Saturday, July 23, 2016

Of Coins And Coffers: A Frustrated Dissertation On Fantasy Currency

Warning! Massive quantities of math ahead!

While this article focuses on the currency of fantasy RPGs, the basic idea of how much cash you can reasonably expect to carry on your person extends to any fictional narrative.

A slight annoyance I have with AD&D, and RPGs in general, is the monetary system. RPGs either ignore the weight and size of coins all together (Elder Scrolls to a ridiculous extent in the later games), ignore weight and size in favor of a wealth limit (Legend of Zelda and Final Fantasy), pay attention to size but not weight (Mabinogi, sort of, since it's the size of the sacks more than the individual coins that's the limiting factor), or pay attention to the weight but not the size (dang near every tabletop RPG in existence, with AD&D making a sort of handwave of all coins being roughly the same size)

Scrooge playing Scrooge.
Why does money have to be so complicated?
And when the weight is a factor it's fairly ridiculous. 1/10 of a pound* in nearly pure gold wouldn't make a horribly large coin (about 0.14 cubic inches, a little larger than a shilling as noted below) but I suspect it would buy most medieval shops in their entirety, never mind the saleable goods.

This isn't necessarily a design flaw, particularly in the case of older video games. As series, Legend of Zelda and Final Fantasy date back to the NES (the original games were released almost a year apart) and so all values, not just money, were limited by what that system could handle. The wallet sizes and a few other details in later games are holdovers from that.

The Elder Scrolls doesn't have that excuse, but, admittedly, the frustration of picking up one bit of dungeon trash only to find yourself over-encumbered would multiply greatly if the same thing could happen with a coin.

Unlike some MMOs, Mabinogi at least tried to take volume, if not weight, into account with its inventory system, though I'm still not sure how a robe could take up more space than a claymore.

All this came to mind after rereading the Dragon Magazine (#80) article "How Many Coins In A Coffer?" by David Godwin. It's still one of my favorite articles even though my relationship with math ranges from grudging acceptance of its necessity to burning hatred. (And all textbooks shall feel my wrath!) A few paragraphs in, I came to the conclusion that handwaving and averages just weren't going to cut it for me. I decided to completely overhaul the currency system.

Ye gods. I owe my continued sanity to online math tools.

So here's a bit of my own personal research. It's mostly based on the English and Roman systems because there's more information readily available about them, and they're a lot simpler than some of the other Mediterranean and Middle Eastern coin systems. Don't even get me started on Asia.

*That 1/10lb comes from "How Many Coins In A Coffer?" which is what I'm basing this article on. The DMG for AD&D's second edition, which came out six years after that article was published, claims that all coins "weigh in at 50 to the pound," which raises it's own set of problems.

Weights Measures

The dates given in the following tables are the closest I could get to the form of the coin I based the other figures on. Coinage changed a lot over the centuries, often from one ruler to the next. The level of variety and importance of having specific metals in coinage is something that a lot of fantasy writers fail to grasp in large part because our currency hasn't worked like that in over a hundred years.

English Currency Metal Weight Diameter Thickness* Volume # To Next Origin
Guinea Gold (22k) 0.25oz 1" 0.2" 0.16 cubic in. 1663
Shilling Silver (0.925) 0.8oz 0.9" 0.2" 0.13 cubic in. 20 mid 1500s
Penny Copper (?) 1oz 1.4" 0.2" 0.3 cubic in. 12 1796
* I fudged on the thickness with these. I couldn't get any sort of information on that aspect for most coins and volume was more than a little iffy in places. The fact that these coins were frequently forged, debased, and otherwise changed over the centuries doesn't help at all.

