Monthly Archives: February, 2017

On the State of Mapping Software

A couple weeks ago there was a conversation about what people use for creating RPG maps. I decided to do a brief rundown of my view of existing software.

Available Mapping Software

Presented in no particular order, let’s begin.

Campaign Cartographer 3

CC3: many people like it, and I admit it is a powerful tool. I used earlier versions (back to the MS-DOS days, when I had to lie to it to get it to use my printer). Learning curve was always steep and long, can’t honestly say what it’s like now because it’s more expensive than I’m willing to pay.

Does a nice job, if the style is to your liking. I must say that they have probably the prettiest symbols — a great step up from the CC1 in MS-DOS days — of all the mapping software I’m familiar with.

While much of the emphasis in galleries is on overland maps, Campaign Cartographer can do city and dungeon maps as well, and has software expansions specifically to support and expand on these topics.

https://secure.profantasy.com/products/cc3.asp

Freie Lande CC3 Sample

Freie Lande CC3 Sample

Inkarnate

A couple people have pointed out that I missed Inkarnate. Mea culpa, I’d completely forgotten it because while I am aware of it, I haven’t had a chance to explore it. I will correct this soon.

Not only is this a popular program, a quick look shows me it builds some beautiful maps.

http://inkarnate.com/

I took about 10-15 minutes and took a run at Inkarnate. No instructions, just messed with the web application a bit to see what I could figure out. The map is busier than I’d normally aim for, mostly because I wanted to see how the objects interacted: the work around each other pretty nicely. I’d first laid the mountain range down the west coast, then the hills around those, and later came back and added the mountains and hills just to the east of those, and the ones on the center peninsula. Select “place object’ tool, select the object, and just scribble. If there’s room, it’ll be added.

All in all I think there’s a lot of potential here. The symbol set is small at this point, the landform sculptor could really use some options to make it not-smooth (right now you sculpt hexes, squares, or sweep with a circular brush). I’d rather see some more jaggy, ‘fractal shape’ to the landform.

I’d give this pretty high marks for ease of use, and the symbol sets look very good. I understand they’re still in development (there was an option to sign up for the beta), but if there were a ‘consumer version’ that was ready to go with a bigger symbol set (I see it’s possible to import symbols, but I like how these look and I’d like to see the same style, expanded… I see mention in earlier news on the site that more symbols are available, but I haven’t seen how to access them), the ability to make jaggy landforms, and the ability to add linear features such as roads or rivers (that aren’t just narrow waterways cut out of the landform) I could see paying for this tonight.

Inkarnate Test Map

Inkarnate Test Map

AutoREALM

AutoREALM was an early piece of software, did a decent job but it was crude compared to CC. To the best of my knowledge — which is pretty good, I was involved in the project for a time — Andy Gryc, the original creator, has abandoned it, and despite a few efforts to pick it up and make a more modern version, it’s basically frozen where it was. On the other hand, price is great (free).

To be honest, it was hard to find an image that gave a good representation of what could be done with AutoREALM. It was quite easy to throw a map together, but quite difficult — steep learning curve — to do something that really looked good. I did find one map that looked very impressive, but it would have taken an inordinate amount of time and expertise: it would have been unfair, I think, to include it as an example of what a regular person might do.

https://sourceforge.net/projects/autorealm/

Fractal Mapper

Fractal Mapper was, for a time, my mapping software of choice. I still use it on occasion when I have something I want to do quickly. Much easier to learn and much gentler on the pocket than CC, more capable than AutoREALM. Good introductory software, and for a long time the closest I’d found to “the mapping software I would write”.

The screenshot below is an overland map, but Fractal Mapper can handle dungeon and city mapping as well. It does not have the same degree of development for these that Campaign Cartographer does, but it works pretty easily. Also, you can associate game information (room descriptions) with the map elements and Fractal Mapper will generate the adventure text for you.

