What's my chance at Paladin? Gnome illusionist?: AD&D Character Gen Statistics Wizardry, Pt. 1

When we rolled up characters for my current AD&D 1e campaign, one player rolled the ideal Paladin. 17 chararisma. 17 dex. Everything else you could want. Another player made ranger. A third player was hoping for a gnome illusionist, and though I was rooting for him, the the dice didn't deliver. Then there was some talk along the lines of, "huh, what are the odds?" Well, our would-be gnome illusionist (and real-life math wiz) set off to find the answer, and here, gentle reader, are the cold hard facts. All credit goes to him.

I had the players use a fairly standard system to make characters. They rolled stats in order, rolling 4d6 and keeping the sum of the highest 3. I also let them roll five characters total and keep one to play and one as a backup. This seemed to me middle-of-the-road in terms of how brutal the odds stacked against the characters, and even with the allowance of a pool of characters to choose from, less easy-going than just about any method that lets players arrange stats to their liking afterward.

In this first of three posts, I present the breakdown of what your chance is to be which character, according to a million simulated stat lines and using the method of rolling 4d6, keep the highest three, stats rolled in order. Here are the numbers looking strictly at class.

Class	% chance of eligibility
thief	85.45
cleric	85.43
magicuser	85.42
fighter	84.01
assassin	27.17
druid	13.60
ranger	2.94
illusionist	2.92
paladin	1.40
monk	0.91

And here is what it looks like listed by class and race. This gives the chance at every possible character.

Character type	% chance of eligibility
human thief	85.45
half-elf thief	85.45
human cleric	85.43
half-elf magicuser	85.42
human magicuser	85.42
half-elf cleric	84.44
human fighter	84.01
half-elf fighter	83.95
gnome thief	80.18
gnome fighter	79.23
elf magicuser	77.75
elf thief	76.49
elf fighter	75.59
halfling thief	67.77
halfling fighter	67.04
dwarf fighter	58.27
dwarf thief	58.24
half-elf assassin	27.17
human assassin	27.17
gnome assassin	25.91
elf assassin	25.21
half-orc fighter	23.06
half-orc cleric	22.46
half-orc thief	22.44
dwarf assassin	19.25
half-elf druid	13.60
human druid	13.60
half-orc assassin	5.89
human ranger	2.94
half-elf ranger	2.94
human illusionist	2.92
gnome illusionist	2.75
human paladin	1.40
human monk	0.91

Glaringly obvious findings:

• You have just a 1.4 % chance of being a paladin, and though you are twice as likely to be eligible to be a gnome illusionist, the odds are against you in a big way for either.
• The monk is the rarest of characters.
• I can dispell any doubt I had as to whether I was being a softy GM for giving the players five stat lines to choose from.

If you have other thoughts or insights, please share them in the comments!

Stay tuned next week for the next in the series of posts! My friend expands the inquiry to compare various popular methods of character generation presented in the 1e Dungeon Masters Guide.