Non riverside cottages supported by HR, are they worth it? After analyzing Unconquered Sun's posts in CE vs SE war this question popped into my head. I decided to work it out and post it here to see if my math was right.
Important info:
Citizen cost is going to be 2 GPT, which I think is right at Deity, 2 GPT adds up for the civics: bureaucracy, HR, slavery, decentralization, and paganism. HR supported and unit cost added. On Deity you don't get many free units so I think it is appropriate.
According to Unconquered Sun, every 10 turns, roughly all production is devalued by 10%. I haven't seen any better value for devaluement, so I'm going to take this even though it says production, since I'm pretty sure it's the same for commerce.
Spoiler will have the math for epic speed, normal is coming soon
Spoiler:
Turn 1 of cottage: -1 BPT (1-2=-1)
Turn 2- 15: -1 BPT (1-2=-1)
Total loss adjusted for devaluing: -14.5 Beakers (turn 1-10: -1x10=-10)(turn 11-15: 1-10%=.9. .9x5=4.5)
Turn 16-45: breaks even
Loss: 0 Beakers
Total loss adjusted for devaluing: -14.5 Beakers
Turn 46: +1 BPT
Turns 47-105: +1BPT
Gain from 46-50 adjusted for devaluing: 3.2805 Beakers (.9-10%=.81. .81-10%=.729. .729-10%=.6561. .6561x5=3.2805)
Gain from 51-60 adjusted for devaluing: 5.9049 (.6561-10%=.59049. .59049x10=5.9049)
Gain from 61-70 adjusted for devaluing: 5.31441(.54049-10%=.531441. .531441x10=5.31441)
Gain from turn 71 adjusted for devaluing: .4782969 (.531441-10%=.4782969)
Add these all together and we get 14.9781069. Since that is over 14.5 we have just made a profit
Conclusion: It takes 71 turns for a non riverside cottage to make a profit on deity with HR supported unit upkeep citizen, which is appropriate for Deity.
Normal Speed calculations
Spoiler:
Turn 1: -1 BPT(1-2=0)
Turns 2-10: -1BPT(1-2=0)
Total Loss including devaluing: 10 Beakers
Turn 11: 0BPT (2-2=0)
Turns 12-30: 0BPT 92-2=0)
Loss: 0
Total loss including devaluing: 10 Beakers
Turn 31: +1BPT (3-2=1)
Turns 32-70: +1 BPT (3-2=1)
Total gain for 31 to 40 including devaluing: 8.1 Beakers (1-10%=.9. .9-10%=.81. .81x10=8.1)
Total loss including devaluing: 1.9
Gain from 41 including devaluing: .729 (.81-10%=.729)
Gain for turns 42 and 43 including devaluing: 1.458 (.729x2=1.458)
Total loss: -0.287
Conclusion: Non riverside cottage takes 43 turns to make a profit
Turn 1: +2 BPT/GPT (4-2=2)
Turns 2-10: +2BPT/GPT (4-2=2)
Total gain: 20 Beakers/gold
Total lead vs Non riverside cottages: 30 Beakers
Total lead before lead stops growing, before printing press, included devaluing: 119.0460482 beakers (30+22.5+14.58+6.561+3.2805+5.9049+5.31441+4.782969+4.3046721+3.87420489+1.743392201)
Note: Without printing press, cottages can never catch up in commerce sense.
2 gpt/citizen come from HR supported citizen.
Basically that mean city cost/citizen + civic cost/citizen - cost of free units citizen provided ~ 1 gpt.
If city need additional garnison, which would cost 1 gp/turn then cost become 2.
With inflation (compensated by commerce/gold conversion improvement) this number stay approximately same for game. So if you use raw commerce against that number you will be right most of the time.
The other consideration is alternative use of that pop. Sometimes, there isn't much for a long time and it's cottage or unimproved forest ---> cottage wins that soundly. Cottages are not inherently bad, and are sometimes your best option, but the trick is recognizing when the are not your best option and using something else.