Roman Currency Metal Weight Diameter Thickness Volume # To Next Origin
Aureus Gold (24k) 0.28oz 0.71" 0.08" 0.03 cubic in. 1st Century BC
Denarius Silver (0.95) 0.16oz 0.71" 0.08" 0.03 cubic in. 25 211 BC
Sestertius Brass (?) 0.99oz 1.34" 0.12" 0.17 cubic in. 4 23 BC
As Copper (?) 0.34oz 0.98" 0.12" 0.09 cubic in. 4 23 BC

Okay, well 1/20 of a pound seems like a pretty good starting point. That much pure silver takes up 0.13 cubic inches of space (the same as the English shilling, but that's after rounding, it and the Roman denarius are more than 9/10 pure). Before we get into the exact dimensions of the coinage, let's simplify the exchange rate for gaming (and sanity) purposes.

Exchange Rate By Coins Exchange Rate By Weight Volume By Pure Metal Weight
Gold Silver Copper Gold Silver Copper Metal Weight Volume
1 20 320 0.0008oz 0.05oz 1oz Gold 0.25oz 0.02 cubic in.
1/20 1 16 0.0125oz 0.8oz 16oz (1 pound) Silver 0.8oz 0.13 cubic in.
1/320 1/16 1 0.25oz 16oz (1 pound) 20 pounds Copper 1oz 0.19 cubic in.

Suddenly this doesn't feel so simple. But, basically, 1 copper coin is an ounce, 16 coins make a pound, one pound of copper is equal to 1 silver coin. One silver coin is 4/5 ounce, 20 make a pound, one pound equals 1 gold coin. One gold coin is 1/64 pound or ¼ ounce.

Now back to volume.

Let's start at the top and work down. A gold coin that's ¾" in diameter and 1/20" thick has a volume 0.02 or 1/50 cubic inches (wow, that's rounded, but still, on my first try). So a workable coin could be nearly pure gold. Four stacks of 60 gold coins arranged in a square would then be 3 inches on a side. That's 240 coins or 3¾ pounds.

That makes things a little complicated later, though, if only because it sets the standard for coin purity pretty high. Let's go with a 1" coin that's 1/10" thick. That's 0.08 or 2/25 cubic inches, roughly in-between the Roman aureus and English guinea in terms of purity. It also means that a 1" stack of (10) gold coins weighs 2½ ounces.

On to silver. For simplicity (in manufacturing as well as game design) let's go with 1" diameter again but increase the thickness to 1/6". That's 0.13 or 13/100 cubic inches, close to the purity of a shilling considering I had to do some rounding. Yay me. So a 1" stack of (6) silver coins is 4 4/5 ounces. That could get messy...

Fine. Try again. Seventh inch works even less, so we'll go with 1/5" with a volume of 0.16 or 4/25 cubic inches. That gives us a 1" stack of (5) silver coins weighing 4 ounces. It's significantly less pure than the English shilling and Roman denarius but reasonable considering the purity of my gold coin.

Lastly, copper. Finding a workable coin size shouldn't be this hard. Anyway, a 1" coin that's 1/5" thick is 0.16 or 4/25 cubic inches. Close enough. So a 1" stack of (5) copper coins is 5 ounces.

Such math. Much pain.
Very need help!
Let's review.

A one inch diameter gold coin that's 1/10th of an inch thick weighs 1/4th of an ounce.

A one inch diameter silver coin that's 1/5th of an inch thick weighs 4/5th of an ounce.

A one inch diameter copper coin that 1/5 of an inch thick weighs 1 ounce.

If you think these coins sound a little big, think how big an AD&D coin would be. Mr. Godwin figured, through a dizzying set of formulas and leaps of logic, that one coin of any type was 1 1/2" in diameter and 1/10" thick while weighing slightly over one and a half ounces. A Morgan silver dollar is 1 1/2" in diameter and 9/100" thick. It weighs slightly less than an ounce (0.94oz after rounding).

And this is why I'm revamping the coinage system.

Now on to some of the details discussed by Mr. Godwin. Neatly stacked coins take up the least amount of space, but they won't fill a whole cubic inch because the stack's a cylinder. For future reference, we need to figure out the effective volume of each coin (the volume of a rectangular solid in the same space) instead of it's actual volume. I'm rather grateful my silver and copper coins are the same size, now.

