One of my friends, mellonbread, wrote up a dungeoncrawling game. If you follow the blog, you've seen me mention it before. I've been helping him turn it into a complete system by writing up a bestiary. Most of my inspiration was drawn from B/X, though I grabbed some cool monsters from AD&D and other editions and retroclones. A lot of these monsters are people, or rather, humans with class levels.
This poses a particular problem for magic-users, as their spell selections are to be determined randomly. Lots of other games make this pretty easy. A wizard has a number of spells of a certain level that they can cast per day. You consult the table and roll up the appropriate amount of spells. WotC made it even simpler in 5e by giving archmages and priests set spell lists in their statblocks.
However, that doesn't work for Begone. There aren't any spell slots per day of a certain level. It's more vancian than any TSR or WotC edition of D&D ever was. The more powerful you are, the more powerful spells you can hold in your head. This could either by one big spell, a lot of little spells, or a mix of something in between. So how do we decide what "loadout" a wandering wizard has?
We could take the easy route and directly port over the spells, but that would result in magic-users that vastly outpower characters of a similar level. Wizards in B/X are limited to lower level spells than Begone characters with MIND are, but they still have many more spells. A fifth level MU has two 1st level spells, two 2nd level spells, and one 1st level spell. A Begone character would need 9 MIND to carry all that magic around, and at fifth level, they can only have 6 MIND, and that's assuming they rolled MIND for their starting stat and only took MIND upgrades since. This discrepancy only grows with higher levels.
Instead, we run up against a very tricky math problem. For any given N, what is the set of sets of positive integers that add to N? To break that down into more layman's terms, we're looking for all the different combinations of numbers that add to a different number. Because that's what this problem about spell slots is all about. 3 MIND can hold three 1st level spells, a 2nd level spell and a 1st level spell, or one 3rd level spell. Fortunately, this math problem has a name and has already been solved by some very smart people. It's called the partition problem.
I found the partitions for N=1 to 12 to represent wizards of levels 1 to 12. Theoretically B/X goes up to 14 so the most powerful wizard would have 14 MIND, but I was tired. Also, you can determine the exact level of name level NPCs in a castle with D4+8 for 9-12 (name level being 9th level, the level where you get a cool castle and a bunch of followers). Yes, I could generate 9-14 with D6+8 but again, I was tired.
So I found the partition solutions and painstakingly copied them down because most of them were stored as PNGs and other images. I ignored anything that had a number greater than 6 in it, partially because B/X spells only go up to sixth level, but also because I think even in AD&D, those higher level spells can either be adjusted down for 6th level or are boring. Because I am insane, I also decided to make all these roll tables weighted. The more powerful spells the sets held, the less likely a wizard would have them. Eg: five 1st level spells would be a more common loadout result than one 5th level spell for a 5th level wizard.
(1,1,1,1), (1,1,2), (1,3), (2,2), (4)
I did this by taking N and dividing it by the length of the set, AKA: the number of spells the wizard has.
(1,1,1,1):1, (1,1,2):1.333, (1,3):2, (2,2):2, (4):4
Then I divided each of those "frequency ratings" into the largest FR to figure out how relatively likely they were.
1:4, 1.333:3, 2:2, 4:1
Then you multiply those relative likelihoods by the amount of sets that exist. There's only one 1 FR, so you have 4, then you add 3 for the one 1.333 FR, then 2x2 for the two 2 FR sets, and then add 4 for the last one. That brings you to 12.
The likelihoods tell you how many of that range belong to a specific set. The range handily corresponds to a D12 so we can use this to create a roll table. Unfortunately, past N=4, the probabilities don't match up nicely to die sizes, so I had to fudge a lot of numbers into the closest approximations.
Here are the roll tables below. All you have to do is roll the appropriate die for the MIND that the wizard has. That'll give you their spell loadout. Then once you know how many spells of which levels they have, you can roll for those.
