ipynb/ProbabilitySimulation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "<div style=\"text-align: right\">Peter Norvig, Feb 2020</div> \n",
    "\n",
    "# Estimating Probabilities with Simulations\n",
    "\n",
    "In [another notebook](http://nbviewer.jupyter.org/url/norvig.com/ipython/Probability.ipynb) I showed how to solve problems by computing probabilities. The computations are simple: count the frequency of the \"favorable\" outcomes and divide by the frequency of all possible outcomes&mdash;the \"sample space.\" (In [yet another notebook](http://nbviewer.jupyter.org/url/norvig.com/ipython/Probability.ipynb) I tackle some probability paradoxes.)\n",
    "\n",
    "\n",
    "But sometimes it is inconvenient, difficult, or even impossible to explicitly enumerate all possible outcomes. Perhaps the sample space is infinite, or perhaps it is just very large and complicated, with a bunch \n",
    "of low-probability outcomes that don't seem very important. In that case, we might feel more confident in writing a program to *simulate* a random outcome. *Random sampling* from such a simulation\n",
    "can give an accurate estimate of probability.\n",
    "\n",
    "# Simulating Monopoly\n",
    "\n",
    "<img src=\"http://buckwolf.org/a.abcnews.com/images/Entertainment/ho_hop_go_050111_t.jpg\" style=\"float:right\">\n",
    "\n",
    "Consider [problem 84](https://projecteuler.net/problem=84) from the excellent [Project Euler](https://projecteuler.net), which asks for the probability that a player in the game Monopoly ends a roll on each of the squares on the board.  To answer this we need to take into account die rolls, chance and community chest cards, and going to jail (from the \"go to jail\" space, from a card, or from rolling doubles three times in a row). We do not need to take into account anything about acquiring properties or exchanging money or winning or losing the game, because these events don't change a player's location. \n",
    "\n",
    "A game of Monopoly can go on forever, so the sample space is infinite. Even if we limit the sample space to say, 1000 rolls, there are $21^{1000}$ such sequences of rolls. So it is infeasible to explicitly represent the sample space. There are techniques for representing the problem as\n",
    "a Markov decision problem (MDP) and solving it, but the math is complex (a [paper](https://faculty.math.illinois.edu/~bishop/monopoly.pdf) on the subject runs 15 pages).\n",
    "\n",
    "The simplest approach is to implement a simulation and run it for, say, a million rolls.  Below is the code for a simulation. Squares are represented by integers from 0 to 39, and we define a global variable for each square: `GO`, `A1` (for the first property in the first monopoly), `CC1` (the first community chest square), and so on.  Wiithin the function `monopoly` the variable `loc` keeps track of where we are, and dice rolls and cards can alter the location. We use `visits[square]` to count how many times we end a roll on the square.\n",