One gold coin is effectively 1"x1"x1/10" or... 1/10 cubic inch? That doesn't sound right to me, either, but I tested my method with Mr. Godwin's results (1 1/2"x1 1/2"x0.1"=0.225 cubic inches) and it matches.

This is if it's all neatly stacked, however. Most people aren't that careful, so the chances of an adventurer stumbling on such a well organized monster horde is close to impossible. Once again, Mr. Godwin provides a tidy figure of 110% volume per loose coin. It makes a slightly awkward number, 0.11, for a gold coin. Though he mentions that 110% isn't a hard and fast rule, I'm loath to round up too... (much frustration with decimal points later) Stuff it, I'm rounding.

Taking It With You

Before discussing hard-sided containers, let's follow Mr. Godwin's lead and get cloth and leather containers out of the way. There's just one itty-bitty problem. "A backpack, for instance, supposing it to be just the right size for a standard spell book, is 16"×12"×6" (1,152 cubic inches), pretty close to the size of a modern camping backpack."

Okay, two problems. First, what he, and probably the AD&D rules, assumed to be a standard spellbook size. I know medieval books were larger than typical books today because of the thickness of vellum and the fact they were hand-written, but what sadist would try lugging around a codex that size everywhere he went?

For reference, the Book of Kells (in it's current form, it's been reconstructed at least once) is roughly 13"x10" and contains most of the four Gospels. One source suggested that the original dimensions were closer to 14 1/2"x11". I haven't been able to find any information on how thick the book is, though it originally consisted of 740 pages. If we assume an average page thickness of 0.009 (using modern vellum as a guide) then the book without the binding would have been about 6 2/3" thick.

An even larger book, the Codex Gigas, is 36"x20"x8.7" with half of that being the entire Vulgate Bible.

Neither of these books were intended to be moved often. Bibles were sometimes chained to their stands during the Middle Ages not because the monks didn't want people reading them but because they were unique works of art, often decorated in gold leaf, represented decades of labor, and were thus insanely valuable.

If you can't imagine someone stealing a Bible, someone did a few years back at my home parish. It wasn't even a particularly valuable one aside from ceremonial use.

A detailed analysis of book sizes will have to wait for another article.

The second problem with Mr. Godwin's assumption is the "pretty close to the size of a modern camping backpack" statement. I don't know where he got his camping gear, but it's obviously not where I do. Going by the Eastern Mountain Sports website (not where I shop, but they have some good articles), an average pack for 1-2 nights should hold 30-50 liters. That averages to 40 liters or 2,440.95 cubic inches (EMS rounds it up to 2,441), over twice what Mr. Godwin estimated and pretty close to the army surplus ALICE pack I use.

Still, just for the sake of comparison, let's go with Mr. Godwin's 1,152 cubic inches bag. To figure how many gold coins that holds we divide the volume of the backpack by the volume of a loose coin. That's 7,680 gold pieces or 1,920 pounds! Mr. Godwin only came up with 460+ pounds, comparable to the 460.8 pounds I got when I plugged his numbers into the formula that resulted in that mind-blowing number. Obviously, even if you could lift that much, the backpack wouldn't survive the attempt.

On the other hand, we now know that a lot more gold will fit into a given volume with my currency than with AD&D's.

So we need to figure out how much these things can actually carry. The DMG says that a large sack can carry 400 gp and a small sack can carry 100 gp. The Character Folder gives 300 gp as the carrying capacity for backpacks and Mr. Godwin assumed that's the carrying capacity for saddlebags (I'm guessing he meant for each bag rather than the paired set). Of course, this is for the 1/10 pound coins, but let's see what that'd come to in my system.

300 gold coins at 0.25 ounces each comes to 4 pounds 11 ounces.

That's... not a lot.

