 155 191 232
40 20 26 37 58 81 108 138 174 215 261
44 22 29 41 64 89 119 153 193 238 291
48 24 32 45 70 98 131 168 212 262 321
52 26 35 49 76 107 142 184 231 287 350
56 28 37 53 82 115 154 199 251 311 381
60 30 40 57 88 124 166 214 270 335 411
64 32 43 61 94 133 177 229 290 360 442
68 34 45 64 100 141 189 245 310 385 473
72 36 48 68 106 150 201 260 330 410 504
76 38 51 72 112 159 213 276 349 435 535
80 40 54 76 118 167 225 292 370 461 567
84 42 56 80 124 176 237 307 390 486 598
88 44 59 84 130 185 249 323 410 512 630
92 46 62 88 137 194 260 339 430 537 662
96 48 64 92 143 203 273 354 451 563 694
100 50 67 95 149 211 285 370 471 589 727Here's an equivalent table detailing the cost per unit
Code:
Turns
Units 1 20 50 100 150 200 250 300 350 400
4 0.50 0.50 0.75 1.3 1.8 2.3 2.8 3.5 4.3 5.0
8 0.50 0.63 0.88 1.4 1.9 2.4 3.0 3.8 4.5 5.4
12 0.50 0.67 0.92 1.3 1.9 2.5 3.2 3.9 4.8 5.7
16 0.50 0.63 0.88 1.4 1.9 2.6 3.3 4.0 4.9 5.9
20 0.50 0.65 0.90 1.4 2.0 2.6 3.3 4.1 5.0 6.1
24 0.50 0.67 0.92 1.4 2.0 2.6 3.3 4.2 5.1 6.2
28 0.50 0.64 0.93 1.4 2.0 2.6 3.4 4.2 5.2 6.3
32 0.50 0.66 0.94 1.4 2.0 2.7 3.4 4.3 5.3 6.4
36 0.50 0.67 0.94 1.4 2.0 2.7 3.4 4.3 5.3 6.4
40 0.50 0.65 0.93 1.5 2.0 2.7 3.5 4.4 5.4 6.5
44 0.50 0.66 0.93 1.5 2.0 2.7 3.5 4.4 5.4 6.6
48 0.50 0.67 0.94 1.5 2.0 2.7 3.5 4.4 5.5 6.7
52 0.50 0.67 0.94 1.5 2.1 2.7 3.5 4.4 5.5 6.7
56 0.50 0.66 0.95 1.5 2.1 2.8 3.6 4.5 5.6 6.8
60 0.50 0.67 0.95 1.5 2.1 2.8 3.6 4.5 5.6 6.9
64 0.50 0.67 0.95 1.5 2.1 2.8 3.6 4.5 5.6 6.9
68 0.50 0.66 0.94 1.5 2.1 2.8 3.6 4.6 5.7 7.0
72 0.50 0.67 0.94 1.5 2.1 2.8 3.6 4.6 5.7 7.0
76 0.50 0.67 0.95 1.5 2.1 2.8 3.6 4.6 5.7 7.0
80 0.50 0.68 0.95 1.5 2.1 2.8 3.7 4.6 5.8 7.1
84 0.50 0.67 0.95 1.5 2.1 2.8 3.7 4.6 5.8 7.1
88 0.50 0.67 0.95 1.5 2.1 2.8 3.7 4.7 5.8 7.2
92 0.50 0.67 0.96 1.5 2.1 2.8 3.7 4.7 5.8 7.2
96 0.50 0.67 0.96 1.5 2.1 2.8 3.7 4.7 5.9 7.2
100 0.50 0.67 0.95 1.5 2.1 2.9 3.7 4.7 5.9 7.3Edit: Small caveat, I still have to check if the game floors or rounds the values after calculating the function.
Edit2: Ok, the game floors so I updated the tables
KrikkitTwo
Immortal
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Does that include 'gold bought tiles'?
and what is the formula for the cost of those tiles?
alpaca
King of Ungulates
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No, gold tiles don't increase culture-cost, but the reverse is true. As far as I know, every tile the city has in excess of it's inner ring adds 5 to the gold buy cost for the next tile, no matter whether it was claimed by culture or bought. I don't know how the base cost is calculated, but it seems like flat terrain and the tiles your city would culturally claim next are cheaper than hills and forests.
ccubed
Chieftain
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Disclaimer: I'm horrible at math and have next to zero skill with spreadsheets.
That said, I was wondering if anyone could put some of these calculations together into spreadsheets for relative ease of use to calculate some of the costs. I'm specifically thinking about something where you could input or just cross-reference the number of social policies you have with the number of cities you have founded/annexed to determine when you'll next be getting an additional SP.
I usually hold off for quite awhile to get Renaissance and Industrial age SPs, but I'm never quite sure how many I'll be able to get all at once when I qualify. I'd love to just type in 2 purchased SPs and 5 cities and get a number. Is that possible?
That said, I was wondering if anyone could put some of these calculations together into spreadsheets for relative ease of use to calculate some of the costs. I'm specifically thinking about something where you could input or just cross-reference the number of social policies you have with the number of cities you have founded/annexed to determine when you'll next be getting an additional SP.
I usually hold off for quite awhile to get Renaissance and Industrial age SPs, but I'm never quite sure how many I'll be able to get all at once when I qualify. I'd love to just type in 2 purchased SPs and 5 cities and get a number. Is that possible?
Alpaca, are you sure the unit maintenance tables correspond to the current formula listed? Shouldn't the total cost go up linearly with the amount of units, with just a +-1 for rounding as the number of units is only included as a final multiplier? Instead, looking at, say, the turn 300 column at 20 unit intervals, the cost goes up by 82, 92, 96, 100, 101. Quickly checking with a calculator I get ~67.432 per 20 units from the formula listed (0.5n=10).
Ceterum censeo, this is a horribly kludgy way of defining unit maintenance costs. It's the only thing in game affected by inflation, and if it's supposed to model more modern units requiring more maintenance, that would be better done by raising the costs either by the amount of techs or defining it separately for each unit type.
Ceterum censeo, this is a horribly kludgy way of defining unit maintenance costs. It's the only thing in game affected by inflation, and if it's supposed to model more modern units requiring more maintenance, that would be better done by raising the costs either by the amount of techs or defining it separately for each unit type.
alpaca
King of Ungulates
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No, it doesn't increase linearly in the amount of units. The formula for a fixed number of turns is c = k*n^k' where k and k'>1 are constants for each turn. This means the formula increases in a higher-than-linear fashion with the number of units, the more strongly the further you are in the timeline. For turn 300, k' = 1.085 approximately so if you go to high unit number you'll definitely notice the non-linearity. The tables were created using the formula, by the way, they are not in-game values. I think they match, but didn't check a huge number of them (instead, I conducted controlled experiments to figure out the parameters).
I agree that this solution for maintenance isn't great.
Ah yes, just noticed that it's (n*k)^(k') , not (n)*(k^k') as I first read.
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