And inflation isn't a big factor, because he's racing for an advantage by ~150. Deity doesn't have dramatically increased inflation, it just doesn't have the 5% per level discount (though I have to check this).
When a set of civics is chosen, then the upkeep cost is largely determined by the size of your empire: the number of cities in your empire (M) and the total size of your population (N). Also the organized trait (O) and the difficulty level (D) will have a large effect on the final upkeep cost.
Government civics upkeep:
[D * [ O * ( [ P * (N-8) ] + [ C * (M-1) ] ) ] ]
Legal civics upkeep:
[D * [ O * ( [ P * (N-9) ] + [ C * M ] ) ] ]
Labor civics upkeep:
[D * [ O * ( [ P * (N-10) ] + [ C * (M+1) ] ) ] ]
Economy civics upkeep:
[D * [ O * ( [ P * (N-11) ] + [ C * (M+2) ] ) ] ]
Religion civics upkeep:
[D * [ O * ( [ P * (N-12) ] + [ C * (M+3) ] ) ] ]
In civilization 4 version 1.52, the variable C is equal to 0 for civics with no upkeep cost, 0.4 for civics with low upkeep cost, 0.5 for civics with medium upkeep cost and 0.6 for civics with high upkeep cost.
The variable O is 1/2 if your civilization is organized and 1 if your civilization is not organized. The difficulty level modifier for the human player is 1 at deity, immortal or emperor level, 0.95 at monarch level, 0.9 at prince level, 0.8 at noble level, 0.7 at warlord level, 0.6 at chieftain level and finally 0.5 at settler level.
In civilization 4 version 1.52, the variable P is equal to 0 for civics with no upkeep cost, 0.08 for civics with low upkeep cost, 0.12 for civics with medium upkeep cost and 0.16 for civics with high upkeep cost.
In summary, civic upkeep will increase by population by a factor of D*O*P=P on deity, no organized. In civilization 4 version 1.52, the variable P is equal to 0 for civics with no upkeep cost, 0.08 for civics with low upkeep cost, 0.12 for civics with medium upkeep cost and 0.16 for civics with high upkeep cost.
Bureaucracy is high, slavery/caste is medium, paganism/hr is low, so
each population will increase civic upkeep by .16+.12+.08x3=0.52. Of course you may not have bureaucracy until past turn 100, so it's going to range from 0.44 to 0.52
unit cost past cap is 1 gold for 2 units, so each pop is 0.94 to 1.02 gold per turn.
However we left out number of cities maintenance, which increases by population.
Here it is: http://forums.civfanatics.com/showpost.php?p=8500783&postcount=13
MAX_DISTANCE_CITY_MAINTENANCE * DISTANCE_TO_NEAREST_CAPITAL * ((CITY_POPULATION + 7) / 10) * WORLD_MODIFIER * DIFFICULTY_MODIFIER * CIVIC_MODIFIER / MAX_DISTANCE
or for standard maps, deity
# city maintenance for all cities = N*((Total Pop+17*N)*WorldSize_m*Handicap_m/18+1/2)
Distance maintenance = Difficulty*Distance*(Pop+7)/29 for standard map
so increasing pop by 1 in some city increases maintenance by
N*.3/18+Distance/29=number of cities/60+distance/29
Inflation
C:\Program Files\Firaxis Games\Sid Meier's Civilization 4\Beyond the Sword\Assets\XML\GameInfo
<iInflationPercent>30</iInflationPercent>
<iInflationOffset>-90</iInflationOffset>
<iInflationPercent></iInflationPercent> The rate at which upkeep increases.
<iInflationOffset></iInflationOffset> How long before upkeep increases.
Inflation %=(Game Turn-Offset) x Difficulty Factor
Inflation cost=Other Costs x Inflation %
So the first 90 turns, no inflation.