Fractal Mapper also includes a scripting language (“Goblin API”, a repurposed BASIC, sort of) if you want to delve that deeply. As a professional programmer I appreciate the capability, but didn’t find that I needed it for what I wanted to do.

http://nbos.com/products/fractal-mapper

Fractal Mapper 8 continent screenshot

Fractal Mapper 8 continent screenshot

Other World Mapper

Other World Mapper is even closer to being “the mapping software I would write”, but is still in beta (which I’ve toyed with a bit, beta 0.6 was released Dec 31). I am really looking forward to the finished version.

http://www.otherworldmapper.com/

The image below is only one-quarter the size from the Other World Mapper gallery. The original image is 4000×2500 pixels, I reduced it quite a bit so it would fit at all on the page. This renders the labels illegible, so click on the image below to see the original.

Farangor -- Other World Mapper Sample

Farangor — Other World Mapper Sample

Dundjinni

Dundjinni, I can’t say much about. I tried it, found it didn’t suit me well, walked away. It looks like things are about dead over there.

http://www.dundjinni.com/

Dundjinni Graveyard

Dundjinni Graveyard

Hexographer

Hexographer, from Inkwell Ideas, is a little clunky at times but does a decent enough job at hex maps — especially if you get the extended symbol sets, but the default ‘class hex symbols’ are pretty nostalgic. I will be getting the newer version when Joe’s finished updating the software.

I have not done anything with his Cityographer or Dungeonographer, but I do like breaking out the Coat of Arms Design Studio for making holy symbols (thanks Joe, for adding ’round shields’ to the list).

http://www.hexographer.com/

The sample image below is taken from an Inkwell article on how to draw “Greyhawk-style” maps.

Hexographer Sample, Greyhawk Style

Hexographer Sample, Greyhawk Style

 

Fantastic Mapper

Jonathan Roberts (“Fantastic Maps”, did the maps for _The Lands of Ice and Fire_ book) is working on a project he calls “Fantastic Mapper”. Last update was a while ago, but it appears it’s still running.

http://fantasticmapper.com/

Fantastic Mapper Sample

MapTool

I was prompted also to discuss MapTool, and I don’t have much to say. We did use it many years ago as a virtual tabletop (VTT) while playing games in IRC (text via IRC, map via MapTool), but I didn’t know anyone in our group who actually used it to make maps. However, since it seems I’m going for more completeness than originally expected, I’ll include the link here.

I think it important to mention that it appears this is an open source project, with access to the source code via GitHub. This gives people the option to join in and help develop it further (as do AutoREALM and Dave’s Mapper, actually).

http://www.rptools.net/toolbox/maptool/

Dave’s Mapper

Also, just for the shiggles, Dave’s Mapper takes (with permission!) geomorphs and provides an easy means of building maps with them. Basically give it the size of map you want and style (cavern, dungeon, cavern/dungeon mix, city, sci-fi ship, or side-view — this one’s really trippy) and let it do its thing.

Source code is available via Dave’s GitHub. When I finally get around to buying the Dungeons in Blue geomorph sets I’d love to plug them in… but I’m awfully sure Mark (the creator of Dungeons in Blue) would not be cool with making this public, so I’d need a private server (no problem, I can do that) and the geomorphs are multi-phase (Dave’s Mapper appears to expect geomorphs following the Dyson protocol — 100-foot square geomorphs with openings at 3 and 8 on each side), so it might be necessary to adjust the software to accommodate such multi-phase geomorphs.

http://davesmapper.com/

I admit, I love the side-view option more than the normal option.

Dave's Mapper Sample

Dave’s Mapper Sample

Dave's Mapper Side View Sample

Dave’s Mapper Side-View Sample

Other Links

A couple of other relevant links.

Polygon Map Generation Demo

This technically is a mapping program, but the user has almost no control over what happens. However, I find it involves a fascinating bit of research and theory that I’d like to explore further in creating random maps.

Amit makes the code available under the MIT license, which allows commercial use. I have not had a chance to look at it, though.

http://www-cs-students.stanford.edu/~amitp/game-programming/polygon-map-generation/demo.html

Generating Fantasy Maps

Speaking of generating maps, Uncharted Atlas has created a truly nifty tool for doing just that. Where Amit provides a description (in a linked page) of how his software works, Mewo2 not only explains in the page below, but lets you see the intermediate steps and affect the outcome. The intermediate steps sometimes have options to show some of the decision-making information, such as when placing cities you can have it show ‘city location scores’.

