Another dice as resources post: the mathening.

I wanted to test my intuition from last time that the dice expressions I was giving were fair.

So I monte-carlo’d it, results at bottom:

from random import randint as r
import numpy
dice = [20,12,10,8,6,4]

def experiment(i=0, critical=1, failure=3):
  loop = 0
  while True:
  if i>=len(dice):
    return loop
  val = r(1,dice[i])
  if val <= critical: i+=1
  if val <= failure: i+=1
  loop += 1

results = {}

for i in range(len(dice)):
  results[i] = [experiment(i) for j in range(10000)]

for i in range(len(dice)):
  print "d", dice[i], "failed in", \
    numpy.median(results[i]), "median", \
    numpy.mean(results[i]), "mean"

output = """
d 20 failed in 15.0 median 16.3829 mean
d 12 failed in 10.0 median 10.7343 mean
d 10 failed in 7.0 median 7.6144 mean
d 8 failed in 4.0 median 5.0133 mean
d 6 failed in 2.0 median 2.8603 mean
d 4 failed in 1.0 median 1.3304 mean
"""

I kind of like those odds, and I kind of don’t. Mean higher than median means that the winning tail is long — if you go big, you likely go (relatively!) very big — and in all cases, these are numbers that actually come up and matter in play.

The d4 feels very slightly mean — er, I suppose, “cruel” — to me. Its odds of failure are so vast.

I tweaked it and ran the same experiment with 1-2 instead of 1-3 (still “doubling down” on 1s as double failures). Those odds are:

d 20 failed in 20.0 median 22.6337 mean
d 12 failed in 13.0 median 14.7605 mean
d 10 failed in 9.0 median 10.5486 mean
d 8 failed in 6.0 median 7.0481 mean
d 6 failed in 3.0 median 3.9912 mean
d 4 failed in 1.0 median 2.0154 mean

These feel a little fairer to me. There’s a point to rolling, even at the d4 (though, yes, your odds suck). Importantly, the d8 matches the by-the-book 7 charges which a wand should have, so I can use it there. That’s cool.

I’m definitely going to try these out for morale and loyalty — my two hidden NPC stats. I’m also probably going to reintroduce these for wands, scrolls etc.

I could use these for other things, too — death saves feel particularly “fun” to roll on your hit dice, with failures shrinking your hit dice (but not hit points) until such time as you can re-grow them. Wouldn’t work super well for characters whose hit dice are exhausted or multiclass. Might just say “a single instance of your largest hit die, used purely for this tracking mechanism” or something.