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pop levels pt1
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‎src/SUMMARY.md‎

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- [Towns](./towns.md)
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- [Ticks](./towns/ticks.md)
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- [Population](./towns/population.md)
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- [Consumption](./towns/population/consumption.md)
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- [Satisfaction](./towns/population/satisfaction.md)
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- [Levels](./towns/population/levels.md)
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- [Ware Prices](./towns/ware-prices.md)
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- [Base Price](./towns/ware-prices/base-price.md)
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- [Thresholds](./towns/ware-prices/thresholds.md)

‎src/towns/population.md‎

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# Population
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## Consumption
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The `do_population_consumption` function is at `0x00527D40`.
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At `0x00672860` there is a table that contains the daily consumptions for 100 citizens of every population type:
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|Ware|Rich|Wealthy|Poor|Beggars|
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|-|-|-|-|-|
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|Grain|90|120|150|120|
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|Meat|110|87|12|5|
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|Fish|40|80|100|110|
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|Beer|65|130|65|75|
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|Salt|1|1|1|1|
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|Honey|50|25|5|2|
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|Spices|4|2|2|0|
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|Wine|150|38|0|0|
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|Cloth|50|35|15|1|
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|Skins|60|30|0|0|
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|WhaleOil|50|35|10|0|
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|Timber|80|80|40|20|
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|IronGoods|100|75|25|0|
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|Leather|44|35|5|0|
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|Wool|10|40|20|5|
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|Pitch|0|0|0|0|
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|PigIron|0|0|0|0|
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|Hemp|5|3|2|3|
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|Pottery|30|18|12|1|
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|Bricks|1|1|0|0|
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|Sword|0|0|0|0|
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|Bow|0|0|0|0|
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|Crossbow|0|0|0|0|
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|Carbine|0|0|0|0|
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If a town is not under siege and a ware is in oversupply, more of it is consumed.
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**TODO clarify**
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**TODO pitch consumption (sieged and unsieged), winter/famine/plague modifiers**
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## Satisfaction
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P3's setting "Needs of the citizens" changes how easy it is to increase the satisfaction, and how fast it changes.
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The *satisfaction classes* are displayed in-game: *Very happy*, *happy*, *very satisfied*, *satisfied*, *dissatisfied*, and *annoyed*.
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The satisfaction for each population type is stored in the town's *satisfactions* array at offset `0x300`, holding an `i16` for every population type except Beggars.
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The function `prepare_citizens_menu_ui` at `0x0040B570` calculates the satisfaction classes by converting the `i16` into an `f32`, and picking the highest applicable class:
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|Satisfaction >|Satisfaction Class|
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|-|-|
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|29.5|Very Happy|
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|19.5|Happy|
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|9.5|Very Satisfied|
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|0.5|Satisfied|
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|-10.5|Dissatisfied|
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|-Infinity|Annoyed|
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The function `update_citizen_satisfaction` at `0x0051C830` calculates the *current satisfaction* each population type would have.
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The satisfaction is then increased or decreaseed by the respective *step size*, depending on whether it was bigger or smaller than the current satisfaction, but it won't go beneath -40 or above 80.
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At `0x006736AC` there is a table that contains for every difficulty the step sizes for increments and decrements to the satisfaction:
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|Needs Setting|Increment|Decrement|
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|-|-|-|
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|Low|3|1|
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|Normal|2|1|
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|High|1|2|
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|Unused|1|1|
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At `0x006736A0` there is a table that contains for every difficulty the *base satisfaction* for every population type:
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|Needs Setting|Rich|Wealthy|Poor|
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|-|-|-|-|
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|Low|-7|-12|-20|
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|Normal|-13|-18|-27|
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|High|-20|-25|-32|
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Within `update_citizen_satisfaction` 6 *situational modifiers* are implemented:
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|Situation|Impact|
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|-|-|
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|Siege|-10|
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|Pirate Attack|-8|
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|Plague|-10|
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|Blocked|-6|
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|Boycotted|-4|
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|Famine|-10|
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At `0x00672938` there is a table that defines *ware satisfaction weights* for every population type:
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|Ware|Rich|Wealthy|Poor|
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|-|-|-|-|
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|Grain|2|4|8|
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|Meat|5|4|4|
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|Fish|2|6|6|
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|Beer|2|6|6|
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|Salt|2|2|4|
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|Honey|3|2|0|
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|Spices|3|0|0|
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|Wine|5|2|0|
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|Cloth|5|4|0|
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|Skins|3|2|0|
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|WhaleOil|3|4|4|
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|Timber|3|4|6|
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|IronGoods|2|2|0|
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|Leather|2|2|4|
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|Wool|2|6|4|
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|Pitch|0|0|0|
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|PigIron|0|0|0|
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|Hemp|0|0|0|
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|Pottery|3|2|4|
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|Bricks|0|0|0|
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|Sword|0|0|0|
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|Bow|0|0|0|
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|Crossbow|0|0|0|
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|Carbine|0|0|0|
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The current satisfaction is calculated as follows:
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```
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def get_ware_satisfaction(ware_id, population_type):
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if wares[ware_id] >= 2 * weekly_consumption[ware_id]:
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return satisfaction_weights[population_type][ware_id]
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else:
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return (wares[ware_id] - weekly_consumption[ware_id])
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* satisfaction_weights[population_type][ware_id]
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// weekly_consumption[ware_id]
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current_satisfaction = 2 * (
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base_satisfaction
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+ situational_modifiers
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+ unknown_modifiers # 9 total, 8 capped at 4
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+ ware_satisfactions
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)
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```
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All things related to the population are handled during the town's tick call.
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The following subsections explain the identified functions.

