# The Secret Ratio

by Alex

A secret ratio recurs repeatedly throughout ACKS. It is 1:33, and it is implicit in many of the game mathematics. Interestingly, the 1:33 ratio *emerged* from the assumptions of the system; it wasn't initially designed in. The first place the secret ratio appeared was in the average rate of return on gold invested per month in support of mercantile activities, which is 3% (3/100 or 1/33). I noticed the ratio when I was building spreadsheets to model landlords and merchants.

- 1,000gp invested in agricultural improvement will attract on average 5.5 peasants yielding around 6gp per month, or 33gp. (3.3%)*
- 18,000gp invested in cargo and a small sailing ship will return 600gp in profits per month (3.3%)
- 36,500gp invested in cargo and a 40-wagon caravan will return 1,100gp in profits per month (3.0%)
- 50,000gp invested in cargo and a large sailing ship will return 1,800gp in profits per month (3.6%)

*I shed a single tear of joy when I noticed that 99gp was very close to the average starting income of a PC (105gp), suggesting that your average adventurer's equipment roughly represented the net worth of a peasant who has liquidated his farm and cows. The perfection with which this worked out represents either the Providence of Divine Gygax, or really good baseline assumptions.

This ratio became very useful in other areas of play as it allowed us to work out the approximate "capital" of individuals with known income, or conversely, the approximate income of individuals with a known amount of capital. (Note that capital is loosely defined here -- a fighter who has spent thousands of gold carousing while bragging of his exploits has essentially "invested" in his reputation. We assume for the sake of simplicity that coin, equipment, training, carousing, etc all have an equal rate of return).

Examples:

- A peasant, earning 3gp per month, probably has (3x33) 99gp in capital. This is probably seed, farming implements, and perhaps some domestic animals.
- An alchemist, earning 75gp per month, probably has (75x33) 2,475gp in capital - lab equipment, books, chemical mixtures, potions, and coin.
- The emperor of a massive domain, with an income of 360,000gp per month, has capital of around 11,880,000gp.
- A warrior (2nd level fighter) with 1,500gp invested in equipment, training, and so on, would expect to earn 45gp per month (1500/33).

Since about 80% of experience points in ACKS are derived from gold, its easy to determine the capital of an NPC by multiplying his XP by 80%. That in turn enables one to calculate the amount of money the character would expect to earn per month. This solves the age-old problem of "how much does it cost to hire an NPC of such-and-such level".

Even better, since we know the average income of various ranks of nobility, it also shows how the wages of characters of various levels compare against that of nobility. At 9th level a character's income from his skills suggest he should be earning as much as an earl or count - which, in turn, suggests that your 9th level warlord who has built a stronghold and carved out a domain can safely style himself as an earl or count.

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## Comments

Jul 08, 2011 04:00 PM

Execllent number-crunching - knowing the capital NPC's can draw on can be really useful - especially when ransoming prisoners, which happens a lot in my group's games because historically it was very profitable:

http://sean-n-sorcery.blogspot.com/2010/12/ransoming-prisoners-in-s.html

Jul 08, 2011 08:30 PM

I hadn't thought of that, but you are exactly correct. Very cool. I like your chart of ransom prices, too!

Apr 29, 2014 07:07 PM

Alex, I'm having a hard time understanding the math behind the 1,000gp agricultural investment/99gp starting gold calculation.

Could you unpack that for me? I'm probably missing something obvious.

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