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@ludwigschwardt
Last active September 11, 2015 21:21
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Stikeez Part 1
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Stikeez Part 1: Can you afford to collect them all?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"> This [Jupyter](https://jupyter.org/) notebook is a supplement to the corresponding $++ [blog post](http://dollarpp.com/2015/09/03/stikeez-part-1/). You can play around with it in two ways:\n",
">\n",
"> - Install Python, Jupyter and the rest of the required Python packages on your computer and run the notebook there. I would recommend a computing-oriented Python distribution such as [Anaconda](http://continuum.io/anaconda/) to get you up and running with the minimum fuss.\n",
">\n",
"> - Register for a free cloud computing service such as [SageMathCloud](https://cloud.sagemath.com), upload this notebook to their site and run it \"in the cloud\". [Wakari](http://wakari.io) also seems like a good option, but their software is currently too old to open this notebook.\n",
">\n",
"> Both options allow you to tweak the values and methods in this notebook and rerun the experiment to your heart's delight."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We start off with some common Python package imports for data analysis but also include [seaborn](http://stanford.edu/~mwaskom/software/seaborn/index.html), which makes some dashing plots on top of matplotlib."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import matplotlib as mpl\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We pick a minimal seaborn plotting style and pick the same font and text colour as in the blog theme ([Penscratch](http://penscratchdemo.wordpress.com)). This assumes that you installed the Roboto Slab Light font on your system, but it should fall back to the default font if not."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# That Penscratch grey\n",
"textcolor = str(102 / 255.)\n",
"sns.set(style='ticks', font='Roboto Slab',\n",
" rc={# Increase DPI to ensure sufficient pixels in output PNG\n",
" # Remember that notebook figures are actually saved images...\n",
" 'savefig.dpi': 200,\n",
" # The Penscratch theme uses Roboto Slab Light as its base font\n",
" 'font.weight': 'light', 'axes.labelweight': 'light',\n",
" # Change text and axes markings from black to base font colour\n",
" 'text.color': textcolor, 'axes.edgecolor': textcolor,\n",
" 'axes.labelcolor': textcolor, 'xtick.color': textcolor})"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The heart of the calculation is a routine that simulates one person's quest to collect all 24 Stikeez. It is assumed that the items / Stikeez are uniformly distributed and therefore equally likely to appear in a draw.\n",
"\n",
"The number of unique items *(num_items)* can be set to keep things generic. To speed things up, the person always draws a fixed number of items *(max_draws)* that should be more than enough to ensure a complete set. The routine returns the number of draws it took to achieve a complete set."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def collect_items(num_items, max_draws):\n",
" \"\"\"Collect items until a full set has been completed.\n",
"\n",
" Parameters\n",
" ----------\n",
" num_items : integer\n",
" Number of unique items that form a set\n",
" max_draws : integer\n",
" Maximum number of draws before giving up\n",
"\n",
" Returns\n",
" -------\n",
" draws_till_success : integer\n",
" Number of draws that resulted in a complete set\n",
"\n",
" \"\"\"\n",
" # Generate all random draws at once, up to the maximum\n",
" items = np.random.randint(num_items, size=max_draws)\n",
" # Each row of indicator corresponds to a draw, and has a single 1\n",
" # in the column corresponding to the drawn item (and 0 elsewhere)\n",
" indicator = np.zeros((max_draws, num_items), dtype=np.int)\n",
" indicator[range(max_draws), items] = 1\n",
" # The n'th row of counts contains the tally of items after n draws\n",
" counts = indicator.cumsum(axis=0)\n",
" # Find the number of rows with any columns containing 0,\n",
" # i.e. the number of draws that resulted in an incomplete set\n",
" draws_incomplete = (counts < 1).any(axis=-1).sum()\n",
" # The next draw after all the incomplete ones completes the set\n",
" return draws_incomplete + 1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The next routine simulates the number of unique items a person has collected after a fixed number of draws."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def count_unique_items(num_items, num_draws):\n",
" \"\"\"Number of unique items after a fixed number of draws.\n",
"\n",