‎src/towns/population/consumption.md‎

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# Consumption
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The `do_population_consumption` function is at `0x00527D40`.
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At `0x00672860` there is a table that contains the daily consumptions for 100 citizens of every population type:
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|Ware|Rich|Wealthy|Poor|Beggars|
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|-|-|-|-|-|
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|Grain|90|120|150|120|
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|Meat|110|87|12|5|
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|Fish|40|80|100|110|
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|Beer|65|130|65|75|
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|Salt|1|1|1|1|
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|Honey|50|25|5|2|
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|Spices|4|2|2|0|
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|Wine|150|38|0|0|
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|Cloth|50|35|15|1|
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|Skins|60|30|0|0|
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|WhaleOil|50|35|10|0|
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|Timber|80|80|40|20|
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|IronGoods|100|75|25|0|
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|Leather|44|35|5|0|
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|Wool|10|40|20|5|
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|Pitch|0|0|0|0|
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|PigIron|0|0|0|0|
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|Hemp|5|3|2|3|
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|Pottery|30|18|12|1|
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|Bricks|1|1|0|0|
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|Sword|0|0|0|0|
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|Bow|0|0|0|0|
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|Crossbow|0|0|0|0|
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|Carbine|0|0|0|0|
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If a town is not under siege and a ware is in oversupply, more of it is consumed.
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**TODO clarify**
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**TODO pitch consumption (sieged and unsieged), winter/famine/plague modifiers**

‎src/towns/population/levels.md‎

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# Levels
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The `town_update_population_levels` function at `0x0051C650` determines how many citizens are promoted and demoted and how many poor citizens emigrate.
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The following pseudocode denotes the calculation:
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```python
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class Town:
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citizens: list[int]
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satisfactions: list[int]
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has_mint: bool
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dwellings_capacity: list[int]
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def __init__(
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self,
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rich: int,
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wealthy: int,
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poor: int,
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satifsaction_rich: int,
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satisfaction_wealthy: int,
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satisfaction_poor: int,
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has_mint: bool = False,
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dwellings_capacity_rich: int = 999999,
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dwellings_capacity_wealthy: int = 999999,
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dwellings_capacity_poor: int = 999999,
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):
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self.citizens = [rich, wealthy, poor]
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self.satisfactions = [
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satifsaction_rich,
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satisfaction_wealthy,
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satisfaction_poor,
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]
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self.has_mint = has_mint
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self.dwellings_capacity = [
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dwellings_capacity_rich,
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dwellings_capacity_wealthy,
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dwellings_capacity_poor,
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]
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def update_population_levels(self):
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self.update_population_level(0)
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self.update_population_level(1)
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# TODO poor emigration
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def update_population_level(self, level: int):
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target = (
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self.citizens[2]
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* (self.satisfactions[level] + 40)
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// self.get_divisor(level)
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)
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target = min(max(target, 1), self.dwellings_capacity[level])
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LOGGER.debug(f"{level} target: {target} stock: {self.citizens[level]}")
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if target < self.citizens[level]:
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# Current stock exceeds target
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demoted = 2 * self.citizens[level] / target + 1
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if demoted > self.citizens[level]:
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demoted = self.citizens[level] - 1
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self.citizens[2] += demoted
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self.citizens[level] -= demoted
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else:
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# Target exceeds current stock
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if self.citizens[level]:
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promoted = 2 * target // self.citizens[level] + 1
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else:
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promoted = 1 # Avoid division by zero
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if self.citizens[2] > promoted:
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LOGGER.debug(f"promoting {promoted} poors to {level}")
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self.citizens[2] -= promoted
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self.citizens[level] += promoted
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def get_divisor(self, level):
70+
if level == 0:
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return 213 if self.has_mint else 320
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elif level == 1:
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return 160
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raise Exception()
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```
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For a fixed number of total inhabitants and satisfactions, the groups converge:
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![image](levels1.png)