Okay, so let's go with the AD&D 1/10 pound coin. That means that a large sack can carry 40 pounds, a small sack can carry 10 pounds, and a backpack/saddlebag can carry 30 pounds. Didn't even need a calculator. (This is almost certainly why 1/10 pound per coin was chosen for the AD&D system. Very simple carrying capacity calculations.)

So how many of my coins would this take? Well, after converting pounds to ounces, we get the following table for the cloth containers.

Number of Coins Per Container By Carry Weight
Carry Weight Gold Silver Copper
40lb/640oz 2,560 800 640
30lb/480oz 1,920 600 480
10lb/160oz 640 200 160

My system is starting to look a lot better right now. Sure, you can't carry nearly as many copper coins in any given container as you can gold coins, but it's still more coins than the AD&D base rules would allow since their rules state that all coins weigh the same (absolutely ridiculous amount).

The only problem is this doesn't take into account the volume of the coins in relation to the containers. AD&D is silent on the actual size of any of these bags and Mr. Godwin didn't extrapolate further. The ALICE pack I mentioned before can carry over 100 pounds (the bag can, I most certainly can't). It's at least partially made from modern materials, though.

Trying to figure this out led me to the gunny sack, a 23-24"x40" sack that holds 100 pounds of potatoes. I couldn't find anything on the exact volume of the sack itself, but apparently 100 pounds of potatoes can vary in volume from 3,600-4,366 cubic inches. Since potatoes are very irregular in shape, I'm going to round that up to 4,400 cubic inches. With that as a guide, a 10-pound sack would be 440 cubic inches in volume. With 640 loose gold coins taking up 96 cubic inches we're probably pretty safe. Just to be sure, the 40-pound sack would be 1,760 cubic inches and 2,560 loose gold coins would take up 384 cubic inches.

I really want to do that article on container sizes now, because the 30-pound weight limit for backpacks sounds absolutely laughable.

This is where Mr. Godwin moved to the titular coffer, which he initially defined as 5"x7"x1 1/2" or 52 1/2 cubic inches. Not sure where he got that size, but let's run with it. Mr. Godwin figured this allows for 180 neatly stacked AD&D coins with some room for sideways stacks around the edges for a total of 235 coins. Loose coins, a much more realistic possibility, would fill the space at 210.

My coins would fill the space a little differently depending on whether they were gold or silver/copper. Neatly stacked, they'd all make 5 rows with 7 columns but only the gold coins would have stacks of exactly 1 1/2" (15 coins to a stack). That's 525 gp. Silver and copper would only allow for stacks of 12 coins, a total of 420. But remember that loose coins take up 110% as much space. That's 350 of loose gold or 210 of either other coin.

Yeah, my silver and copper coins ended up with the same loose volume as normal AD&D coins. Did not intended for that to happen.

The next container is a 18"x30"x18" or 9,720 cubic inch chest. That would make 540 neat stacks with each stack containing either 180 gold coins or 90 silver/copper coins. How would you spend 97,200gp? Assuming the original owner of the chest wasn't obsessive compulsive, you'd be more likely to find 64,800gp, which is still a very tidy haul (and 16,200lb, good luck moving it anywhere).

And that's almost reasonable compared to the 20'x20' room carpeted in a 1' layer of copper coins. (What module was that and what was the author thinking?) That's 240"x240"x12" for 691,200 cubic inches or 2,764,800 copper coins!

That much copper weighs 172,800 pounds, by the way. With 20 pounds of copper to 1 gold coin, that's 8,640 gp.

This is when Mr. Godwin mentioned the go-to solution of many a player character, the portable hole. That spell has a carrying capacity of 283 cubic feet (10' deep with a 6' diameter, so he's rounding up), well under the 400 cubic feet of coins in that room.

He didn't mention this, but the other go-to solution, a bag of holding, has a capacity of 30-250 cubic feet and can carry 600-2,400 pounds (the bag itself can weigh 15-60lb, the carry weight is 40 times this).

