dice percent calc.py

# author: github.com/zardoru
# usage: python3 script.py dicecount dicesides

from math import floor
from scipy.misc import comb

import sys

# source:
# http://mathworld.wolfram.com/Dice.html
# equation 10
def probability(points, dice, sides):
    div = 1 / (sides ** dice)

    limit = floor((points - dice) / sides)
    sumval = 0
    for k in range(0, limit + 1):
        sign = (-1) ** k
        tcombination = comb(points - sides * k - 1, dice - 1)
        sumval += sign * comb(dice, k) * tcombination

    return sumval * div

dicecount = int(sys.argv[1])
dicesides = int(sys.argv[2])

minroll = dicecount
maxroll = dicesides * dicecount + 1
totalsum = 0
print("{:3} {:^9} {:^10}".format("sum", "chance", "at most"))
for i in range(minroll, maxroll):
    value = probability(i, dicecount, dicesides) * 100
    totalsum += value
    print("{:3d} {:>9.6f} {:>10.6f}".format(i, value, totalsum))