‎src/towns/population/levels.py‎

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import logging
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from matplotlib import pyplot as plt
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from matplotlib.ticker import PercentFormatter
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import numpy as np
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import math
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import pytest
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LOGGER = logging.getLogger()
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logging.basicConfig()
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logging.getLogger().setLevel(logging.DEBUG)
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class Town:
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citizens: list[int]
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satisfactions: list[int]
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has_mint: bool
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dwellings_capacity: list[int]
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def __init__(
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self,
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rich: int,
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wealthy: int,
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poor: int,
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satifsaction_rich: int,
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satisfaction_wealthy: int,
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satisfaction_poor: int,
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has_mint: bool = False,
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dwellings_capacity_rich: int = 999999,
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dwellings_capacity_wealthy: int = 999999,
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dwellings_capacity_poor: int = 999999,
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):
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self.citizens = [rich, wealthy, poor]
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self.satisfactions = [
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satifsaction_rich,
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satisfaction_wealthy,
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satisfaction_poor,
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]
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self.has_mint = has_mint
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self.dwellings_capacity = [
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dwellings_capacity_rich,
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dwellings_capacity_wealthy,
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dwellings_capacity_poor,
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]
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def get_divisor(self, level):
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if level == 0:
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return 213 if self.has_mint else 320
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elif level == 1:
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return 160
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raise Exception()
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def update_population_levels(self):
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self.update_population_level(0)
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self.update_population_level(1)
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def update_population_level(self, level: int):
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target = (
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self.citizens[2]
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* (self.satisfactions[level] + 40)
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// self.get_divisor(level)
61+
)
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target = min(max(target, 1), self.dwellings_capacity[level])
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LOGGER.debug(f"{level} target: {target} stock: {self.citizens[level]}")
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if target < self.citizens[level]:
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# Current stock exceeds target
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demoted = 2 * self.citizens[level] / target + 1
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if demoted > self.citizens[level]:
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demoted = self.citizens[level] - 1
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self.citizens[2] += demoted
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self.citizens[level] -= demoted
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else:
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# Target exceeds current stock
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if self.citizens[level]:
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promoted = 2 * target // self.citizens[level] + 1
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else:
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promoted = 1 # Avoid division by zero
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if self.citizens[2] > promoted:
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LOGGER.debug(f"promoting {promoted} poors to {level}")
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self.citizens[2] -= promoted
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self.citizens[level] += promoted
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def plot_example1():
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plt.clf()
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labels = ["Rich", "Wealthy", "Poor"]
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fig, (axs) = plt.subplots(1, 4, sharey="all", sharex="all", figsize=(10, 4))
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plot_example1_subplot(axs[0], 5, False)
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plot_example1_subplot(axs[1], 5, True)
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plot_example1_subplot(axs[2], 80, False)
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plot_example1_subplot(axs[3], 80, True)
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ax2 = axs[-1].twinx()
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ax2.set_ylim(*axs[-1].get_ylim())
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ax2.yaxis.set_major_formatter(PercentFormatter(1000))
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fig.suptitle("Convergence of 1000 Inhabitants")
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fig.legend(
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labels,
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bbox_to_anchor=(1, 1),
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loc="upper left",
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# bbox_transform=plt.gcf().transFigure,
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)
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plt.tight_layout()
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plt.savefig("levels1.png", dpi=100, bbox_inches="tight")
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def plot_example1_subplot(ax, satisfaction: int, has_mint: bool):
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ax.grid(axis="y")
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town = Town(50, 50, 900, satisfaction, satisfaction, satisfaction, has_mint)
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x = []
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sat_y_rich = []
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sat_y_wealthy = []
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sat_y_poor = []
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for i in range(0, 10):
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town.update_population_levels()
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for i in range(0, 60):
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x.append(i)
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sat_y_poor.append(town.citizens[2])
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sat_y_wealthy.append(town.citizens[1])
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sat_y_rich.append(town.citizens[0])
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town.update_population_levels()
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ax.plot(x, sat_y_rich, label="Rich")
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ax.plot(x, sat_y_wealthy, label="Wealthy")
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ax.plot(x, sat_y_poor, label="Poor")
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ax.set_title(f"{satisfaction} Satisfaction {"(Mint)" if has_mint else "(no Mint)"}")
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def plot_example2():
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pass
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plot_example1()
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plot_example2()

‎src/towns/population/levels1.png‎

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