{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Lecture 7: Gambler's Ruin & Random Variables\n", "\n", "\n", "## Stat 110, Prof. Joe Blitzstein, Harvard University\n", "\n", "----" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Gambler's Ruin\n", "\n", "Two gamblers $A$ and $B$ are successively playing a game until one wins all the money and the other is ruined (goes bankrupt). There is a sequence of rounds, with a one dollar bet each time. The rounds are independent events. Let $p = P(\\text{A wins a certain round})$ and the inverse is $q = 1 - p$, by convention.\n", "\n", "_What is the probability that $A$ wins the entire game?_\n", "\n", "Some clarifications:\n", "\n", "* there is a total of $N$ dollars in this closed system game (no other money comes into play)\n", "* $A$ starts with $i$ dollars, $B$ starts with $N-i$ dollars\n", "\n", "But where do we begin to solve this problem?\n", "\n", "### Random Walk\n", "\n", "A [random walk](https://en.wikipedia.org/wiki/Random_walk) between two points on a number line is very similar to the Gambler's Ruin.\n", "\n", "![title](images/L0701.png)\n", "\n", "How many rounds could a game last? Is it possible for the game to continue on to infinity?\n", "\n", "Well, notice how this has a very nice __recursive nature__. If $A$ loses a round, the game can be seen as starting anew at $i-1$, and if he wins, the game would start anew at $i+1$. It is the same problem, but with a different starting condition.\n", "\n", "### Strategy\n", "\n", "Conditioning on the _first step_ is called __first step analysis__.\n", "\n", "Let $P_i = P(\\text{A wins the entire game|A starts with i dollars})$. Then from the Law of Total Probability, we have:\n", "\n", "\\begin{align}\n", " P_i &= p P_{i+1} + q P_{i-1} \\text{, } & &\\text{where }1 \\lt i \\lt N-1 \\\\\n", " & & & P_0 = 0 \\\\\n", " & & & P_N = 1 \\\\\n", "\\end{align}\n", "\n", "See how this is a recursive equation? This is called a [__difference equation__](http://mathworld.wolfram.com/DifferenceEquation.html), which is a discrete analog of a differential equation.\n", "\n", "### Solving the Difference Equation\n", "\n", "\n", "\\begin{align}\n", " P_i &= p P_{i+1} + q P_{i-1} & & \\\\\n", " \\\\\n", " \\\\\n", " P_i &= x^i & &\\text{see what happens when we guess with a power} \\\\\n", " \\Rightarrow x^i &= p x^{i+1} + q x^{i-1} \\\\\n", " 0 &= p x^2 - x + q & &\\text{factoring out } x^{i-1} \\text{, we are left with a quadratic}\\\\\n", " \\\\\n", " x &= \\frac{1 \\pm \\sqrt{1-4pq}}{2p} & &\\text{solving with the quadratic formula} \\\\\n", " &= \\frac{1 \\pm \\sqrt{(2p-1)^2}}{2p} & &\\text{since }1-4pq = 1-4p(1-p) = 4p^2 - 4p - 1 = (2p -1)^2 \\\\\n", " &= \\frac{1 \\pm (2p-1)}{2p} \\\\\n", " &\\in \\left\\{1, \\frac{q}{p} \\right\\} \\\\\n", " \\\\\n", " \\\\\n", " P_i &= A(1)^i + B\\left(\\frac{q}{p}\\right)^i & &\\text{if } p \\neq q~~~~ \\text{(general solution for difference equation)} \\\\\n", " \\Rightarrow B &= -A & &\\text{from }P_0 = 1\\\\\n", " \\Rightarrow 1 &= A(1)^N + B\\left(\\frac{q}{p}\\right)^N & &\\text{from } P_N = 1\\\\\n", " &= A(1)^N - A\\left(\\frac{q}{p}\\right)^N \\\\\n", " &= A\\left(1-\\frac{q}{p}\\right)^N \\\\\n", " \\\\\n", " \\\\\n", " \\therefore P_i &=\n", " \\begin{cases}\n", " \\frac{1-\\left(\\frac{q}{p}\\right)^i}{1-\\left(\\frac{q}{p}\\right)^N} & \\quad \\text{ if } p \\neq q \\\\\n", " \\frac{i}{N} & \\quad \\text{ if } p = q \\\\\n", " \\end{cases}\n", "\\end{align}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example calculations of $P_i$ over a range of $N$\n", "\n", "Assuming an unfair game where $p=0.49$, $q=0.51$:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "With N=20 and p=0.49, probability that A wins all is 0.40\n", "With N=100 and p=0.49, probability that A wins all is 0.12\n", "With N=200 and p=0.49, probability that A wins all is 0.02\n" ] } ], "source": [ "import math\n", "\n", "def gamblers_ruin(i, p, q, N):\n", " if math.isclose(p,q):\n", " return i/N\n", " else:\n", " return ((1 - (q/p)**i)) / (1 - (q/p)**N)\n", "\n", "\n", "p = 0.49\n", "q = 1.0 - p\n", "\n", "N = 20\n", "i = N/2\n", "print(\"With N={} and p={}, probability that A wins all is {:.2f}\".format(N, p, gamblers_ruin(i, p, q, N)))\n", "\n", "N = 100\n", "i = N/2\n", "print(\"With N={} and p={}, probability that A wins all is {:.2f}\".format(N, p, gamblers_ruin(i, p, q, N)))\n", "\n", "N = 200\n", "i = N/2\n", "print(\"With N={} and p={}, probability that A wins all is {:.2f}\".format(N, p, gamblers_ruin(i, p, q, N)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And assuming a fair game where $p = q = 0.5$:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "With N=20 and p=0.5, probability that A wins all is 0.50\n", "With N=100 and p=0.5, probability that A wins all is 0.50\n", "With N=200 and p=0.5, probability that A wins all is 0.50\n" ] } ], "source": [ "p = 0.5\n", "q = 1.0 - p\n", "\n", "N = 20\n", "i = N/2\n", "print(\"With N={} and p={}, probability that A wins all is {:.2f}\".format(N, p, gamblers_ruin(i, p, q, N)))\n", "\n", "N = 100\n", "i = N/2\n", "print(\"With N={} and p={}, probability that A wins all is {:.2f}\".format(N, p, gamblers_ruin(i, p, q, N)))\n", "\n", "N = 200\n", "i = N/2\n", "print(\"With N={} and p={}, probability that A wins all is {:.2f}\".format(N, p, gamblers_ruin(i, p, q, N)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Could the game ever continue forever on to infinity?\n", "\n", "Recall that we have the following solution to the difference equation for the Gambler's Ruin game:\n", "\n", "\\begin{align}\n", " P_i &=\n", " \\begin{cases}\n", " \\frac{1-\\left(\\frac{q}{p}\\right)^i}{1-\\left(\\frac{q}{p}\\right)^N} & \\quad \\text{ if } p \\neq q \\\\\n", " \\frac{i}{N} & \\quad \\text{ if } p = q \\\\\n", " \\end{cases}\n", "\\end{align}\n", "\n", "The only time you'd think the game could continue on to infinity is when $p=q$. But\n", "\n", "\\begin{align}\n", " P(\\Omega) &= 1\\\\\n", " &= P(\\text{A wins all}) + P(\\text{B wins all}) \\\\\n", " &= P_i + P_{N-i} \\\\\n", " &= \\frac{i}{N} + \\frac{N-i}{N}\n", "\\end{align}\n", "\n", "The above implies that aside from the case where $A$ wins all, and the case where $B$ wins all, there is no other event in $\\Omega$ to consider, hence the game can never continue on to infinity without either side winning.\n", "\n", "This also means that unless $p=q$, you __will__ lose your money, and the only question is how fast will you lose it.\n", "\n", "----" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Random Variables\n", "\n", "Consider these statements:\n", "\n", "\\begin{align}\n", " x + 2 &= 9 \\\\\n", " x &= 7\n", "\\end{align}\n", "\n", "_What is a variable?_\n", "* variable $x$ is a symbol that we use as a substitute for an arbitrary _constant_ value.\n", "\n", "\n", "_What is a __random__ variable?_\n", "\n", "* This is not a _variable_, but a __function from the sample space $S$ to $\\mathbb{R}$__.\n", "* It is a \"summary\" of an aspect of the experiment (this is where the randomness comes from)\n", "\n", "Here are a few of the most useful _discrete random variables_.\n", "\n", "----" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bernoulli Distribution\n", "\n", "### Description\n", "A probability distribution of a random variable that takes the value 1 in the case of a success with probability $p$; or takes the value 0 in case of a failure with probability $1-p$.\n", "\n", "A most common example would be a coin toss, where heads might be considered a success with probability $p=0.5$ if the coin is a fair.\n", "\n", "A random variable $x$ has the Bernoulli distribution if\n", "- $x \\in \\{0, 1\\}$\n", "- $P(x=1) = p$\n", "- $P(x=0) = 1-p$\n", "\n", "### Notation\n", "\n", "$X \\sim \\operatorname{Bern}(p)$\n", "\n", "### Parameters\n", "\n", "$0 < p < 1 \\text{, } p \\in \\mathbb{R}$\n", "\n", "### Probability mass function\n", "\n", "The probability mass function $P(x)$ over possible values $x$\n", "\n", "\\begin{align}\n", " P(x) = \n", " \\begin{cases}\n", " 1-p, &\\text{ if } x = 0 \\\\\n", " p, &\\text{ if } x = 1 \\\\\n", " \\end{cases} \\\\\n", "\\end{align}\n", "\n", "### Expected value\n", "\n", "\\begin{align}\n", " \\mathbb{E}(X) &= 1 P(X=1) + 0 P(X=0) \\\\\n", " &= p\n", "\\end{align}\n", "\n", "### Special case: Indicator random variables (r.v.)