City Placement, Initial State

City Placement, Initial State

City Placement, City Scores

City Placement, City Scores

Purple is ocean, green is land, yellow is a favorable location (cities like to be near fresh water), and as I recall the algorithm expects people don’t want to climb hills to get away from water.

They also don’t want to get too close to their neighbors. After placing a city the city scores in the region around the city get depressed. the I expect to see a city at the mouth of one of the two rivers to the northwest, then probably on the eastern river in the large north-facing bay just to the east of the center of the map.

City Placement, First City

City Placement, First City

City Placement, Second City

City Placement, Second City

As should be evident, after placing the first and second cities, the relative appeal of other locations increases (the score seems to be presented in a ‘most attractive to least attractive’ gradient, not fixed score). After the second city is placed the southern islands become much more attractive than anywhere remaining on the norther island.

… in any case, I’m getting distracted here. Like Amit’s, this program offers source code and provides theory I’d love to examine in more depth, so I can include it in other works. Still, since it does not truly allow map creation and editing as the other software intends it, I’m going to leave this one at an honorable mention. It fascinates me and creates cool stuff, but it’s probably not going to be useful to most people.

http://mewo2.com/notes/terrain/

Uncharted Atlas Map

Uncharted Atlas Map

GIMP and Photoshop

Many ‘serious mappers’ use normal image and photography software. I’ve used GIMP for years now as my go-to raster image tool, and I’ve used GIMP to make overland maps. I’ve also written a couple of mountain tutorials, starting with one at the Cartographers’ Guild, and back in April I had a brief series here.

First was how to manipulate a very simple mountain range (straight line with simple gradient slope) to get something that looked ‘properly irregular’, followed by how to pick a better landform to start with, then how to draw several mountain ranges together, and finally how I apply color to the mountains.

Mapping Landforms 3 Brown 40%, Grass Bumped

Cartographers’ Guild

I mentioned the Cartographers’ Guild above. Compared to many there I am a rank beginner at this. Their tutorial section is “kind of huge” and covers an immense range of material in an eclectic mix of subjects, techniques, and tools (software or otherwise). I recommend it highly to anyone interested in taking up RPG mapping.

Ornamentation: The Payoff

Hope Diamond, By David Bjorgen

Hope Diamond, By David Bjorgen

Finally, time for the article whose idea prompted this entire series.

This is much more detailed than the core “plus 1,200 gp worth of jewelry” entries in the treasure tables… but not particularly different.

Wearable jewelry is typically fairly light, all things considered. ‘Heavy earrings’, according to a bit of research, might each weigh about the same as a Canadian quarter (~4.4gm), and often less than that. Given that I’ve got a man’s ring at nominally one coin’s weight (1/50 of a pound) this might be 1/100 of a pound for the pair, and potentially only a fraction of that.

Because the base value of crafted jewelry is five times the weight of the metal, I’m going to say that the smallest unit of measure, a pennyweight (pw), will be 1/5 of a coin’s weight (1/250 of a pound avoirdupois, slightly less than 2 grams). This means the smallest gold earring (1 pw) is worth 1 gp, before considering quality and whatnot. Larger items will be measured in coin weight (cw), and then into pounds.

From here the process is mostly pretty simple. Chose the base item and metal, add gems if you want, then total everything up.

Choosing the Base Item

This whole thing was prompted by describing ornamented weapons, so that’s where I’ll start.

I think for weapons and armor, a quality bonus will still increase the market value of the whole (i.e. it increases the base item value as well), but crudely decorated armor and weapons are still usable armor and weapons, so penalties don’t apply to the base item. With normal gems and jewelry the value can be hidden fairly easily, but a sound breastplate is still a sound breastplate.

Weapons

Assume that weapons can have up to one-fifth of their weight as ‘jewelry’ and ornamentation without adversely affecting their use. I’m leaving off simple ornamentation such as enameling, instead I’m looking at inlays and accoutrements, decorated hilts and guards, and so on.

