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Mining Math

Page history last edited by Aryx 9 years, 9 months ago

Mine Type

GP Value per Load Ore Mined per Week (Stone) Metal Weight per Load Expected Value per Week (50% quality) Weekly Costs Weekly Profits Minimum Quality for Profit
Copper 200 50 100 50 42.5 7.5 5
Tin 200 100 100 100 45 55 3
Lead 200 150 100 150 47.5 102.5 2
Iron 200 200 100 200 50 150 2
Silver 600 2 4 150 60 90 3
Electrum 600 4 4 300 80 220 2
Gold 600 6 4 450 100 350 2
Platinum 600 8 4 600 120 480

2

 

I have done everything in terms of weeks because I started with the Complete Book of Dwarves and it uses weeks.  To transition to months, simply multiply by 4.  This will introduce some roundoff error, but it is really not worth the effort to multiply by 30/7 instead.  If you want to be able to use both the weekly numbers and the monthly numbers in the same campaign, clearly the lost 2 days are because of sicknesses and injuries common among miners causing you to lose productivity.

 

The weekly costs are smelting costs and manpower costs; a mining team costs 40 gp per week to pay, and smelting requires 1 gp per 20 stone for common ore (copper, tin, lead, iron) or 10 gp per stone for precious ore (silver, electrum, gold, platinum).  You must additionally purchase a smelter. Note that the costs for smelting include both the materials required and the manpower required to man a smelter (the major difference in cost between common ore and precious ore is due to the need to hire trained men to smelt precious ore, or unskilled laborers to smelt common).

 

A small smelter costs 1,000 gp to set up and can process 20 stone of ore per week.

A medium smelter costs 4,000 gp to set up and can process 100 stone of ore per week.

A large smelter costs 16,000 gp to set up and can process 500 stone of ore per week.

 

(Math note:  Each time you increase your level of smelter, you increase the price by 4x and the capacity by 5x.  This is intended to make sure that it is not more efficient to stack the lower levels of smelter; you should buy the one with the capacity you need.  However, I also want there to be a meaningful tradeoff, so you don't just buy a large smelter every time and just wait until you actually need the capacity.)

 

Roll (1d20) Quality Chance of Occurrence
1 1 5%
2-3 2 10%
4-5 3 10%
6-8 4 15%
9-12 5 20%
13-15 6 15%
16-17 7 10%
18 8 5%
19 9 5%
20 10 5%

 

Mine Chance Below Minimum Profit Quality
Copper 40%
Tin 15%
Lead 5%
Iron 5%
Silver 15%
Gold 5%
Electrum 5%
Platinum 5%

 

Every week of work by a mining team (40 gp of work) cuts out 200 cubic feet of rock.  In a normal 10' by 10' tunnel, this is 2 feet of length.  This number was arrived at by adding up the values of work of a master, two journeymen, four apprentices, and 10 unskilled laborers, which came out to 42 gp/week; I rounded to 40. Assuming that chopping through rock is half as difficult as building a stone wall (as I assume that building a stone wall requires half investment in quarrying/dragging stone, and half in actually putting the wall together), this costs .125 gp of work per cubic foot; 200 cubic feet is only 25 GP of work.  What happened to the other 15 gp of work?  Shoring braces.  Shoring braces require 30 cubic feet of wood (45 gp of work) every 10 feet of tunnel length (1,000 cubic feet).  This increases the cost per cubic foot from .125 to .125 + (45/1000) = .17.  200 cubic feet at .17 gp per cubic foot is 34 gp of work.  The last 6 GP is roundoff error, because I think in this case, it's better to have nice round numbers than it is to maintain perfect accuracy.  Clearly, mining and excavating is a little bit harder than similar work aboveground and therefore carries a bit of a penalty with it.  (If you want to follow the formulas perfectly and the devil take rounding, then you have 42 gp of work at .17 gp per cubic foot, or 247.0588 cubic feet per week.)

 

If it wasn't for the fact that I'm valuing round numbers to make it easier on the running end, I would definitely go with 42 gp/week for cost and 250 cubic feet/week for progress (2.5 feet in length).  Moving from 40 to 42 gp per week lets you get much closer to a reasonably round number for progress (40 gp/.17 comes out to about 235 cubic feet of progress).

