1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 #! /bin/python2 # die-probability.py: a collection of tests about the theory of probability # see: http://alimsvi.ir/blog/posts/ehtemal-dar-python-1.html # Copyright (c) 2015 Ali Mousavi # # Permission is hereby granted, free of charge, to any person obtaining a copy # of this software and associated documentation files (the "Software"), to deal # in the Software without restriction, including without limitation the rights # to use, copy, modify, merge, publish, distribute, sublicense, and/or sell # copies of the Software, and to permit persons to whom the Software is # furnished to do so, subject to the following conditions: # # The above copyright notice and this permission notice shall be included in # all copies or substantial portions of the Software. # # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR # IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, # FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE # AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER # LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, # OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE # SOFTWARE. from matplotlib import pyplot import random def roll_die(num_sides, true_random=False): '''simulates rolling a die, if true_random is set, it will use random.org to produce true random numbers. be careful though, it might take a lot of time and the difference is really not that much.''' if true_random is True: import randomdotorg r = randomdotorg.RandomDotOrg('alimsvi.ir') return r.randrange(1, num_sides + 1) return random.randrange(1, num_sides + 1) def plot_fairness_line(num_sides, max_trials, step, side): '''tests the difference between expected average and the real average produced after rolling a die for a range of trials.''' diff_data = [] num_trials_data = [] for num_trials in range(1, max_trials, step): side_count = 0 for dummy_idx in range(num_trials): result = roll_die(num_sides) if result == side: side_count += 1 statistical_prb = 1.0 / 6 computed_prb = side_count / float(num_trials) diff_data.append(computed_prb - statistical_prb) num_trials_data.append(num_trials) pyplot.plot(num_trials_data, diff_data) pyplot.xlabel("Number of trials ran on dice.") pyplot.ylabel("Difference between expected and computed results") pyplot.grid(True) pyplot.ylim((-0.5, 0.5)) pyplot.title("Fairness of a Die in Python") pyplot.show() plot_fairness_line(6, 10000, 10, 2) def plot_fairness_bar(num_sides, num_trials, true_random=False): '''rolls the die for "num_trials" times and calculates the number of times each side of the die was shown, it then shows a bar plot''' data = {key: 0 for key in range(1, num_sides + 1)} for dummy_idx in range(num_trials): data[roll_die(num_sides, true_random)] += 1 x_data = [key for key in data.keys()] y_data = [value for value in data.values()] pyplot.bar(x_data, y_data, width=0.3, align='center') pyplot.title("Fairness of a Die in Python") pyplot.xlabel("side of the die") pyplot.ylabel("Number of times the number produced") pyplot.grid(True) pyplot.show() plot_fairness_bar(6, 3000) plot_fairness_bar(6, 3000, true_random=True)