Modified Turn = (Turn – Inflation Offset)
Rate = Inflation Percent * Handicap Percent * Modifier
RP = (Modified Turn * Rate / 100) + [Modified Turn * (Modified Turn - 1)* Rate * Rate / 2000000]
At turn 190 turns, it will increase by roughly 30+90*89*30/2000000=30 %
At turn 100, it will be 3%, 110, 6%, 120, 9%, and at turn 150 18%.
Since we're caring before turn 150, I would roughly estimate inflation at 5-10% for the time periods in question.
So the total cost per population growth is
(0.44 to 0.52 (civic) + distance / 29 + 0.5 (HR past the free unit)) x (1 to 1.18)
So it can range from 0.44 (capital, no bureaucracy, free unit/happiness)
to say for a city 10 away
(0.52+0.34+0.5)x1.18 = 1.6 (city 10 away, no courthouse, bureaucracy, using hr past free units, turn 150)
@StopStopp
That post he talked about was basically a discussion of whether to use HR to grow one more pop and work a cottage. But good work on analysing, although the 15 turns thing... well I play normal :\. So -2gpt including unit upkeep would be about right, but you'd have also include cost of building the unit.
Oops, I forgot cottages were scaled by speed, sorry about that. I'll make a separate spoiler for normal, then marathon. And I edited the post to include it is HR supported.
@Damprain
One thing at a time, I don't want to analyze every little thing yet, my understanding of the game doesn't go that far, yet.
Oops, I forgot cottages were scaled by speed, sorry about that. I'll make a separate spoiler for normal, then marathon. And I edited the post to include it is HR supported.
@Damprain
One thing at a time, I don't want to analyze every little thing yet, my understanding of the game doesn't go that far, yet.
The basic point is that your figure of 2 GPT per extra pop was too high, even when considering the variables. This difference greatly skews the end results of the calculations.
One other use for cottages is not only the commerce they provide, but also the growth toward Towns. At Village and Town status, they have some signficant gains:
Village:
+1 commerce with Printing Press
Town:
+1 commerce with Printing Press
+2 commerce with Free Speech
+1 production with Universal Suffrage
If you know you can easily go from cottages to towns within the relevant timeframe, it's a no-brainer that even non-riverside cottages are worth developing. The trick is in deciding when these situations are at hand. The amount of variability between a 1-commerce cottage and a 7-commerce/1-hammer town is incredible, that it can easily overshadow the amount of initial investment you put into it the first several turns.
My analysis is seeing whether HR supported non riverside cottages (mainly on deity, because the amount of free units is so low) are better than the different alternatives you get early game using HR. The bonuses you get late game shouldn't be ignored in your consideration to build cottages, but whether the late game bonuses are worth the early game alternatives like specialists or hills, both which early game beat non riverside cottages.
This must be wrong: more pop increase the free unit limit, lowering total costs. The additional pop should subtract 0.5 for "HR past the free unit", not add it.
So it can range from 0.44 (capital, no bureaucracy, free unit/happiness)
to say for a city 10 away
(0.52+0.34+0.5)x1.18 = 1.6 (city 10 away, no courthouse, bureaucracy, using hr past free units, turn 150)
This must be wrong: more pop increase the free unit limit, lowering total costs. The additional pop should subtract 0.5 for "HR past the free unit", not add it.
Not exactly...a higher population gives you more free units, but not at the rate required to pay for the extra upkeep of more units for HR.
In fact, the rate of increase for free units is small enough compared to the rate of increase in upkeep needed for HR, that the original numbers are still closer to the actual, even when considering the increase of free units from higher population.
wait...why is it 1 gold for 2 units, and not 1 unit?
So the total cost per population growth is
(0.44 to 0.52 (civic) + distance / 29 + 0.5 (HR past the free unit)) x (1 to 1.18)
So it can range from 0.44 (capital, no bureaucracy, free unit/happiness)
to say for a city 10 away
(0.52+0.34+0.5)x1.18 = 1.6 (city 10 away, no courthouse, bureaucracy, using hr past free units, turn 150)
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