%matplotlib inline
import numpy as np
import itertools
import matplotlib.pyplot as plt
import re
import sys

# Copyright (c) 2014, Casey Webster.
# All rights reserved.
# Licensed under BSD 3-clause license.
# get a copy at http://opensource.org/licenses/BSD-3-Clause

def roll(dicestr):
    p = re.compile(r"""
    \(?
    (?P<ndice>\d+)?
    [dD]
    (?P<dtype>\d+)
    (?:\+
    (?P<add>\d+)
    )?
    \)?
    (?:[xX*]
    (?P<mult>\d+)
    )?
    """, re.VERBOSE)
    m = p.match(dicestr)
    if not m:
        raise ValueError("Invalid string contents")
    if m.group('ndice') == None:
        ndice = 1
    else:
        ndice = int(m.group('ndice'))
    dtype = int(m.group('dtype'))
    if m.group('add') == None: 
        add = 0
    else:
        add   = int(m.group('add'))
    if m.group('mult') == None: 
        mult = 1
    else:
        mult  = int(m.group('mult'))
    
    rollinfo(ndice,dtype,add,mult)

def rollinfo(ndice,nsides,add,mult):
    min = (ndice+add)*mult
    max = ((ndice*nsides)+add)*mult
    n = max-min+1
    rolls = list(itertools.product(range(1,nsides+1),repeat=ndice))
    outcomes = len(rolls)
    rolls = [(sum(x)+add)*mult for x in rolls]
    counts = list(np.zeros(n))
    for i in rolls:
        counts[i-min] += 1
    sums = list(range(min,max+1,mult))
    # remove 0-valued elements
    counts = list(filter((0.).__ne__,counts))
    
    #calc probability stuff
    p = [float(x/outcomes)*100 for x in counts]
    ap = np.cumsum(p)
    mean = np.mean(rolls)
    std  = np.std(rolls)
    
    plt.plot(sums,p)    
    plt.fill_between(sums,p,0,where=[(x > mean-std) and (x < mean+std) for x in sums], color='0.75')
    plt.plot([mean,mean],[0,np.max(p)], color='k')
    plt.xlim(min,max)
    plt.ylim(0,np.max(p))
    ax2 = plt.twinx()
    ax2.plot(sums,ap)
    ax2.set_ylim(0,100)
    ax2.set_xlim(min,max)
    
    title="{0}d{1}".format(ndice,nsides)
    if add > 0: title +="+{0}".format(add)
    if mult > 1: title +="*{0}".format(mult)
    plt.text(0.05,0.90,title, size='x-large', transform=ax2.transAxes)
    plt.text(0.05,0.85,r"$\mu$ = {0}".format(mean), transform=ax2.transAxes)
    plt.text(0.05,0.80,r"$\sigma$ = {0:1.2f}".format(std), transform=ax2.transAxes)
    plt.text(0.05,0.75,r"range = [{0}-{1}]".format(min,max), transform=ax2.transAxes)
    #plt.xticks([np.arange(min,mean+1,1),np.arange(mean,max,1)])

roll("2d6")

roll("(3d6+6)*2")

roll("4d6")

roll("4d6+6")

roll("5d8")

roll("d20")

roll("4d10*10")