\n", "\n", "\\begin{align}\n", " &X = \n", " \\begin{cases}\n", " 1, &\\text{ if event A occurs} \\\\\n", " 0, &\\text{ otherwise} \\\\\n", " \\end{cases} \\\\\n", " \\\\\n", " \\\\\n", " \\Rightarrow &\\mathbb{E}(X) = P(A)\n", "\\end{align}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Binomial Distribution \n", "\n", "### Description\n", "\n", "The distribution of the number of successes in $n$ independent Bernoulli trials $\\operatorname{Bern}(p)$, where the chance of success $p$ is the same for all trials $n$. \n", "\n", "Another case might be a string of indicator random variables.\n", "\n", "### Notation\n", "\n", "$X \\sim \\operatorname{Bin}(n, p)$\n", "\n", "### Parameters\n", "\n", "- $n \\in \\mathbb{N}$\n", "- $p \\in [0,1]$" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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nCIIgCIIgiHoGiXiCIAiCIAiCqGeQiCcIgiAIgiCIegaJeIIgCIIgCIKoZ5CI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\nCv7+979Dp9P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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "from matplotlib.ticker import (MultipleLocator, FormatStrFormatter,\n", " AutoMinorLocator)\n", "from scipy.stats import binom\n", "\n", "%matplotlib inline\n", "\n", "plt.xkcd()\n", "\n", "_, ax = plt.subplots(figsize=(12,8))\n", "\n", "# a few Binomial parameters n and p\n", "pop_sizes = [240, 120, 60, 24]\n", "p_values = [0.2, 0.3, 0.4, 0.8]\n", "params = list(zip(pop_sizes, p_values))\n", "\n", "# colorblind-safe, qualitative color scheme\n", "colors = ['#a6cee3','#1f78b4','#b2df8a','#33a02c']\n", "\n", "for i,(n,p) in enumerate(params):\n", " x = np.arange(binom.ppf(0.01, n, p), binom.ppf(0.99, n, p))\n", " y = binom.pmf(x, n, p)\n", " ax.plot(x, y, 'o', ms=8, color=colors[i], label='n={}, p={}'.format(n,p))\n", " ax.vlines(x, 0, y, color=colors[i], alpha=0.3)\n", "\n", "# legend styling\n", "legend = ax.legend()\n", "for label in legend.get_texts():\n", " label.set_fontsize('large')\n", "for label in legend.get_lines():\n", " label.set_linewidth(1.5)\n", "\n", "# y-axis\n", "ax.set_ylim([0.0, 0.23])\n", "ax.set_ylabel(r'$P(x=k)$')\n", "\n", "# x-axis\n", "ax.set_xlim([10, 65])\n", "ax.set_xlabel('# of successes k out of n Bernoulli trials')\n", "\n", "# x-axis tick formatting\n", "majorLocator = MultipleLocator(5)\n", "majorFormatter = FormatStrFormatter('%d')\n", "minorLocator = MultipleLocator(1)\n", "ax.xaxis.set_major_locator(majorLocator)\n", "ax.xaxis.set_major_formatter(majorFormatter)\n", "\n", "ax.grid(color='grey', linestyle='-', linewidth=0.3)\n", "\n", "plt.suptitle(r'Binomial PMF: $P(x=k) = \\binom{n}{k} p^k (1-p)^{n-k}$')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Probability mass function\n", "\n", "\\begin{align}\n", " P(x=k) &= \\binom{n}{k} p^k (1-p)^{n-k}\n", "\\end{align}\n", "\n", "### Expected value\n", "\n", "\\begin{align}\n", " \\mathbb{E}(X) = np\n", "\\end{align}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## In parting...\n", "\n", "Now think about this true statement as we move on to Lecture 3:\n", "\n", "\\begin{align}\n", " X &\\sim \\operatorname{Bin}(n,p) \\text{, } Y \\sim \\operatorname{Bin}(m,p) \\\\\n", " \\rightarrow X+Y &\\sim \\operatorname{Bin}(n+m, p)\n", "\\end{align}" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "----\n", "\n", "## Appendix A: Solving $P_i$ when $p=q$ using l'Hopital's Rule\n", "\n", "To solve for for the case where $p = q$, let $x = \\frac{q}{p}$.\n", "\n", "\\begin{align}\n", " lim_{x \\rightarrow 1}{\\frac{1-x^i}{1-x^N}} &= lim_{x\\rightarrow1}{\\frac{ix^{i-1}}{Nx^{N-1}}} &\\text{ by l'Hopital's Rule} \\\\\n", " &= \\frac{i}{N}\n", "\\end{align}\n", "\n", "\n", "----" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "View [Lecture 7: Gambler's Ruin and Random Variables | Statistics 110](http://bit.ly/2PmMbdV) on YouTube." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.3" } }, "nbformat": 4, "nbformat_minor": 1 }