I've been putting some thought into the design of my mega-dungeon. My plan is to rely fairly heavily on the tables in the original Dungeons & Dragons booklets, but before I get too far in I want to check the math on the dungeon treasure tables. Because treasure is the main method of player character advancement in the game, it's vital that a mega-dungeon has enough treasure to facilitate that advancement for a decent number of characters. So strap in folks, because today I'm crunching some numbers and figuring out, on average, just how much treasure those tables provide. Yep, it's a math post! What else would I do on a lovely summer Sunday afternoon?
Here's the table I'm talking about:
This is the only guidance that original D&D gives for stocking a dungeon with treasure. Many monsters have "treasure types", for randomly generating a large hoard when that monster is encountered in its lair, but those are usually only used for wilderness adventures. For the dungeon, it's the table above, and that's what I'll be crunching the numbers on today.
For starters, let's assume that every dungeon level has 100 keyed areas. This is larger than most levels would normally be, but it makes the math easier for me.
The random monster distribution rule says that a roll of 1-2 on 1d6 for each area will indicate the presence of a monster. So let's assume that we have 33 occupied rooms, and 67 unoccupied. Half of the occupied rooms will have treasure (so 16.5), and 1-in-6 of the unoccupied rooms will have treasure (11.2). This results in 27.7 out of 100 rooms that will have treasure. Let's round that up to 28 rooms with treasure per dungeon level.
As per the table above, every one of the rooms will have silver pieces. Half of them will have gold pieces. The percentages shown indicate how many gems, jewelry, and magic items there will be, but I need to do some more involved math to find the average value of gems and jewelry.
Average Value of Jewelry
Luckily for my sanity, the average value of jewelry doesn't change based on dungeon level. Below is the jewelry value table.
The average value of the first category is 1,050gp; the average value of the middle category is 3,500gp; and the average value of the last category is 5,500gp. If I assume 100 rolls on this table, 20 will be of the lower value, 60 will be of the middle value, and 20 will be of the higher value. If I add all those figures up and divide by 100, that will give the average value of jewelry throughout the dungeon:
(20 x 1,050) + (60 x 3,500) + (20 x 5,500) =
21,000 + 210,000 + 110,000 =
341,000
Divide that figure by the number of pieces of jewelry rolled (100), and we arrive at an average total of 3,410gp. That wasn't too difficult!
Average Value of Gems
As with jewelry, the value of gems doesn't change based on dungeon level, so this also shouldn't be too difficult.
Once again assuming that we generate 100 gems, we would have 10 of 10gp value, 15 of 50gp value, 50 of 100gp value, 15 of 500gp value, and 10 of 1,000gp value. Let's add all of those:
(10 x 10) + (15 x 50) + (50 x 100) + (15 x 500) + (10 x 1,000) =
100 + 750 + 5,000 + 7,500 + 10,000 =
23,350
Divided by 100, that gives an average gem value of 233.5. Simple again! But wait... What fresh horror is this...?
Well, that certainly complicates matters. It's been a long time since I've done this kind of math, but I guess it's time to roll up my metaphorical brain-sleeves and get to work.
Any gem has, of course, a 1-in-6 chance of going up to the next higher value. To go up twice, it has a chance of 1-in-36. Three times is 1-in-216, four times is 1-in-1,296, five times is 1-in-7,776, six times is 1-in-46,656, seven times is 1-in-279,936, eight times is 1-in-1,679,616, nine times is 1-in-10,077,696, and ten times is 1-in-60,466,176. So yes, that means that a 10gp value gem has about a one-in-sixty-million chance of being elevated to the value of 500,000gp. A 1,000gp value gem's chance of the same is 1-in-46,656; still extremely unlikely. But these chances still need to be factored into my average gem value.
To do this, I assumed 100 gems would be rolled, distributed exactly as the table indicates. Then I had to figure out how many of each would be increased to the next value. I'll show my working for the 1,000gp gems below.
Out of 100 gems, ten will have a value of 1,000gp.
1-in-6 (or 1.67) of these gems will increase in value to 5000gp.
1-in-36 (or 0.278) will increase to 10,000gp.
1-in-216 (or 0.0463) will increase to 25,000gp
1-in-1,296 (or 0.007716) will increase to 50,000gp
1-in-7,776 (or 0.001286) will increase to 100,000gp
1-in 46.656 (or 0.0002143) will increase to 500,000gp
This leaves 7.997 that will remain at the base value of 1,000gp
To figure out how much these ten gems would be worth in total, I multiply the number of gems by their value and then add them all together, as follows.
(7.997 x 1,000) + (1.67 x 5,000) + (0.278 x 10,000) + (0.0463 x 25,000) + (0.007716 x 50,000) + (0.001286 x 100,000) + (0.0002143 x 500,000) =
7,997 + 8,350 + 2,780 + 1,157.5 + 385.8 + 128.6 + 107.15 =
20,906.05
That figure of 20,906.05 is the average total value you'd get by rolling ten gems.
