Calculate a probability distribution of totals acquired from rolling an arbitrary number of dice, each with an arbitrary configuration of non-negative, integer face values.

DiceProb.py

import re

dice = [] #Input dice as polynomial coefficients	

print "Enter face values as non-negative integers, separated by spaces, commas, or semicolons. (e.g. \"1,2;3 4 5 6\")"
while True:
	rawdie = [] #List of face values
	qty = 1 #Quantity of a single die spec

	inp = raw_input("Die " + str(len(dice) + 1) + "? ")
	if inp == "":
		break
	#rawdie = [int(face) for face in inp.split(" ")]
	rawdie = [int(face.strip()) for face in re.split(" |,|;", inp) if face.strip()]
	qty = raw_input("Quantity? [1] ")

	if qty == "":
		qty = 1
	else:
		qty = int(qty)

	die = [0] * (max(rawdie) + 1)
	for i in rawdie:
		die[i] += 1

	dice += [die for i in range(qty)]

	print(str(rawdie) + " x " + str(qty))

lastresult = dice[0]

for current in dice[1:]:
	result = [0] * (len(lastresult) + len(current) - 1)
	for x, v1 in enumerate(lastresult):
		if v1 == 0:
			continue
		for y, v2 in enumerate(current):
			result[x + y] += v1 * v2
	lastresult = result

skipzero = True
p = 0.0
fcum = 0.0
for i in lastresult:
	p += i

print "Permutations: {:.0f}".format(p)
print "{:<6} {:<12} {:>10} {:>10} {:>10}".format("Total","Freq","Prob", "p>=", "p<=")
for i, f in enumerate(lastresult):
	fcum += f
	if f == 0 and skipzero:
		continue
	skipzero = False
	print "{:<6} {:<12} {:>10.3%} {:>10.3%} {:>10.3%}".format(i, f, f / p, (p - fcum + f) / p, fcum / p)