Math in Banished – Maximum Population

enfo131 posted a 4000+ population reddit yet I think some of the popular models/conclusions might be wrong so I decide to write this paper.

The majority of this paper is based on theory and is yet to be testified.

The game is so time consuming that I don't even know if I'll be able to test my theory.

Trader mechanics

According to pollackey 2, 5 types of merchants visit randomly every 6 months if dismissed immediately. Otherwise traders stay at the dock for an additional 3 months, making the interval 9 months in total.

Towns with population greater than 150 have fully developed merchants.

firewood or ale?

Several limitations of the game:

  • a finite number of trading posts
  • finite land capacity, thus finite production rate
  • ...

Generally one want to maximize the production rate while can still convert these production to useful / correct mixture of resources.

A typical citizen use the following resources per year, observed from a late game of no trading.

  • 0.175 tool @12
  • 5.65 fuel @4
  • 100 food @1
  • 0.35 clothes @25

in total, 133.45 production is required for each citizen.

A general goods merchant can carry 20 \times 200 logs or 20 \times 2000 food (400 people) on request.

A resource merchant can carry 5 \times 200 logs (707 people), or 5 \times 100 tools (2857 people), or 5 \times 50 clothes (714 people) on request, or 5 \times 100 wool (1428 people) roughly 1:4:1:2.

A food merchant can carry 15 \times 2000 food on request.

One has several choices on deciding firewood or ale.

5000 firewood solution

All capacity of general goods merchant and resource mechant goes to logs. This create 5000/2.5 = 2000 logs import, or an 8000 annual firewood export. Later we will find that, even at maximum capacity, the production of firewood is still quite low.

8000 export requires >10 wood cutters, and 5000 \times 11/2.5/2/250 = 44 sq stockpile per trading post.

40000 food, 30000 ale resource, firewood, steel tools, and wool

All capacity of general goods merchant goes to beans (vegatable), wheat(grain), and chestnut(meat), amount for 40000 food per boat.

All capacity of food merchat goes to apple (for ale), amount for 30000 per boat.

This is a calculated move, as 30000 apple produces 10000 ale, or 80000 production, just more than the 70000 cost. Besides, one need something else to buy from the resource merchant, and may take the risk that citizens took apple as food (maybe produce more apple from orchard to cover this lost).

Capacity of the resource merchant... well it's complicated. For 7 posts, we want 4 on logs, 2 on wool, and 1 on tools, to provide just enough for 2800 people. If you buy clothes directly, this would not be enough.

In actual production, for each post, total anunal cost is

(40000 + 30000 + (2000 \times 4+2500 \times 2+6000)/7)/2.5 = 29086, or 3636 ale.

We need 11 tavens(!), 2 wood cutter, 2 tailor for each post, and storage space (40000 + 30000 + (500 \times 10 \times 2+500 \times 10)/7)/2.5/2 = 14428 roughly 2.5 storage barns, and 1000 \times 11/2.5/2/250=8.8 sq stockpile.

Direct total labor cost is 11(brewers)+2(wood cutters)+2(tailors)+n(vendors)=15+n, and they can serve 2800 people!

With a map of 75 trading posts, this could be 210000 people from trading only.

Then it comes to the problem, that 512 \times 512/20, one can only have 13107.2 houses. Then, the problem become clear, that the maximum population is not trade bottlenecked, it's land bottlenecked.

I lose interest of the game upon finding this conclusion.

Misc and Tips

Seed 298 with 89 trading posts available, credit to enfo3.

Market is still required even though all the food is imported and has a considerable diversity, since herbs can only be distributed by markets.

Do not build hospitals near schools - common sense.

Use graveyard cancelling trick.