I won't bore you all by going through my workings for the other base values, but here are the totals for each:
- Total average value of ten base 10gp gems = 232.08gp
- Total average value of fifteen base 50gp gems = 1,217.32gp
- Total average value of fifty base 100gp gems = 11,343.65gp
- Total average value of fifteen base 500gp gems = 11,723.1gp
- Total average value of ten base 1,000gp gems = 20,906.05gp
Adding the above figures and dividing by 100 gives an average gem value of 454.22gp. I think this is correct, but if anyone who is actually good at maths wants to correct me, feel free.
Thankfully, the hard part is out of the way, and I can get down to calculating the amount of treasure per dungeon level.
DUNGEON LEVEL 1
Remember we have 28 rooms. All of those will have silver (100 x 1d6), and half will have gold (10 x 1d6). 5% will have gems, and 5% will have jewelry (1d6 of each if present). 5% will have a magic item.
- Silver Pieces: 28 rooms x 350sp = 9,800sp
- Gold Pieces: 14 rooms x 35gp = 490gp
- Gems: 1.4 rooms x 3.5 gems = 4.9 gems x 454.22gp average value = 2,225.69gp
- Jewelry: 1.4 rooms x 3.5 pieces of jewelry = 4.9 pieces of jewelry x 3,410gp average value = 16,709gp
- Average number of Magic Items: 1.4
- Total Experience Points from Treasure = 20,404.69
This is enough to get any character to level 5, or ten fighters or clerics to level 2 (magic-users would reduce that figure slightly. That seems about right to me, but the magic item number seems very low.
DUNGEON LEVELS 2-3
28 rooms, all of those will have silver (100 x 1d12), and half will have gold (100 x 1d6). 10% will have gems, and 10% will have jewelry (1d6 of each if present). 5% will have a magic item.
- Silver Pieces: 28 rooms x 650sp = 18,200sp
- Gold Pieces: 14 rooms x 350gp = 4,900gp
- Gems: 2.8 rooms x 3.5 gems = 9.8 gems x 454.22gp average value = 4,451.37gp
- Jewelry: 2.8 rooms x 3.5 pieces of jewelry = 9.8 pieces of jewelry x 3,410gp average value = 33,418gp
- Average number of Magic Items: 1.4
- Total Experience Points from Treasure = 44,589.37
- Cumulative Dungeon XP Total (level 2) = 64,994.06
- Cumulative Dungeon XP Total (level 3) = 109,583.43
A four-person party that's cleared level 2 would be around 4th or 5th level, and one that's cleared level 3 would be around 5th or 6th. That's a little more than I'd like. But let's assume that some of this treasure won't be found, and a single party won't clear out every encounter. Ideally I'd want multiple parties adventuring in my mega-dungeon. This level of treasure would get 25 to 43 characters to 2nd level by the end of dungeon level 2, and 21 to 36 characters to 3rd level by the end of dungeon level 3.
DUNGEON LEVELS 4-5
28 rooms, all of those will have silver (1,000 x 1d6), and half will have gold (200 x 1d12). 20% will have gems, and 20% will have jewelry (1d6 of each if present). 10% will have a magic item.
- Silver Pieces: 28 rooms x 3,500sp = 98,000sp
- Gold Pieces: 14 rooms x 1,500gp = 21,000gp
- Gems: 5.6 rooms x 3.5 gems = 19.6 gems x 454.22gp average value = 8,902.75gp
- Jewelry: 5.6 rooms x 3.5 pieces of jewelry = 19.6 pieces of jewelry x 3,410gp average value = 66,836gp
- Average number of Magic Items: 2.8
- Total Experience Points from Treasure = 106,538.75
- Cumulative Dungeon XP Total (level 4) = 216,122.18
- Cumulative Dungeon XP Total (level 5) = 322,660.93
Our theoretical and thorough party of 4 would all be 7th or 8th level by the end of level 5. Treasure up through dungeon level 4 is enough to get 21 to 36 characters to 4th level, and up through dungeon level 5 it's enough to get 16 to 26 characters to 5th level.
DUNGEON LEVELS 6-7
28 rooms, all of those will have silver (2,000 x 1d6), and half will have gold (500 x 1d6). 30% will have gems, and 30% will have jewelry (1d6 of each if present). 15% will have a magic item.
- Silver Pieces: 28 rooms x 7,000sp = 196,000sp
- Gold Pieces: 14 rooms x 1,750gp = 24,500gp
- Gems: 8.4 rooms x 3.5 gems = 29.4 gems x 454.22gp average value = 13,354.13gp
- Jewelry: 8.4 rooms x 3.5 pieces of jewelry = 29.4 pieces of jewelry x 3,410gp average value = 100,254gp
- Average number of Magic Items: 4.2
- Total Experience Points from Treasure = 157,708.13
- Cumulative Dungeon XP Total (level 6) = 480,369.06
- Cumulative Dungeon XP Total (level 7) = 638,077.19
Our four-person party by the end of dungeon level 7 would be 8th or 9th level. Treasure up through dungeon level 6 is enough to get 13 to 19 characters to 6th level. Up through dungeon level 7 has enough to get 9 to 12 characters to 7th level. Things are dramatically slowing down as the XP requirements get steeper.