Ingots are a whole other can of worms. Mr. Godwin mentioned an ingot weighing 200 gp (20 pounds). An ingot of that weight made of pure gold would be 28 2/3 cubic inches, he used 2 1/2"x2 7/8"x4" as possible dimensions. He then got into a lot of math that makes my head hurt on the best of days.

By the way, the current standard weight for a gold ingot is 438.9 ounces or almost 27 1/2 pounds. I haven't been able to find much information on historical ingot sizes, but one 6th century gold ingot weighed about 7/10 ounces and was about 5 1/2" long. A silver ingot described as being typical of the Viking period was 1 1/10" long and weighed 7/20 ounces. These were intended to be carried (or worn in the case of the gold ingot, as it was twisted into the shape of a bracelet) and used as currency without bothering with details like 'legal tender.'

So, let's summarize. If you have a container with a known volume and you want to know how many coins will fit in it, just divide the container volume by the volume of the coin you're using. To get the weight, you take the number of coins and multiply by the weight per coin.

Fantasy Wealth Management

Something that Mr. Godwin didn't mention but has become fairly obvious to me through this whole process is that there's something seriously wrong with the economy of a typical AD&D world. Taking the averages of all the 'Lair Treasures' in the 2nd edition DMG, a party of adventurers could expect any one lair to contain 2,778 cp (14% of the time), 3,122 sp (18% of the time), and/or 3,844 gp (32% of the time).

Now, is it just me, or does it seem unreasonable for gold coins to be more common than the other denominations? And even if you did just find copper in that horde, 173lb 10oz is a lot to try carrying out. Especially after fighting through all the monsters guarding it.

But what do things actually cost in the AD&D world? A normal riding horse is listed at 75 gp, which comes to 1 pounds and 2 3/4 ounces of gold. That doesn't sound too unreasonable, except a homing pigeon (a fairly common means of communication, particularly in wartime) is listed at 100 gp! A regular pigeon is only 1 cp, by the way.

Well, what about lodging? Monthly rent for a common room at a boarding house is 20 gp. Boarding houses in the real world were primarily a product of the Industrial Revolution when a lot of young men were coming to the city looking for work in factories. The rent would have reflected the wages of the time. According to one source, a decent room in turn-of-the-century San Francisco went for 35 cents a night, roughly $8 today. The same source showed a photo advertising rooms for 60 cents, whether that was nightly, weekly, or monthly wasn't stated.

Figuring out if any of this reflected prices at any point in the Middle Ages is probably an exercise in futility. The economy was based on bartering, most countries didn't even bother minting coins until the High Middle Ages (defined roughly as the end of the Viking Age in the early 11th century to the end of the 13th century). The first attested use of the term 'middle class' was in 1745. Before that, the nearest equivalent was the bourgeoisie, a product of the 11th century development of commercial cities. Guilds, as a derivative of the Roman craft associations, were hardly heard of and mostly limited to stonecutters and possibly glassmakers until this same time.

In short, I'm going to have to leave fixing the economy for another article.

Friday, July 1, 2016

Putting the "Fun" In Functional Part 2: More Power!

"An author's ability to solve conflict with magic is directly proportional to how well the reader understands said magic."
— Brandon Sanderson's First Law of Magic
And if the reader is to understand magic, then the author has to understand it better.

If the last post in this series felt a little scattered, please accept my apologies. The idea was to establish the real-world basis for fantasy magic. In this article, I'll introduce the steps I'm using to build a functional magic system and delve into the first of those steps.

This isn't just about roleplaying games. Though what I'm building here is an alternative to AD&D's Vancian nightmare, I'm hoping to apply it to my various non-RPG stories as well.

Check out my Dad's DeviantArt account. And whatever you do, don't touch the modern art.