1 MIND (1 option)
D1: 1: (1)
2 MIND (2 options)
D2: 1: (1,1), 2: (2)
3 MIND (3 options)
D6: 1-3: (1,1,1), 4-5: (2,1), 6: (3)
4 MIND (5 options)
D12: 1-4: (1,1,1,1), 5-7: (2,1,1), 8-9: (2,2), 10-11: (3,1), 12: (4)
5 MIND (7 options)
D20: 1-5: (1,1,1,1,1), 6-9: (2,1,1,1), 10-12: (2,2,1), 13-15: (3,1,1) 16-17: (2,3), 18-19: (4,1), 20: (5)
6 MIND (11 options)
D100: 1-15: (1,1,1,1,1,1), 16-28: (2,1,1,1,1), 29-39: (2,2,1,1), 40-50: (3,1,1,1), 51-59: (2,2,2), 60-68: (3,2,1), 69-77: (4,1,1), 78-84: (3,3), 85-90: (4,2), 91-96: (5,1), 97-100: (6)
7 MIND (14 options)
D100: 1-13: (1,1,1,1,1,1,1), 14-25: (2,1,1,1,1,1), 26-35: (2,2,1,1,1), 36-45: (3,1,1,1,1), 46-54: (2,2,2,1), 55-61: (3,2,1,1), 62-68: (4,1,1,1), 69-73: (3,2,2), 74-78: (3,3,1), 79-83: (4,2,1), 84-88: (5,1,1), 89-92: (4,3), 93-96: (5,2), 97-100: (6,1)
8 MIND (20 options)
D100: 1-8: (1,1,1,1,1,1,1,1), 9-16: (2,1,1,1,1,1,1), 17-22: (2,2,1,1,1,1), 23-28: (3,1,1,1,1,1), 29-34: (2,2,2,1,1), 35-40: (3,2,1,1,1), 41-46: (4,1,1,1,1), 47-51: (2,2,2,2), 52-56: (3,2,2,1), 57-61: (3,3,1,1), 62-66: (4,2,1,1), 67-71: (5,1,1,1), 72-75: (3,3,2), 76-79: (4,2,2), 80-83: (4,3,1), 84-87: (5,2,1), 89-91: (6,1,1), 92-94: (4,4), 95-97: (5,3), 98-100: (6,2)
9 MIND (26 options)
1D100: 1-9: (1,1,1,1,1,1,1,1,1), 10-15: (2,1,1,1,1,1,1,1), 16-20: (2,2,1,1,1,1,1), 21-25: (3,1,1,1,1,1,1), 26-30: (2,2,2,1,1,1), 31-35: (3,2,1,1,1,1), 36-40: (4,1,1,1,1,1), 41-44: (2,2,2,2,1), 45-48: (3,2,2,1,1), 49-52: (3,3,1,1,1), 53-56: (4,2,1,1,1), 57-60: (5,1,1,1,1), 61-63: (3,2,2,2), 64-66: (3,3,2,1), 67-69: (4,2,2,1), 70-72: (4,3,1,1), 73-75: (5,2,1,1), 76-78: (6,1,1,1), 79-81: (3,3,3), 82-84: (4,3,2), 85-87: (4,4,1), 89-90: (5,2,2), 91-93: (5,3,1), 94-96: (6,2,1), 97-98: (5,4), 99-100: (6,3)
10 MIND (34 options)
D100: 1-5: (1,1,1,1,1,1,1,1,1,1), 6-10: (2,1,1,1,1,1,1,1,1), 11-15: (2,2,1,1,1,1,1,1), 16-20: (3,1,1,1,1,1,1,1), 21-24: (2,2,2,1,1,1,1), 25-28: (3,2,1,1,1,1,1), 29-32: (4,1,1,1,1,1,1), 33-36: (2,2,2,2,1,1), 37-40: (3,2,2,1,1,1), 41-44: (3,3,1,1,1,1), 45-48: (4,2,1,1,1,1, 49-52: (5,1,1,1,1,1), 53-55: (3,2,2,2,1), 56-58: (3,3,2,1,1), 59-61: (4,2,2,1,1), 62-64: (4,3,1,1,1), 65-67: (5,2,1,1,1), 68-70: (6,1,1,1,1), 71-72: (3,3,2,2), 73-74: (3,3,2,2), 75-76: (4,2,2,2), 77-78: (4,3,2,1), 79-80: (4,4,1,1), 81-82: (5,2,2,1), 83-84: (5,3,1,1), 85-86: (6,2,1,1), 87-88: (4,3,3), 89-90: (4,4,2), 91-92: (5,3,2), 93-94: (5,4,1), 95-96: (6,2,2), 97-98: (6,3,1), 99: (5,5), 100: (6,4)
11 MIND (44 options)