    "\n",
    "The trickiest part of the simulation is the cards: chance and community chest. We'll implement a deck of cards as a double-ended queue (so we can take cards from the top and put them on the bottom). Each card can be:\n",
    "- A square, meaning to advance to that square (e.g., `R1` (square 5) means \"take a ride on the Reading\").\n",
    "- A set of cards (e.g., `{R1, R2, R3, R4}` means \"advance to nearest railroad\").\n",
    "- The number -3, which means \"go back 3 squares\".\n",
    "- `'$'`, meaning the card has no effect on location, but involves money.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline \n",
    "import matplotlib.pyplot as plt\n",
    "import random\n",
    "from collections import Counter, deque\n",
    "\n",
    "# The Monopoly board, as specified by https://projecteuler.net/problem=84\n",
    "board = \"\"\"\n",
    " GO    A1  CC1  A2   T1  R1  B1   CH1  B2  B3 \n",
    " JAIL  C1  U1   C2   C3  R2  D1   CC2  D2  D3  \n",
    " FP    E1  CH2  E2   E3  R3  F1   F2   U2  F3  \n",
    " G2J   G1  G2   CC3  G3  R4  CH3  H1   T2  H2\"\"\".split()\n",
    "\n",
    "for i, sq in enumerate(board): # Make the square names be global variables\n",
    "    globals()[sq] = i\n",
    "    \n",
    "def Deck(cards):\n",
    "    \"\"\"A deck of cards; draw from the top and put it on bottom.\"\"\"\n",
    "    random.shuffle(cards)\n",
    "    return deque(cards)\n",
    "    \n",
    "CC_cards = Deck([GO, JAIL] +  14 * ['$'])\n",
    "CH_cards = Deck([GO, JAIL, C1, E3, H2, R1, -3, {U1, U2}]\n",
    "                + 2 * [{R1, R2, R3, R4}] + 6 * ['$'])\n",
    "\n",
    "def roll() -> int: return random.randint(1, 6)\n",
    "\n",
    "def monopoly(rolls):\n",
    "    \"\"\"Simulate a number of dice rolls of a Monopoly game, \n",
    "    and return the counts of how often each square is visited.\"\"\"\n",
    "    visits = len(board) * [0]  # Counts of how many times each square is visited\n",
    "    doubles = 0                # Number of consecutive doubles rolled\n",
    "    loc = GO                   # Location on board\n",
    "    for _ in range(rolls):\n",
    "        d1, d2 = roll(), roll()\n",
    "        doubles = ((doubles + 1) if d1 == d2 else 0)\n",
    "        loc = (loc + d1 + d2) % len(board) # Roll, move ahead, maybe pass Go\n",
    "        if loc == G2J or doubles == 3:\n",
    "            loc = JAIL\n",
    "            doubles = 0\n",
    "        elif loc in (CC1, CC2, CC3):\n",
    "            loc = do_card(CC_cards, loc)\n",
    "        elif loc in (CH1, CH2, CH3):\n",
    "            loc = do_card(CH_cards, loc)\n",
    "        visits[loc] += 1\n",
    "    return visits\n",
    "\n",
    "def do_card(deck, loc):\n",
    "    \"Take the top card from deck and do what it says; return new location.\"\n",
    "    card = deck[0]                        # The top card\n",
    "    deck.rotate(1)                        # Move top card to bottom of deck\n",
    "    return (loc if card is '$' else       # Don't move\n",