A Recipe For Mysticism

  • What is magic?
    • And what powers it?
  • Who can use magic?
    • How common is magic?
    • How well known is magic?
    • How do people view magic?
  • How is magic accessed?
    • And how is it learned?
  • Why use magic?
    • What power levels are there, if any?
    • What are the benefits?
    • What are the costs?
      • What are the side effects?
    • What can't magic do?

Let's Make Some Magic

Most stories written in the last few decades assume that magic=energy. That works, I guess, considering how many stories make that assumption, but to me it's a bit like saying electronics=batteries. There's a lot more to it than that. Sure, you need a power source for your radio. You also need capacitors, receivers, and a few other items along with enough knowledge to tell whether you're making a radio or a television.

Another problem is where the magic comes from. TVTropes' So You Want To Write A Functional Magic System page lists a number of possibilities including "Magic comes from god/s."

If the god in question is a stand-in for the Judeo-Christian God, that's one thing. He is, after all, the origin of all creation. However, most magic systems based on this idea have a pantheon of gods with domains ranging from 'all living things' to 'that one tree over there.' Do these gods generate magic within themselves?

Chances are the answer is 'no.' Take Norse mythology for example. Obtaining magic cost Odin an eye and a few uncomfortable days hanging from Yggdrasil. As far as the Norse were concerned, magic worked the same way for the gods as it did for mere mortals.

So, rather than magic being power, my starting assumption is that magic is knowledge of how the world works and the ability to manipulate it. This still requires fuel, but at least now we won't mistake gasoline for an automobile.

Gas, Diesel, or E-85

What does magic run on, though? Just about anything you want. Life energy, emotions, electromagnetism... You aren't even limited to a single power source. Maybe different magical disciplines rely on different fuels. Here are a few popular options with a little commentary.

Life-force is probably a lot more common than most people think. As an example, Final Fantasy VII's magic comes from materia, which is crystallized Lifestream. The name is kind of a give away to its nature. Life-force also seems to be what limit breaks and 'desperation attacks' in other games run on.

One can argue that a god that requires a living sacrifice to bestow magic on his followers is using life-force.

It's also the basis for the tropes Cast From Hit Points and Cast From Lifespan. Note that both of those tropes are typically last resort techniques. Draining hit points from other living things to replenish your own also counts.

By the way, am I the only one kinda creeped out by that last one? It's a fairly common spell type in Final Fantasy and Elder Scrolls games, and can be very useful, but I just feel dirty using them. Very dirty. To the point that I actively avoid spells and most weapons with that effect regardless of the disadvantage that puts me at.

Psychic energy is a slightly-less-likely-to-kill-you variant on life-force. The sci-fi staples of telepathy and telekinesis are obvious uses of this energy source, but it has many more applications in both sci-fi and fantasy.

Taking Final Fantasy VII as an example again (it's one of my favorite games, can you tell?), using the spells stored in materia requires MP. What MP is exactly is left fairly vague in the original game, but a few pieces of the Compilation strongly imply that its a representation of mental stamina.
I rather like this approach as it comes with a set of real world consequences and limitations. Ever burned out your brain studying for an exam? Ever tried to hold a coherent conversation while drunk or recovering from anesthesia? Heck, just having a cold can adversely affect your mental abilities. The possibilities are hilarious.

Mystic Electromagnetism is what things like The Force and any system involving 'ley lines' sound like to me. This energy source is everywhere but may be more heavily concentrated in certain locations. It's also a lot more vague than real world electromagnetism and a whole lot easier to abuse. There aren't any built in limitations here, so if you do decide to use it you better make sure to set up some serious limitations on how it can be accessed and used.

I'm going to say it again. Setting up limitations is very important! Just look at the Star Wars expanded universe.

My recommendation for this brand of power source is going with something more along the lines of chemistry or general physics. There's potential energy everywhere, the trick is getting the right sort going in the right direction.

So, there are a few basic power sources for magic. I haven't covered every possibility, of course, but this is good for a start.