#!/usr/bin/env python3
# calculate outcomes of 3d6

import random

d6 = range(1,6+1)

def roll_d6():
    return random.choice(d6)

def probability_distribution():
    result = {}
    for d1 in range(1,7):
        for d2 in range(1,7):
            for d3 in range(1,7):
                try:
                    result[d1+d2+d3] += 1
                except KeyError:
                    result[d1+d2+d3] = 1
    return result

dist = probability_distribution()
sum_ = sum(dist.values())

# calculate Expected value from probability distribution
Ex = 0
for k,v in dist.items():
    print(k,v,v/sum_,k*v/sum_)
    Ex += k*v/sum_
print(Ex)

# game it out with the average result of many 3d6 rolls
rolls = [roll_d6()+roll_d6()+roll_d6() for i in range(4096)]
print(sum(rolls) / len(rolls))