D100: 1-6: (1,1,1,1,1,1,1,1,1,1,1), 7-11: (2,1,1,1,1,1,1,1,1,1), 12-15: (2,2,1,1,1,1,1,1,1), 16-19: (3,1,1,1,1,1,1,1,1), 20-22: (2,2,2,1,1,1,1,1), 23-25: (3,2,1,1,1,1,1,1), 26-28: (4,1,1,1,1,1,1,1), 29-31: (2,2,2,2,1,1,1), 32-34: (3,2,2,1,1,1,1), 35-37: (3,3,1,1,1,1,1), 38-40: (4,2,1,1,1,1,1), 41-43: (5,1,1,1,1,1,1), 44-45: (2,2,2,2,2,1), 46-47: (3,2,2,2,1,1), 48-49: (3,3,2,1,1,1), 50-51: (4,2,2,1,1,1), 52-53: (4,3,1,1,1,1), 54-55: (5,2,1,1,1,1), 56-57: (6,1,1,1,1,1), 58-59: (3,2,2,2,2), 60-61: (3,3,2,2,1), 62-63: (3,3,3,1,1), 64-65: (4,2,2,2,1), 66-67: (4,3,2,1,1), 68-69: (4,4,1,1,1), 70-71: (5,2,2,1,1), 72-73: (5,3,1,1,1), 74-75: (6,2,1,1,1), 76-77: (3,3,3,2), 78-79: (4,3,2,2), 80-81: (4,3,3,1), 82-83: (4,4,2,1), 84-85: (5,2,2,2), 86-87: (5,3,2,1), 88-89: (5,4,1,1), 90-91: (6,2,2,1), 93: (6,3,1,1), 94: (4,4,3), 95: (5,3,3), 96: (5,4,2), 97: (5,5,1), 98: (6,3,2), 99: (6,4,1), 100: (6,5)
12 MIND (59 options)
D100: 1-3: (1,1,1,1,1,1,1,1,1,1,1,1), 4-6: (2,1,1,1,1,1,1,1,1,1,1), 7-8: (2,2,1,1,1,1,1,1,1,1), 9-10: (3,1,1,1,1,1,1,1,1,1), 11-12: (2,2,2,1,1,1,1,1,1), 13-14: (3,2,1,1,1,1,1,1,1), 15-16: (4,1,1,1,1,1,1,1,1), 17-18: (2,2,2,2,1,1,1,1), 19-20: (3,2,2,1,1,1,1,1) , 21-22: (3,3,1,1,1,1,1,1), 23-24: (4,2,1,1,1,1,1,1), 25-26: (5,1,1,1,1,1,1,1), 27-28: (2,2,2,2,2,1,1), 29-30: (3,2,2,2,1,1,1), 31-32: (3,3,2,1,1,1,1), 33-34: (3,3,2,1,1,1,1), 35-36: (4,2,2,1,1,1,1), 37-38: (4,3,1,1,1,1,1), 39-40: (5,2,1,1,1,1,1), 41-42: (6,1,1,1,1,1,1), 43-44: (2,2,2,2,2,2), 45-46: (3,2,2,2,2,1), 47-48: (3,3,2,2,1,1), 49-50: (3,3,3,1,1,1), 51-52: (4,2,2,2,1,1), 53-54: (4,3,2,1,1,1), 55-56: (4,4,1,1,1,1), 57-58: (5,2,2,1,1,1), 59-60: (5,2,2,2,1), 61-62: (5,3,1,1,1,1), 63-64: (6,2,1,1,1,1), 65-66: (3,3,2,2,2), 67-68: (3,3,3,2,1), 69-70: (4,2,2,2,2), 71-72: (4,3,2,2,1), 73-74: (4,3,3,1,1), 75-76: (4,4,2,1,1), 77-78: (5,3,2,1,1), 79-80: (5,4,1,1,1), 81: (6,2,2,1,1), 82: (6,3,1,1,1), 83: (3,3,3,3), 84: (4,3,3,2), 85: (4,4,2,2), 86: (4,4,3,1), 87: (5,3,2,2), 88: (5,3,3,1), 89: (5,4,2,1), 90: (5,5,1,1), 91: (6,2,2,2), 92: (6,3,2,1), 93: (6,4,1,1), 94: (4,4,4), 95: (5,4,3), 96: (5,5,2), 97: (6,3,3), 98: (6,4,2), 99: (6,5,1), 100: (6,6)
If you want an automated version of the above, you can use these links below. They'll create a popup window that tells you how many spells of what level a wizard with N MIND has prepared. The later ones are also more accurate to the probabilities required by my method.
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