    "            loc - 3 if card == -3 else    # Go back 3 spaces\n",
    "            card if isinstance(card, int) # Go to destination named on card\n",
    "            else min({s for s in card if s > loc} or card)) # Advance to nearest"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "Let's run the simulation for a million dice rolls and print a bar chart of probabilities for each square:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "N = 10**6\n",
    "\n",
    "visits = monopoly(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def bar(visits): \n",
    "    plt.rcParams[\"figure.figsize\"] = [10, 7]\n",
    "    plt.grid(axis='y')\n",
    "    plt.xticks(range(40), board, rotation=90)\n",
    "    plt.xlabel(\"Squares\"); plt.ylabel(\"Percent\")\n",
    "    plt.bar(board, [100 * visits[s] / N for s in range(40)])\n",
    "    \n",
    "bar(visits)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "If the squares were all visited equally, they'd each be 100% / 40 = 2.5%. In actuality, we see that most of the squares are between about 2% and 3%, but a few stand out:  `JAIL`is over 6%; `G2J` (\"Go to Jail\") is 0%, because you can't end a roll there; and the three chance squares (`CH1`, `CH2`, and `CH3`) are each at around 1%, because 10 of the 16 chance cards send the player away from the square. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Central Limit Theorem \n",
    "\n",
    "The [Probability notebook](http://nbviewer.jupyter.org/url/norvig.com/ipython/Probability.ipynb) covered the concept of *distributions* of outcomes. You may have heard of the *normal distribution*, the *bell-shaped curve.* In Python it is called `random.normalvariate` (also `random.gauss`). We can plot it with the help of the `repeated_hist` function defined below, which samples a distribution `n` times and displays a histogram of the results. (*Note:* in this section I am implementing \"distribution\" as a function with no arguments that, each time it is called, returns a random sample from a probability distribution.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statistics import mean\n",
    "from random import normalvariate, triangular, choice, vonmisesvariate, uniform\n",
    "\n",
    "def normal(mu=0, sigma=1): return random.normalvariate(mu, sigma)\n",
    "\n",
    "def repeated_hist(dist, n=10**6, bins=200):\n",
    "    \"Sample the distribution n times and make a histogram of the results.\"\n",
    "    plt.rcParams[\"figure.figsize\"] = [6, 4]\n",
    "    samples = [dist() for _ in range(n)]\n",
    "    plt.hist(samples, bins=bins, density=True)\n",
    "    plt.title(f'{dist.__name__} (μ = {mean(samples):.1f})')\n",
    "    plt.grid(axis='x')\n",
    "    plt.yticks([], '')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Histogram of Normal distribution\n",
    "repeated_hist(normal)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Why is this distribution called *normal*? The **Central Limit Theorem** says  that it is the ultimate limit of other distributions, as follows (informally):\n",
