dice_distribution.py

import sys
import itertools
import numpy as np
from collections import Counter
from matplotlib import pyplot as plt

def dice_prob(n):
    sides = [(1,2,3,4,5,6) for x in xrange(n)]
    combined = itertools.product(*sides)
    sums = [sum(i) for i in combined]
    pop = len(sums)
    pairs = Counter(sums)
    
    for value, times in pairs.iteritems(): 
        pairs[value] = times * 1.0 / pop
        
    return pairs

def graph(n):
    data = dice_prob(int(n))
    x = []
    y = []

    for value, prob in data.iteritems():
        x.append(value)
        y.append(prob)

    minx = min(x)
    maxx = max(x)
    maxy = max(y)

    plt.xticks(np.arange(minx, maxx+1, 1))
    plt.yticks(np.arange(0.0, maxy, 0.005))

    plt.scatter(x, y, color="blue")
    plt.show()

if __name__ == "__main__":
    graph(sys.argv[1])