import numpy as np
import random
from matplotlib import pyplot as plt

def random_sum(nlist=[6,8,8]):
    domainlist = [[1+x for x in range(n)] for n in nlist]
    choicelist = [random.choice(domain) for domain in domainlist]
    return sum(choicelist)

def trial(nlist=[6,8,8], num_samples=1000):
    data = []
    for n in range(num_samples):
        data += [random_sum(nlist=nlist)]
        if n%100000==0:
            print str(float(n)/num_samples*100)+'% complete'
    plt.xlim([min(data)-0.5, max(data)+0.5])
    bins = [1.5+n for n in range(sum(nlist))]
    plt.hist(data, bins=bins, alpha=0.5, normed=True)
    plt.title('{0} rolls with dice of sides {1}'.format(*[num_samples, nlist]))
    plt.xlabel('sum')
    plt.ylabel('frequency')
    plt.show()