OSR: Treasure Curves & Generation Procedures

Work continues on the Treasure Overhaul, and that means math.

Part 1: Gem and Jewellery Generation

The book will include treasure tables, so I've spent quite a bit of time digging into their function, their challenges, and their deceptive math.

Treasure Type A is bandit treasure. Sure, in AD&D it's also associated with the Lich, Locathah, Troglodytes, and the Giant Squid, but it is, in most system that include treasure tables, A is "the chest at the heart of the encampment" treasure. It's a useful point of comparison. We'll ignore coins and magic items for the time being.

OD&D: 50% chance of 6x1d6 gems /  50% chance of 6x1d6 pieces of jewellery
AD&D: 60% chance of 4x1d10 gems / 60% chance of 4x1d10 pieces of jewellery
OSE:  50% chance of 6d6 gems /  50% chance of 6d6 pieces of jewellery*
TO: 50% chance of 6d6 gems /  50% chance of 6d6 pieces of jewellery*

*The average of 6d6 and 6x1d6 is the same: 21, but the distribution changes significantly. OSE's treasure results fall in the middle of a curve instead of spreading out. 

 Yanping Wang, Sand

Gem Procedure

I started with:

For each gem or batch of 5 or 10 gems: 
1d20
1-4: 10gp
5-9: 50gp
10-14: 100gp
15-18: 500gp
19: 1,000gp
20: 5,000gp

For each gem or batch with a roll of 15+, roll an additional d20. 
1-16: No effect
17-19: x2
20: x10

This procedure looks good. It passes the back-of-a-napkin math test. But it doesn't pass the complicated math test. 

When simulated, the results look like this:

I've charted them alongside OD&D, AD&D, and OSE's gem results for Type A treasure.OSE has a small gem value table and no way to increase a rolled value. It's tidy, but it's flat. 

You can see that the Treasure Overhaul's results spike way higher than the reference systems. Around 15% of results are above 20,000. The general shape looks OK, and the lower end of the range lines up nicely, but it clearly needs some tweaks. 

After some guesswork and tests, the revised procedure looks like this:

For each gem or batch of 5 or 10 gems:
1d20
1-4: 10gp
5-9: 50gp
10-14: 100gp
15-18: 500gp
19: 1,000gp
20: 2,000gp

For each result of 15+, roll an additional d20. 
1-16: No effect
17-19: x2
20: x3

Tweaking the top of the modifier table to x4 results in an overshot. I could fiddle around with the 19 and 20 results on the main table to get the perfect top-of-the-range match, but that pushes the centre of the curve away from OD&D and A&D.

This method does not have a chance to produce extremely high-value gems, unlike OD&D/AD&D's recursive lottery, but it's a surprisingly close match, and it only requires 2 rolls (or one throw). Gem values are capped at 6,000gp, which is plenty for spell purposes (especially in a batch of 10), and the GM is free to combine gems.

I wanted to keep 6 possible outcomes on the d20 table so that each outcome is associated with a different tier of stone, or with one emblematic D&D / spell component stone.

	TO Gems (Original)	TO Gems (Revised)	OD&D Gems A	AD&D Gems A	OSE Gems A
Average:	4,542gp	3,405gp	3,243gp	3,765gp	2,208gp
>3x Avg:	7%	12%	10%	0%	8%
>2x Avg:	11%	17%	14%	17%	24%
# of Gems Avg	10.5	10.5	10.5	15	10.5
Gem Avg.	433gp	324gp	309gp	251gp	210gp

This gem procedure is fairly elegant; you just roll 2 d20s at once and only reference the second one if the first is 15+. I even made the gem type/description tables d12s and d6s, so you can roll a d12 and a d6 in the same handful and get all the results you could possibly need at once, without interference. I could have used a d100 instead of one of the d20s, but testing confirmed that d100 rolls are annoying for batched results.

Censer c.~1500

Jewellery Procedure

As mentioned in my previous post, jewellery is the meat-and-potatoes of OD&D and AD&D treasure table results. 