A simple dagger (2 gp weapon, weighs 1 pound) could thus have up to 1/5 of a pound (10 cw) of jewelry. Let’s say it’s a silver chasing on the blade, gilt on the guard and a gold pommel. I’ll say this is 30% silver (3 cw, 15pw) and 70% gold (7 cw, 35pw). Assuming this is adequately crafted there are no other modifiers, so the total value of the ornamented dagger is 2 gp (dagger) + 35 gp (gold) + 1.5 gp (silver) = 38.5 gp.

The same weapon that is more finely crafted (exquisitely so, +3 quality) and with a pair of 50 gp bloodstones in the guard would be rather more valuable: the same 38.5 gp as above, plus 100 gp for the bloodstones is 138.5 gp, plus 30% for the sheer artistry of it, for a total of 180 gp (180.05… close enough).

The matching sheathe doesn’t have the same weight limitations, so let’s say there is a highly-decorative sheathe that comes with it that itself weighs a full pound, and is made of silver with gold filigree that is sort of the ‘countercharge’ of the chasing on the blade. There are two more bloodstones here, one near the opening of the sheathe and one at the end. It is as well-made as the dagger, so we end up with: 75 pw of gold, 175 pw of silver, and 100 gp of bloodstones (75 + 17.5 + 100 gp = 192.5 gp), plus 30% is a total of 250 gp (250.25). Together the dagger and sheathe are worth 430 gp.

I specifically do not include the value of masterwork components or enchantment in these calculations. They do not change with the base value of the item, so they don’t change due to ornamentation.

Armor

Armor is quite a bit heavier, and subject to a fair amount of abuse. I would not expect to find fine ornamentation on armor, unless the armor is intended for ceremonial purposes. As a result, I’ll say that armor intended for use will have only up to 1/10 of its weight in inlays and the like, while ceremonial can go up to 1/5, or even higher (though that would be very ostentatiously impractical).

This breastplate (200 gp armor, weighs 30 pounds) could have up to 6 pounds (300 cw) of jewelry. That’ll add an unpleasant amount to its encumbrance, so I’ll say it is decorated with only 3 pounds of silver (150 cw). It was once quite fine (+1 quality), but has seen some abuse in the field (-2 quality). The original value was 200 gp (armor) + 75 gp (silver), +10% (quality), for a total of 300 gp (302.5). In its current state it is not worth as much (200 gp + 60 gp) = 600 gp. (If the same penalty applied to the base armor value it would be a total of 220 gp.)

I specifically do not include the value of masterwork components or enchantment in these calculations. They do not change with the base value of the item, so they don’t change due to ornamentation.

Jewelry

Earrings, pins, and the like are probably measured in pennyweights, 1/250 of a pound. If they have much value at all it is probably because they are enchanted or have gems.

Item Weight (pw) Example Value Actual
Earring (each) 1d6 Fine (+1) silver earring (3 pw) with a tiny (-2) but good (+1) garnet (100 gp)  100 gp 99 gp
Pin 1d10 Impure (-1) but good (+2) gold pin (7 pw) 8 gp 7.7 gp
Ring 2d10 Impure (-1) and poor (-1) gold and platinum (25/75) ring (7 pw @ 7.75 gp) 45 gp 43.4 gp

Many other items are a bit heavier, but still not too heavy. lockets, and so on are probably measured in coin weights, 1/50 of a pound. Instead of providing a random weight for each of these, I suspect it’s more likely to have a weight and need an item, so I inverted it: find the weight you want, then select an item from the table below.

Item Low High
clasp 5 5
bangle 5 10
anklet 5 20
medal 5 20
necklace 5 20
brooch 10 10
buckle 10 25
collar 10 25
comb 10 25
headband 10 25
chain 10 40
seal 10 40
bracelet 15 20
diadem 15 30
goblet 15 30
knife 15 30
locket 15 30
medallion 15 30
pendant 15 30
armband 25 40
chalice 25 40
tiara 25 40
belt 25 50
choker 25 50
coffer 25 50
idol 25 70
orb 25 75
coronet 35 50
decanter 45 70
statuette 50 200
box (small) 55 100
crown 55 100
scepter 100 250

Closing Comments

This rounds off the “how to create and calculate” portion of this series. In the next post in the series I’ll explore what do with the results, and how to bend them to your use — beyond simply providing gold value to the PCs.

