Calculations for non-associativity of dice

1d6d6d6.py

#!/usr/bin/env python3

import collections

class DiscreteProbabilityDistribution:
    def __init__(self, pdict):
        try:
            self.pdict = collections.Counter(pdict)
        except:
            self.pdict = collections.Counter({pdict: 1})
    def __add__(self, other):
        pdict = collections.Counter() 
        for i, p in self.pdict.items():
            for j, q in other.pdict.items():
                pdict[i+j] += p*q
        return DiscreteProbabilityDistribution(pdict)
    def __repr__(self):
        return repr(self.pdict)
    def mean(self):
        return sum(i*p for i,p in self.pdict.items())

DPD = DiscreteProbabilityDistribution

def d(D):
    pdict = collections.Counter()
    try:
        D.pdict
    except AttributeError:
        D=DPD(D)
    for i, p in D.pdict.items():
        for j in range(1,i+1):
            pdict[j] += p*(1/i)
    return DPD(pdict)


def multi(N, D):
    pdict = collections.Counter()
    try:
        N.pdict
    except AttributeError:
        N=DPD(N)
    Y = max(N.pdict.keys())
    x = DPD(0)
    for i in range(Y+1):
        for j, p in x.pdict.items():
            pdict[j] += p * N.pdict[i]
        x = x+D
    return DPD(pdict)
       
print("((1d6)d6)d6: {:f}".format(multi(multi(d(6), d(6)), d(6)).mean()))
print("(1d6)d(6d6): {:f}".format(multi(d(6), d(multi(6, d(6)))).mean()))
print("1d(6d(6d6)): {:f}".format(d(multi(6, d(multi(6, d(6))))).mean()))