DUNGEON LEVELS 8-9
28 rooms, all of those will have silver (5,000 x 1d6), and half will have gold (1,000 x 1d6). 40% will have gems, and 40% will have jewelry (1d12 of each if present). 20% will have a magic item.
- Silver Pieces: 28 rooms x 17,500sp = 490,000sp
- Gold Pieces: 14 rooms x 3,500gp = 49,000gp
- Gems: 11.2 rooms x 6.5 gems = 72.8 gems x 454.22gp average value = 33,067.36gp
- Jewelry: 11.2 rooms x 6.5 pieces of jewelry = 72.8 pieces of jewelry x 3,410gp average value = 248,248gp
- Average number of Magic Items: 5.6
- Total Experience Points from Treasure = 379,315.36
- Cumulative Dungeon XP Total (level 8) = 1,017,392.55
- Cumulative Dungeon XP Total (level 9) = 1,396,707.91
The four-person party will all be name level (around 10th or 11th) by the end of dungeon level 9. Treasure up through dungeon level 8 is enough to get 8 to 13 characters to 8th level. Up through dungeon level 9 has enough to get 5 to 13 characters to 9th level.
DUNGEON LEVELS 10-12
28 rooms, all of those will have silver (5,000 x 1d6), and half will have gold (2,000 x 1d6). 50% will have gems, and 50% will have jewelry (1d12 of each if present). 25% will have a magic item.
- Silver Pieces: 28 rooms x 17,500sp = 490,000sp
- Gold Pieces: 14 rooms x 7,000gp = 98,000gp
- Gems: 14 rooms x 6.5 gems = 91 gems x 454.22gp average value = 41,334.2gp
- Jewelry: 14 rooms x 6.5 pieces of jewelry = 91 pieces of jewelry x 3,410gp average value = 310,310gp
- Average number of Magic Items: 7
- Total Experience Points from Treasure = 498,644.2
- Cumulative Dungeon XP Total (level 10) = 1,895,352.11
- Cumulative Dungeon XP Total (level 11) = 2,393,996.31
- Cumulative Dungeon XP Total (level 12) = 2,892,640.51
DUNGEON LEVELS 13 and below
28 rooms, all of those will have silver (10,000 x 1d6), and half will have gold (5,000 x 1d6). 50% will have gems, and 50% will have jewelry (1d12 of each if present). 30% will have a magic item.
- Silver Pieces: 28 rooms x 35,000sp = 980,000sp
- Gold Pieces: 14 rooms x 17,500gp = 245,000gp
- Gems: 14 rooms x 6.5 gems = 91 gems x 454.22gp average value = 41,334.2gp
- Jewelry: 14 rooms x 6.5 pieces of jewelry = 91 pieces of jewelry x 3,410gp average value = 310,310gp
- Average number of Magic Items: 8.4
- Total Experience Points from Treasure = 694,644.2
- Cumulative Dungeon XP Total (level 13) = 3,587,284.71
THOUGHTS ON THE NUMBERS
The figures above certainly look sufficient to provide enough advancement for a large number of characters. The thing is, I very much doubt that I'll be designing dungeons with 100 keyed areas per level. Maybe I'll approach that on the first few levels, but I expect that the lower it gets the smaller the levels will get. I may be able to supplement this with side levels here and there. But I think that averaging about 60 keyed areas per level might be enough, especially given that dungeon adventuring isn't going to be the sole means of advancement (and also remembering that monster XP is a factor as well, and modifiers due to prime requisites).
I'm a bit concerned about the number of magic items, though. It comes to a total of 58.8 across the whole dungeon, which doesn't seem so bad... but that's very concentrated to the deeper levels. The first three dungeon levels would have about 4, spread over 300 keyed areas... It's quite sparse.
WAYS OF MODIFYING THE NUMBERS
I was thinking that if treasure seems a bit slim, I could use the Treasure Types in areas that have enough monsters to warrant it. I could do this when any group of monsters reaches the number range indicated for a wilderness encounter in Vol. 2 (or maybe by rolling for % in Lair whenever this is the case). This would create some larger treasure hoards here and there, if I feel like they're necessary. The rules suggest that the referee should place some treasure caches before turning to random distribution, so of course my own judgment is always something to fall back on. But I like to systematise these things as much as I can.
As for magic items, that could be alleviated by using the treasure tables as above. I could also roll for magic items whenever a fighting-man, cleric, or magic-user is suggested as an encounter. The entry for Bandits has a method for generating magic items for these types of characters, and that would be a good way to juice up the number of items in the game. I worry that it might tip things over too far in the other direction, but this is all a learning process.
Well, that was time consuming; my sunny summer Sunday afternoon has gone, and now it's well past time I need to find some food. As I said before, if any math-heads stumble over this post, I'd appreciate any corrections. That means you, Dan "Delta" Collins! Anyway, time for some Nando's I think. My brain has earned it.
No comments:
Post a Comment