Ornamentation: Jewelry, Crossing the Streams

Hope Diamond, By David Bjorgen

Hope Diamond, By David Bjorgen

I just realized something about my last two posts.

If I take the ‘jewelry system’ from the previous post and I modify the exponential values table I see something interesting happen.

What if gems scale by one rate and jewelry by another? Specifically, gem value is multiplied by five every six steps and jewelry by ten every six steps? I’ve adapted the exponential values table so a “times ten per +6” column (labeled ‘Metal’ below).

Adjustment Gems Metal Metal Note
-3 44.72 31.62
-2 58.48 46.42
-1 76.47 68.13
0 100.00 100.00 Silver
1 130.77 146.78
2 171.00 215.44
3 223.61 316.23
4 292.40 464.16
5 382.36 681.29
6 500.00 1,000.00 Gold
7 653.83 1,467.80
8 854.99 2,154.43
9 1118.03 3,162.28
10 1462.01 4,641.59
11 1911.81 6,812.92
12 2500.00 10,000.00 Platinum

That is, if you start with a gem worth 100 gp and get +6 (size and quality) to its value, it’s worth 500 gp — as much as the next grade of stone. However, if you craft a piece of jewelry and get +6 (purity and quality) to its value, it’s worth ten times as much — that silver ring is worth as much as a regular ring made of gold.

The math vs. arithmetic problem again, I think, though it does make for a smoother transition between the metal values and it does mean you need less metal for it to be relevant when gems are present. Even the most exquisite gold ring (+6 = *10 value) is worth only about 20gp, hardly noticeable against the 1,000 gp sapphire (though the two together are 1,600 gp).

Keeping this for posterity, in case I have the thought again.

Ornamentation: Jewelry and Its Cost

Hope Diamond, By David Bjorgen

Hope Diamond, By David Bjorgen

I’ve spent a lot of time talking about gems, including how to increase their value (or not) and alternate means of determining their value. Now it’s time to look at jewelry and other items made of precious metal. This will necessarily be greatly simplified; in the real world this is horribly complex.

Let’s look at simple jewelry first: a pretty piece of metal.

Simple Jewelry

Assuming pure metal such as 24kt gold, the absolute minimum value of the piece would be based on its weight. If a gold ring is worth 1/50 of a pound (probably not a horrible guess[1]) and there are fifty coins to a pound, this should be worth a minimum of 1 gp, for metal value alone.

My model of pricing gems doesn’t exactly fit here, because this explicitly accounts for metal weight. However, there are still two factors to consider, the purity of the metal and the quality of the work. I’ll try adapting the table I used for gems. I initially had purity stop at +0 (you can’t be more pure than pure,right?) but if instead we assume most jewelry and the like is alloyed we have some room for a ‘more pure’ version.

d10 Value Purity Quality Alternate Value
<1 -3 Nominal ? not yet named -3 + roll
1 -2 Adulterated Flawed -2
2-3 -1 Impure Poor -1
4-7 +0 Standard Average +0
8-9 +1 Fine Good +1
10 +2 Very Fine Excellent +2
>10 +3 Pure Fabulous +2 + roll – 10

So, a basic man’s silver ring might be 1/50 of a pound of alloyed silver. If you melted it down for its metal value, it’s worth 1 sp. A gold ring of similar nature would be 1 gp, and a copper ring would be 1 cp.

Normally crafting an item, per the rules for the Craft skill, requires raw materials equal to one-third the item’s value. Given that probably not all the raw materials are the metal being used, and that there would be some waste, I’m going to go with a base value of crafted jewelry being five times the value of the metal involved. If you somehow manage to get a -8 penalty to the item’s value (very poor quality, heavily adulterated metal, or general damage) it is scrap worth only the base metal value.