" Parameters\n",
" ----------\n",
" num_items : integer\n",
" Number of unique items that form a set\n",
" num_draws : integer\n",
" Number of draws\n",
"\n",
" Returns\n",
" -------\n",
" unique_items : integer\n",
" Number of unique items after a fixed number of draws\n",
"\n",
" \"\"\"\n",
" # Generate all random draws at once and put them in a set\n",
" items = np.random.randint(num_items, size=num_draws)\n",
" return len(set(items))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we set the main parameters of the experiment and collect the data. The number of trials *(num_trials)* should be as large as possible to ensure a good estimate of the true underlying statistics."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"num_items = 24\n",
"max_draws = 400\n",
"num_trials = 100000\n",
"unique_draws = 24\n",
"\n",
"draws_till_success = [collect_items(num_items, max_draws)\n",
" for n in range(num_trials)]\n",
"unique_items = [count_unique_items(num_items, unique_draws)\n",
" for n in range(num_trials)]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We get the median number of items required (50th percentile), as well as the 10th and 90th percentiles of the data."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"p10, p50, p90 = np.percentile(draws_till_success, (10, 50, 90))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We plot the histogram of the data, together with a smooth kernel density estimate. Please ignore any warnings about fonts as the plots will revert to the default font."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
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Vr6igoMDvedu2bdPzzz+vmTNn6kMf+pByc3OtjAkAlzXkdajqTIepzvgggo3D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\nAcKSWiT8fKHhAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11058cf90>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig1 = plt.figure(figsize=(7.06, 2.36))\n",
"ax = sns.distplot(draws_till_success,\n",
" bins=np.arange(-0.5, max_draws + 1, 5))\n",
"ax.set_xlim(0, 240)\n",
"ax.set(xticks=(0, 24, p10, p50, p90, 160, 200, 240), yticks=[])\n",
"# Highlight the median\n",
"ax.axvline(p50, color='b', linestyle='--')\n",
"ax.set_xlabel('Number of Stikeez required to get a full set')\n",
"ax.set_ylabel('Frequency')\n",
"sns.despine(left=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The probability of getting a complete set after the minimum of 24 attempts is\n",
"\n",
"$$\\frac{24}{24} \\times \\frac{23}{24} \\times \\frac{22}{24} \\times \\cdots \\times \\frac{2}{24} \\times \\frac{1}{24} = \\frac{24!}{24^{24}},$$\n",
"or a chance of one in"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"2149632061.4646716"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"float(24 ** 24) / np.math.factorial(24)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As an interesting aside, plot the distribution of unique Stikeez after you have collected 24 of them."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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nS8Jn48aN+tKXvqR/+7d/09tvv623335bDodDycnJcrvdmp2d1fT09M1vL0pK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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11058c510>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig2 = plt.figure(figsize=(7.06, 2.36))\n",
"# The 'bw' parameter determines smoothness of kernel density estimate\n",
"ax = sns.distplot(unique_items, bins=np.arange(-0.5, 25),\n",
" kde_kws={'bw': 0.4})\n",
"ax.set_xlim(0, 24)\n",
"ax.set(xticks=range(0, 26, 2), yticks=[])\n",
"ax.set_xlabel('Number of unique Stikeez after you collected %d' %\n",
" (unique_draws,))\n",
"ax.set_ylabel('Frequency')\n",
"sns.despine(left=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Finally we save the images to files to use it on the blog."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# fig1.savefig('hist_1set.png', bbox_inches='tight')\n",
"# fig2.savefig('hist_unique_after_24.png', bbox_inches='tight')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### License (BSD 3-Clause)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<small>\n",
"\n",
"Copyright (c) 2015, Ludwig Schwardt\n",
"\n",
"All rights reserved.\n",
"\n",
"Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:\n",
"\n",
"1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.\n",
"\n",
"2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.\n",
"\n",
"3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.\n",
"\n",
"THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n",
"\n",
"</small>"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.10"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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