 

Dwarf Mining Speed

 
Mine Type GP Value per Load Ore Mined per Week (Stone) Metal Weight per Load Expected Value per Week (50% quality) Weekly Costs Weekly Profits Dwarf Profit Bonus Non-Dwarf Owner
Copper 200 62.5 100 62.5 43.125 19.375 11.875 -68.125
Tin 200 125 100 125 46.25 78.75 23.75 -56.25
Lead 200 187.5 100 187.5 49.375 138.125 35.625 -44.375
Iron 200 250 100 250 52.5 197.5 47.5 -32.5
Silver 600 2.5 4 187.5 65 122.5 32.5 -47.5
Electrum 600 5 4 375 90 285 65 -15
Gold 600 7.5 4 562.5 115 447.5 97.5 17.5
Platinum 600 10 4 750 140 610 130 50

 

In these numbers, I'm giving dwarves a 25% productivity boost thanks to their sensitivity to earth and stone.  Any other race or class with that custom power should get the same bonus.  Every week of work by dwarves cuts out 300 cubic feet of rock (3 feet of length).  40 gp/week times 1.25 is 50 gp/week, divided by .17 gp per cubic foot gives us 294.etc cubic feet, which I round to 300.  For those outside of their own clan who hire them, this costs 120 gp/week instead of 40 gp/week.  The Non-Dwarf Owner column shows the profit difference between hiring humans to do the work and hiring dwarves to do the work.  Remember that this assumes 50% quality; the following table shows the minimum quality for various mines to make it worth hiring dwarves to work your vein for you.  It is possible to make a profit with dwarves working a vein of lesser quality than shown on the table (usually about 2-3 quality lower), but you will make less profit that way than just hiring humans to do it.  The table shows you the minimum quality necessary to make it actually worth hiring dwarves over humans.  (Copper is N/A because there is no quality of copper for which it is worth it, though you will make a tiny profit at quality 10.)

 

Mine Type Minimum Dwarf Quality
Copper N/A
Tin 8
Lead 7
Iron 6
Silver 7
Electrum 6
Gold 5
Platinum 5

 

For those using nonstandard means to mine (maybe you have charmed umber hulks or a pair of gnarly gloves of transmute stone to mud), the following table shows you the conversion of 'cubic feet of stone gone through per week' to 'stone of ore gathered per week' by mine.  Note that thanks to rounding errors, the dwarves do not obey this table; they have 50% more cubic footage of stone that they go through but only get 25% more ore.  For game balance, it is important that they only get 25% more ore.  If you have a problem with this rounding error occurring in your campaign, you can use the unrounded (or at least very lightly rounded) cubic footage numbers for human and dwarf progress of 235 and 295 cubic feet respectively.  Alternately, you can simply say that dwarves are chopping out extra stone for future use as living quarters and the like.

 

Mine Type

Ore per Cubic Foot (Stone)

Copper 0.25
Tin 0.5
Lead 0.75
Iron 1
Silver 0.01
Electrum 0.02
Gold 0.03
Platinum 0.04

 

This table does include time spent sorting the ore and hauling rock away.  If those things are not accounted for in the method being used, the Judge will need to apply a penalty based on it.  Excavation, sorting, hauling, and shoring are the four tasks that need to be done; the table below shows what each costs per cubic foot.   Thus, if you have umber hulks excavating for you, they can give you a very large boost to excavation (and to hauling as well), but will be largely unhelpful in shoring or sorting.  An army of charmed umber hulks could give you a roughly 50% productivity boost.  Of course, if you hired sufficient laborers to sort and shore at the speed they could excavate at, it could give you a much greater boost; a normal set of miners (master, journeymen, apprentices, 10 laborers) could perform the sorting and shoring tasks of roughly two miner-weeks when they are freed from the need to excavate and haul.  Thus, in this umber hulk example, every miner team could sort out 400 cubic feet of stone to find the ore from it and provide sufficient bracing for four feet of tunnel per week.  The following table shows the raw GP cost per cubic foot of each sub-task.

 

Task Cost per Cubic Foot (GP)
Excavation 0.0625
Sorting 0.03125
Hauling 0.03125
Shoring 0.045
Total 0.17

 

In other words, a single laborer who does 1 sp of work per day can sort 3.2 cubic feet of stone for ore per day, or 96 cubic feet per month.  If you want to round that to 100, I will not blame you one bit; it's what I would do, but I'm already writing down numbers like .03125, if you care enough to read that many numbers you might actually want to keep the real numbers.  When sorting 100 cubic feet of ore from (let's say) a copper mine, he will find 25 stone of copper ore.  (100 cubic feet of hard stone weighs somewhere in the general vicinity of 1500 stone; most of what is excavated is not metal-bearing.)

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