Mixed and Multiple Metals

The above assumed more or less homogeneous construction, even if the metal is not pure. If a piece consists of more than one type of metal, simply add the values together by percentage and assume the quality modifier handles how well that is done. For instance, a silver and gold ring (75% silver and 25% gold) weight 1/50 of a pound would have a metal worth of 0.75sp + 0.25gp = 3.25sp.

Metal Value per Coin Weight Value (sp)
Copper 1 cp 0.10
Silver 1 sp 1.00
Silver+Gold (75%/25%) 3.25 sp 3.25
Silver+Gold (50%/50%) 5.5 sp 5.50
Silver+Gold (25%/75%) 7.75 sp 7.75
Gold 1 gp 10.00
Gold+Platinum (75%/25%) 3.25 gp 32.50
Gold+Platinum (50%/50%) 5.5 gp 55.00
Gold+Platinum (25%/75%) 7.75 gp 77.50
Platinum 1 pp 100.00

I am tempted to give a bonus to crafting checks for the more valuable metals, especially when it comes to composite pieces (metal and gems). This is partly because the more precious metals tend to be easier to work, and partly to encourage their use in higher-end jewelry — a gold fitting for a sapphire should be worth more than a copper fitting.

A signet ring from the equipment list is worth 5 gp. This is exactly in line with a standard 1-coin-weight ring made of gold, of standard construction and quality. Close enough for now.

This does reveal, though, that even a large ring (heavy as two coins), made of platinum, will have a base value of only 100 gp. (Incidentally, I had cause to check, and right now the spot rate on platinum is about $200 less than for gold!)

Jewelry with Gems

The simplest way to increase the value of jewelry at this point is to add gems. Take a simple but very nice gold ring (5 gp value — 1/50 of a pound of gold) and put a sapphire (lesser precious gem) in it. At a minimum it should be worth the sum of its parts, so 1,000 gp + 5 gp = 1,005 gp… which presumably would be rounded to 1,000 gp.

Knowing my players, they’d immediately pop the sapphire out and keep the scrap for metal value. Every gp counts!

However, this should be a workable minimum.

The easiest way to keep the piece worth more if it’s kept together is to have the workmanship apply to the piece as a whole. That is, apply the ‘Quality value’ above to the piece after adding gems to the metal.

  • A very nice (+2) gold ring (pure gold, +3) is worth 10 gp, by itself.
  • A sapphire (1,000 gp, assuming +0) is worth 1,000 gp, by itself.
  • Put together per the ‘minimum value’ rule, this is 1,010 gp.
  • Put together applying quality after, this is worth (1,006.5 gp * 1.2) = 1,207.8 gp.

At this point I’d round it to 1,200 gp. The gold ring itself isn’t worth much, but the piece as a whole is worth quite a bit more because it is there. Though by this reasoning a silver or even a copper ring would have the same effect.

I thought about doing something about this, such as saying that only the cheapest gems are thus augmented by copper (or better), middling gems by silver (or better), and precious only by gold (or better)… then decided I don’t actually care. This is in part because it interferes with rule of cool, but mostly because the difference, at the 1,000 gp level, between a gold ring and a copper ring is pretty meaningless.

There is an even simpler method: multiply the value of the entire piece by the combined ‘jewelry modifier’:

  • Put together applying the ‘ring bonus’ to the whole, this is worth (1,000 * 1.5) = 1,500 gp.

Unless the value of precious metal is significant compared to the gems involved, I think I’m going to consider just the ‘jewelry modifier’ as a modifier to the gem value. The sapphire ring is worth 1,500 gp (the purity of the gold just makes the entire piece nicer).

At this point the players could separate the two, but there are reasons (500… erm, 490 of them!) for keeping them together.

Very Poor Jewelry

The final result above — multiply the combined component value by the modifier of the metal value — means that a piece could have a market value less than the component value, if the piece is poorly crafted. I’m pretty okay with this: a poor fitting hides the value of the stone, and if it’s recognized the stone could be removed from the setting and be worth more than where it is presented now. I expect this is a rarely-happen event anyway, since the crafter should have a good idea what happened and simply tear it apart himself (or this is where the ‘spoiled materials’ clause of the Craft skill comes in).