I started with:

For each gem or batch of 5 or 10 pieces of jewellery: 
1d20
1-5: 200x1d10gp
6-14: 500x1d10gp
15-20: 1000x1d10gp

For each result of 15+, roll an additional d20. 
1-16: No effect
17-19: x2
20: x10 x3

I'd like to use the same modifier table for both Gems and Jewellery, the so table was adjusted accordingly. It turned out to be exactly what the Jewellery table required. I ran a few tests with tweaked values, but it turns out that the results are nearly perfect as-is, post gem revision.

I'll continue to test this system, just in case the highest value needs to be tweaked from 1,000gp to 900gp, but so far the results are very encouraging.

 

	TO Jewellery A	OD&D A	AD&D A	OSE A
Average:	35,524gp	32,858gp	35,902gp	9,342gp
>3x Avg:	10%	9%	10%	4%
>2x Avg:	25%	23%	19%	26%
# of Pieces Avg	10.5	10.5	13.2	10.5
gp/Piece Avg	3,383gp	3,129gp	2,720gp	8,90gp

 

Part 2: OD&D Treasure Comparisons

Here's a comparison of all the major OD&D treasure types. 200 runs each.

I wish OD&D named its treasure types instead of vaguely implying their function, but, thanks to this chart, some of the principles become more clear. Courtney Campbell broke down the AD&D charts here. Here's my take on OD&D. They're not as baffling they first seem.

A is Men (non-nautical, non-desert) and Centaurs. It's a Bandit Lair / Treasury. 

B is Ghouls, Wights, Hydras, and Nixies. Things that kill adventurers by the dozen. It's Loot / Burrow / Gullet items. The magic items are "Weapon, Armour, or Misc. Weapon." Presumably they didn't work.

C is Gargoyles, Lycanthropes, Minotaurs, Pixies, Gnomes, and Ogres. Ogres add +1,000gp. It's Pocket Change. If it doesn't include jewellery (a 75% chance) it's basically worthless.

D is Orcs, Hobgoblins, Gnolls, Trolls, Mummies, Cockatrices, Manticores, Purple Wurms, and Dryads. I'm calling this Traders and Raiders. Portable, practical wealth.

E is Wraiths, Spectres, Gorgons, Wyverns, Elves, Griffons, and Giants. Giants add +5,000gp. It's Better Pocket Change. I'm not totally sold on this as a unique treasure type. More magic items than C, but otherwise, it's just C + gold pieces + better chances.

F is Vampires, Basilisks, Meduae, and Chimeras. It is heavily jewellery-weighted, with 2-24 pieces. and the magic items stipulate "no weapons". This is Glittering Trinkets. Even an immortal vampire eventually gets tired of being stabbed by decorative mantlepiece swords.  

G is Dwarves. Gold and magic items. It's a Dwarven Trove. There's nothing else it could be. Gold, more gems than jewellery, and a good chance of magic items. You can clearly see the steps of the 1d4x10x1,000gp in the blue coin section.

H is Dragons. It's a Hoard. Lots of everything, but (as previously discussed) more gems and jewellery than coins. 

I is Rocs. It's Shiny Things. Jewellery and gems only; stuff a magpie the size of an elephant would loot.

Some of the categories still don't make any sense to me. Why do Griffons get scrolls? Why aren't weapons scattered around a Basilisk, and why do Chimeras need all that jewellery? But despite a few oddities, these charts really helped me get a grip on OD&D's internal logic. AD&D is... another matter.  

Final Notes

I hope this offers some insight into the rigorous (and peculiar) methods that are applied behind the scenes of the Treasure Overhaul. There are plenty of things that I'm happy to eyeball or write from scratch, but if I'm going to include treasure tables, I want them to be as sturdy as possible.   

EDIT: One potential reason why a lot of calculated average values for OD&D Treasure Type A (or conversions based on it) online and my values are so different might lie in the deceitful 6d6 vs 6x1d6 roll. 6d6 and 6x1d6 have the same average of 21... but think about the distribution. The chance of rolling a 36 on 6d6 is 0.2%. The chance of rolling 36 on 6x1d6 is 16.6%. And when we're talking about gems, where each gem can suddenly increase in value...