Closing Comments

Sometimes looking at something too closely can introduce levels of detail that aren’t needed. In this case I was pretty happy with the rules for gems, and for simple jewelry, but trying to be too precise with combination pieces wasn’t worth the trouble.

It is evident that unless there is a lot of precious metal involved, much of the value of jewelry comes from the gems in it. This aligns pretty well with real life expectations, so I’m okay with it.

Changing Jewelry Modifiers

I think I might change the modifiers to be plus or minus 20% per point, for jewelry. A total of -4 thus reduces a piece to its metal value, and — more importantly to me right now — gets rid of an annoying intermediate decimal value. One coin worth of metal is worth five coins when crafted, plus or minus 20% per point of modifier means it stays whole numbers. If I have a composite piece that applies the quality and metal purity modifiers separately I could get the decimal back in, but it doesn’t annoy me as much at the end.

So the sample sapphire ring above could be

  • 1 gp * 5 = 5 gp base, plus 60% = 8 gp, plus 1,000 gp = 1008 gp, plus 40% = 1,411.2 gp; or
  • 1,000 gp * 100% = 2,000 gp

Different metals (silver and platinum) might be

  • silver: 1 sp * 5 = 5 sp base, plus 60% = 8sp, plus 1,000 gp (10,000 sp) = 10,008 sp, plus 40% = 14,011.2 sp;
  • platinum: 1 pp * 5 = 5 pp base (50 gp), plus 60% = 80 gp, plus 1,000 gp = 1,080 gp, plus 40% = 1,512 gp.

Footnotes:

[1] google shows many men’s rings to be in the 9-11 gram range. To double check, two Canadian quarters together weigh 8.8gm, two US quarters together weigh 11.34gm… which is a pretty good-sized man’s ring. For simplicity and alignment with the coin system, I’ll say a ‘typical’ man’s ring here has the same weight as a coin, so 1/50 of a pound.

[2] google again, modern signet rings appear to range from half the weight to twice the weight I’d assigned to “men’s rings”, so I’ll assume the ‘signet ring’ from the book is relatively large.

Ornamentation: Polishing Gems by the Numbers

Hope Diamond, By David Bjorgen

Hope Diamond, By David Bjorgen

Back in June I wrote some ideas of new rules for gems. I started with the Pathfinder Roleplaying Game rules for gems, which provide standard values and some variation.

I wanted a little more detail, though, so I drafted a table that separated ‘size’ and ‘quality’ so they could each be rolled with weighted frequencies (that is, ‘medium’ is more common than ‘tiny’ or ‘huge’, and ‘average’ is more common than ‘flawed’ or ‘excellent’).

This got me closer to where I wanted to be, but there was one thing still bothering me. The base values of the various gem grades grow unevenly.

Grade Name Standard Value
1 Least Semi-Precious 10 gp
2 Lesser Semi-Precious 50 gp
3 Semi-Precious 100 gp
4 Greater Semi-Precious 500 gp
5 Lesser Precious 1,000 gp
6 Greater Precious 5,000 gp

The progression “10, 50, 100, 500, 1,000, 5,000” is not a smooth curve, and the size and quality adjustments (or the random values from the original table) leave gaps in the values. I prefer a smoother progression (similar thoughts led to the smoother damage progression I posted about this time last year) that transitions between the different grades. I’ve got a couple of progressions in mind.

The first has the value of stone multiply by five every six steps, which means that a lower stone increased by three steps or a higher stone decreased by three steps will have the same value. For instance, a semi-precious stone (base 100 gp value) that has “+3 value” and a greater semi-precious stone (base 500 gp value) would both have the same value: 223 gp.

The second has a shallower curve and spans two steps on the base table, and the value of a stone is multiplied by ten every twelve steps. This would span two grades in the original table (semi-precious, 100 gp, to lesser precious, 1,000 gp), with greater semi-precious at the midpoint between them (316 gp). Each grade is still six steps from the one above or below it, with three steps being the midpoint between those.

Adjustment Exact 5 Exact 10 Approx  5 Approx 10 Ratio 5 Ratio 10
-12 4.00 10.00 4 10 0.04 0.10
-11 5.23 12.12 5 12 0.05 0.12
-10 6.84 14.68 7 14 0.07 0.14
-9 8.94 17.78 9 18 0.09 0.18
-8 11.70 21.54 11 22 0.11 0.22
-7 15.29 26.10 15 26 0.15 0.26
-6 20.00 31.62 20 31 0.20 0.31
-5 26.15 38.31 25 38 0.25 0.38
-4 34.20 46.42 35 46 0.35 0.46
-3 44.72 56.23 45 56 0.45 0.56
-2 58.48 68.13 60 68 0.60 0.68
-1 76.47 82.54 75 82 0.75 0.82
0 100.00 100.00 100 100 1.00 1.00
1 130.77 121.15 130 120 1.30 1.20
2 171.00 146.78 170 145 1.70 1.45
3 223.61 177.83 225 175 2.25 1.75
4 292.40 215.44 290 215 2.90 2.15
5 382.36 261.02 380 260 3.80 2.60
6 500.00 316.23 500 315 5.00 3.15
7 653.83 383.12 650 385 6.50 3.85
8 854.99 464.16 850 465 8.50 4.65
9 1118.03 562.34 1150 560 11.50 5.60
10 1462.01 681.29 1450 680 14.50 6.80
11 1911.81 825.40 1900 825 19.00 8.25
12 2500.00 1000.00 2500 1000 25.00 10.00

These have nice curves, very smooth and consistent, and they scale across all base values the same way. That is, regardless of the value of the stone I put in ‘position 0’, the curve will have the same shape. There is no difference, when using the ‘Exact 5’ method, between starting with a 100 gp stone and adding 6 and 12 to the value (100 gp, 500 gp, and 2,500 gp respectively) and starting with a 500 gp stone and subtracting 6 value, using the base, and adding 6 value (also 100 gp, 500 gp, and 2,500 gp respectively).

Given that I usually prepare things at my computer, it’s no big deal to have a spreadsheet open… but I don’t care for systems that depend on spreadsheets. Looking it over I see some approximations that might work, usually rounded to two or three significant figures. I’d probably still want a calculator, though. Can it be simplified more?

Probably. Given that I’m usually going to be within five points of where I started, I’m going to drop the second option (multiplying or dividing by ten for every twelve steps)

Adjustment Exact 5 Approx  5 Ratio 5 Fraction
-6 20.00 20 0.20 1/5
-5 26.15 25 0.25 1/4
-4 34.20 35 0.35 1/3
-3 44.72 45 0.45 4/9
-2 58.48 60 0.60 6/10
-1 76.47 75 0.75 3/4
0 100.00 100 1.00 1
1 130.77 130 1.30 4/3
2 171.00 170 1.70 10/6
3 223.61 225 2.25 9/4
4 292.40 290 2.90 3
5 382.36 380 3.80 4
6 500.00 500 5.00 5

This gets me down to a total of seven numbers to remember: 1, 4/3, 10/6, 9/4, 3, 4, 5. If I’m reducing quality I simply invert the fractions… and these are fractions I can more or less do in my head (my Grade 9 Maths teacher spent a lot of time drilling us on this sort of thing, thanks Ray!)

Closing Comments

To be completely honest, I don’t know if I’d actually use this in practice. Mathematically I like it, arithmetically it looks like it could be annoying. The approach I described in June (which amounts to “plus or minus ten percent per change”) is simpler, and ‘simpler’ means a lot to me. On the other hand, the fractions above aren’t that difficult for me to work with.

I need to think about this some more, I suppose.

Postscript

I have considered another model that’s even simpler. Each grade of stone is worth three times as much as the previous, and each point of value difference changes the value by ten percent. Thus, each grade at +5 (150% of base) is equal in value to the next grade at -5 (50% of 300% of current base = 150%). It makes for a continuous curve, and relatively simple arithmetic. I’m not as enamored of it, though.