    "- Gather *k* independent distributions. They need not be normal-shaped.\n",
    "- Define a new distribution to be the result of sampling one number from each of the *k* independent distributions and adding them up.\n",
    "- As long as *k* is not too small, and the component distributions are not super-pathological, then the new distribution will tend towards a normal distribution.\n",
    "\n",
    "Here's a simple example: rolling a single die gives a uniform distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "repeated_hist(roll, bins=6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Rolling two dice gives a \"staircase\" distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def sum2dice(): return roll() + roll()\n",
    "\n",
    "repeated_hist(sum2dice, bins=range(2, 14))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But rolling N = 20 dice and summing them gives a near-normal distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 20\n",
    "\n",
    "def sumNdice(): return sum(roll() for _ in range(N))\n",
    "\n",
    "repeated_hist(sumNdice, bins=range(2 * N, 5 * N))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As another example, let's take just *k* = 5 component distributions representing the per-game scores of 5 basketball players, and then sum them together to form the new distribution, the team score. I'll be creative in defining the distributions for each player, but [historically accurate](https://www.basketball-reference.com/teams/GSW/2016.html) in the mean for each distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def SC(): return max(0, normal(12.1, 3) + 3 * triangular(1, 13, 4))                     # 30.1\n",
    "def KT(): return max(0, triangular(8, 22, 15.3) + choice((0, 3 * triangular(1, 9, 4)))) # 22.1\n",
    "def DG(): return max(0, vonmisesvariate(30, 2) * 3.08)                                  # 14.0\n",
    "def HB(): return max(0, choice((normal(6.7, 1.5), normal(16.7, 2.5))))                  # 11.7\n",
    "def BE(): return max(0, normal(17, 3) + uniform(0, 40))                                 # 37.0\n",
    "\n",
    "team = (SC, KT, DG, HB, BE)\n",
    "\n",
    "def Team(team=team): return sum(player() for player in team)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWQAAAEICAYAAABoLY4BAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvIxREBQAADPpJREFUeJzt3X+M5PVdx/Hnq1wpcoAHQhuEhm0FW9DCARXBQtNSVFqwGvWPNjXFiqJJY9qIwSM1TbQxuRrT1phGi6Jo2rRqa2vLJa1Ir6a0EcrPcoAUjFc5+V05Clcwxb79Y74b5tbdvdtl5+Y9x/ORTHa/3/nuzHs2c8/77mdm71JVSJKm7wXTHkCSNGKQJakJgyxJTRhkSWrCIEtSEwZZkpowyJqqJCcluXHac0xCkpckuSvJi6Y9i2aDQdYeJdme5KkkTyTZmeSrSX4jyQsWHPfqJFcneWw47s4kf5Dk8GVu/n3AH032EewuyY8m+UKSR5Ms+Ub8JCckeTrJR5c5Jknen+Rbw+UPkwSgqh4CtgKXrP2j0P7IIGtv/UxVHQocB2wGfge4cv7KJD8BfAn4CvDKqtoAnA88A5yy2A0mORp4PfCZiU7+/30X+Dvg4j0c92Hga3s45hLg5xg9xpOBC4FfH7v+Ywu2pSXF39TTniTZDvxqVf3z2L4zgH8FTq6qbUmuA26pqt9cwe2+HXh7VZ03tq+AE6rq3mH7KmBHVf3umjyY3e//eOCeqsoi170F+HngTuD4qvqlJW7jq8BVVXXFsH0x8GtVdeawvQ74NnBiVX1zrR+D9i+eIWtVquoGYAdwTpL1wFnAp1Z4M68C7l7tDEnOHpZGlrqcvcrbPQz4feDSvTj8R4DbxrZvG/YBUFXPAPeyxE8J0jiDrOfifuAI4HBGz6UH568Y1lJ3JtmVZKmz2w3AE6u986q6rqo2LHO5bpU3/T7gyqq6by+OPQR4fGz7ceCQ+XXkwROMHqu0LIOs5+IY4L+Bx4DvAUfPX1FVlw3ryJ8G1i3x9Y8Bh056yJVIshE4D/jgXn7Jk8BhY9uHAU/W7muBhwI712ZC7c8MslYlyY8xCvJ1VbULuJ7RmutKfB344UX2HzT2+ZJnlknOSfLkMpdzVjgPwOuAOeA/kzwI/DbwC0luXuL4O9h9OeKUYd/8jOuA49l9WUNalEHWiiQ5LMmFwCeAj1bV7cNVlwG/kmRTkhcPxx4LvGyZm7sGOC3JQQv2vyPJAcPZ6huAQ5O8cOEXV9WXq+qQZS5fXuIxZLjPA4ftg8beK3wF8EPAxuHyZ8AW4KeXeAx/A/xWkmOS/CCjdeerxq4/A9juC3raGwZZe+tzSZ4A7gPeA3wAeMf8lcN67bnAa4FvJNkJfJ7RW+H+ZLEbHN6n+0XgZxdcdTDwAPDnwHuBi4bbXivHAU/x7JnsUwwvLlbVd6rqwfkLoyWJp6vqEXj2rHzstj4CfA64HdjGKN4fGbv+bYyiLu2Rb3vTVCU5Cfhr4IyqqoVve5tlw08K/wKcWlVPT3se9WeQ1cr+FGRppVyykKQmPEOWpCY8Q5akJpZ6w/6ijjzyyJqbm1vVHe3atYv169ev6munwXkny3kna9bmhdmbeSXz3nTTTY9W1VF7PLCq9vpy+umn12pt3bp11V87Dc47Wc47WbM2b9XszbySeYEbay8a65KFJDVhkCWpCYMsSU0YZElqwiBLUhMGWZKaMMiS1IRBlqQmDLIkNbGiX53Wys1t2rLs9ds3X7CPJpHUnWfIktSEQZakJgyyJDVhkCWpCYMsSU0YZElqwiBLUhMGWZKaMMiS1IRBlqQmDLIkNWGQJakJgyxJTRhkSWrCIEtSEwZZkpowyJLUhEGWpCYMsiQ1YZAlqQmDLElNGGRJasIgS1ITBlmSmjDIktSEQZakJgyyJDVhkCWpCYMsSU0YZElqwiBLUhMGWZKaMMiS1IRBlqQmDLIkNWGQJamJddMeYH8yt2nLtEeQNMM8Q5akJjxDnrLFzqq3b75gCpNImjbPkCWpCYMsSU0YZElqwiBLUhMGWZKaMMiS1IRBlqQmDLIkNWGQJakJgyxJTRhkSWrCIEtSEwZZkpowyJLUhEGWpCYMsiQ1YZAlqQmDLElNGGRJasIgS1ITBlmSmjDIktSEQZakJgyyJDVhkCWpCYMsSU0YZElqwiBLUhMGWZKaMMiS1IRBlqQmDLIkNWGQJakJgyxJTRhkSWrCIEtSEwZZkpowyJLUhEGWpCYMsiQ1YZAlqQmDLElNGGRJasIgS1ITBlmSmjDIktSEQZakJgyyJDVhkCWpCYMsSU0YZElqwiBLUhPrpj3ALJvbtGWf3O72zRdM5H4k9eIZsiQ1YZAlqQmDLElNGGRJasIgS1ITBlmSmjDIktSEQZakJgyyJDVhkCWpCYMsSU0YZElqwiBLUhMGWZKaMMiS1IRBlqQmDLIkNWGQJakJgyxJTRhkSWrCIEtSEwZZkpowyJLUhEGWpCYMsiQ1YZAlqQmDLElNGGRJasIgS1ITBlmSmjDIktSEQZakJgyyJDVhkCWpCYMsSU0YZElqwiBLUhMGWZKaMMiS1IRBlqQmDLIkNWGQJakJgyxJTRhkSWrCIEtSEwZZkppYN+0BZsXcpi3THkHSfs4gz4DF/jLYvvmCKUwiaZJcspCkJgyyJDVhkCWpCYMsSU0YZElqwiBLUhMGWZKaMMiS1IRBlqQmDLIkNWGQJakJgyxJTRhkSWrCIEtSEwZZkpowyJLUhEGWpCYMsiQ1YZAlqQmDLElNGGRJasIgS1ITBlmSmjDIktSEQZakJgyyJDVhkCWpCYMsSU0YZElqYt20B+jq9v96nF/etGXaY0h6HvEMWZKaMMiS1IRBlqQmDLIkNWGQJakJgyxJTRhkSWpin70PeeH7erdvvmBf3bUkzQTPkCWpCYMsSU0YZElqwiBLUhMGWZKaMMiS1IRBlqQmDLIkNeE/UD+YW/CP0V/6qikNIul5yzNkSWrCIEtSEwZZkpqY2hrywjVb8B8cWomF37+rzl8/pUkkrRXPkCWpCYMsSU0YZElqwiBLUhPPy18MWewFRUmaNs+QJamJVmfIC89cfRucpOcTz5AlqYlWZ8iT4pqxpFnQOsj+Np+k55PWQV4Nz4YlzaqZC7LBlbS/8kU9SWrCIEtSEwZZkppIVe39wckjwDdXeV9HAo+u8munwXkny3kna9bmhdmbeSXzHldVR+3poBUF+blIcmNVvXqf3NkacN7Jct7JmrV5YfZmnsS8LllIUhMGWZKa2JdBvmIf3tdacN7Jct7JmrV5YfZmXvN599kasiRpeS5ZSFITBlmSmph4kJOcn+TuJPcm2TTp+1uNJH+Z5OEk28b2HZHkmiT3DB8Pn+aM45K8NMnWJHcluSPJu4b9LWdOclCSG5LcNsz7e8P+lyW5fpj3b5McOO1ZxyU5IMktSa4ettvOm2R7ktuT3JrkxmFfy+cDQJINST6Z5N+G5/FZXedN8orh+zp/+XaSd09i3okGOckBwIeBNwInAW9NctIk73OVrgLOX7BvE3BtVZ0AXDtsd/EMcGlVnQicCbxz+L52nfl/gHOr6hRgI3B+kjOB9wMfHOZ9DLh4ijMu5l3AXWPb3ed9fVVtHHtvbNfnA8AfA5+vqlcCpzD6Prect6ruHr6vG4HTge8An2YS81bVxC7AWcAXxrYvBy6f5H0+h1nngG1j23cDRw+fHw3cPe0Zl5n9H4GfnIWZgYOBm4EfZ/RbTusWe65M+wIcO/whOxe4GkjzebcDRy7Y1/L5ABwG/AfDmwq6z7tgxp8CvjKpeSe9ZHEMcN/Y9o5h3yx4SVU9ADB8fPGU51lUkjngVOB6Gs88/Ph/K/AwcA3w78DOqnpmOKTbc+NDwGXA94btH6D3vAX8U5Kbklwy7Ov6fHg58AjwV8OS0F8kWU/fece9Bfj48PmazzvpIGeRfb7Pbo0kOQT4FPDuqvr2tOdZTlX9b41+5DsWOAM4cbHD9u1Ui0tyIfBwVd00vnuRQ1vMO3hNVZ3GaHnwnUleO+2BlrEOOA3406o6FdhFk+WJ5QyvGbwZ+PtJ3cekg7wDeOnY9rHA/RO+z7XyUJKjAYaPD095nt0keSGjGH+sqv5h2N16ZoCq2gl8idHa94Yk8/9JQqfnxmuANyfZDnyC0bLFh+g7L1V1//DxYUbrm2fQ9/mwA9hRVdcP259kFOiu8857I3BzVT00bK/5vJMO8teAE4ZXpw9kdLr/2Qnf51r5LHDR8PlFjNZpW0gS4Ergrqr6wNhVLWdOclSSDcPn3wecx+hFnK3ALw6HtZm3qi6vqmOrao7Rc/aLVfU2ms6bZH2SQ+c/Z7TOuY2mz4eqehC4L8krhl1vAO6k6bxj3sqzyxUwiXn3wSL4m4BvMFozfM+0F+WXmPHjwAPAdxn97X0xozXDa4F7ho9HTHvOsXnPZvTj8teBW4fLm7rODJwM3DLMuw1477D/5cANwL2Mfgx80bRnXWT21wFXd553mOu24XLH/J+zrs+HYbaNwI3Dc+IzwOHN5z0Y+Bbw/WP71nxef3VakprwN/UkqQmDLElNGGRJasIgS1ITBlmSmjDIktSEQZakJv4PgHOf/jj3UAUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWQAAAEICAYAAABoLY4BAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvIxREBQAADYdJREFUeJzt3X+M5Hddx/Hnmx609K7ntV6xDa0sRQI9rW0pFgj1FwW9cojEokKIXBMM/gEJJDXk6g+iiZrTGMQYoxLQC2gKaTmg9ETFevVnbLmjP67HtZbKIteWXmuuLT0UvPr2j+93z7np7Nzu3H73+57d5yOZ7H5/zMxrJ9957Wc/+52ZyEwkSf17Vt8BJEkNC1mSirCQJakIC1mSirCQJakIC1mSirCQ1ZuIODUivhQR5/SdpQsRsTMiNvedQ9PDQtaCRcRsRPxXRDwVEYcjYldEnD+wfUdEfLvdPne5a8xNvhP4h8z8evfpj2XcFBF72vyHI+JvI2LTwPbPDeX/dkTsG3N7V0bEvRHxzYjYHREvGNi8HfjNLn8erSwWshbrJzJzHXAu8AjwB0Pbfycz1w1cLh5zW78AfKyroPN4CHgzcBawEbgJ+Pjcxsy8ajA/8C/ADaNuKCI2AjuBX21vbw/wiYHbuh1YHxEv7+hn0QpjIWsimfnfwI3AphPtO0pEfDfwIuC2gXW3RsTPDyxfExH/dLJZB2Xm45k5m81LVAN4GvieeTLOAD/I/L80fgrYn5k3tI/HrwEXR8RLB/a5FdiyJOG14q3pO4CmU0ScDvws8K8T3sRFwL9n5tGTyPD4mM3bM3P7Ca67jmZQ8v55dns78I+Z+ZV5tn8vcGxKJjOPRMQD7fp729UHgCvG5JSOsZC1WJ+OiKM0ZXYI+PGh7b8YEe8eWP5MZm4dcTsbgG+cTJDM3HAy142ItcBW4Kvz7PZ24DfG3Mw64NGhdU8AZwwsf4PmZ5VOyCkLLdab2iI8FXg38PdDZ0n8bmZuGLiMKmOAwxxfXMsuM48Afwx8NCKeN7gtIq4AzqGZlpnPU8D6oXXrOf4XzRnAuJG8dIyFrIlk5tOZuZNmDnaSP8nvBi6IiOG/0k4b+H7syHLobIjhyy8tMMezgNOB5w+t3wrszMynxlx3P3Dsn5btiPtF7fo5FzIwrSGNYyFrItH4SeBMmnnSRcnMg8D9wOVDm34mItZHxNk0UwbrIuLZ89zGujGX35on9+si4tKIOCUi1gMfoBmtHxjY57nATwM7TvBjfAr4voi4OiJOo5mLvjsz7x3Y54eBz53gdiTAQtbifTYingKepDnHdmtmDo4I3zc0Un1szG39CfBzQ+v+g2b0/AWa6YRzgF9ZuvhsAK6nmet9gOYMi83tWRJz3tRu3z185YjYHxFvA8jMR4GraR6Hw8ArgLcM7PsDwJH29DfphMI3qFdfIuJU4A7gysx8OCJuBf48Mz/cb7KlERGfBD6SmX/ZdxZNB8+yUG8y81tMeB7zNMjMq/vOoOnilIUkFeGUhSQV4QhZkopY1Bzyxo0bc2ZmZqI7OnLkCGvXrp3oun0wb7fM261pywvTl3kxeffu3ftYZp59wh0zc8GXyy67LCe1e/fuia/bB/N2y7zdmra8mdOXeTF5gT25gI51ykKSirCQJakIC1mSirCQJakIC1mSirCQJakIC1mSirCQJakIC1mSivDtN1XGzLZdY7fPbt+yTEkmMyp/9cyqxULWshguqx2ba71nwXA+i1R9sJA11olGrdBveS2kSKetbKs/5uqOhawlt5BC2ffgE1yzgP0We7sL2WeS+xo1op/kvrrKZ0GvDBayjtNnyVQ2yS8QWB2PjZaOhbyKrdayWK0/t+qzkKUVYPiXzLUXHX3GiN5pjfo8D1mSirCQJakIC1mSinAOeRXxn1mrm6fK1ecIWZKKsJAlqQgLWZKKsJAlqQgLWZKKsJAlqQhPe1vBPM1N4/iG+vU4QpakIixkSSrCQpakIixkSSrCQpakIixkSSrCQpakIixkSSrCQpakIixkSSrCl06vEPsefOIZnzIsLZafKtIvR8iSVISFLElFWMiSVISFLElFWMiSVISFLElFWMiSVISFLElFWMiSVISFLElFWMiSVISFLElFWMiSVISFLElFWMiSVISFLElF+Ab1U2r4jcSvvainIFrRho8z8E3ru+QIWZKKsJAlqQgLWZKKsJAlqQgLWZKKsJAlqQgLWZKKsJAlqQgLWZKKsJAlqQgLWZKKsJAlqQgLWZKKsJAlqQgLWZKKsJAlqQgLWZKKsJAlqQgLWZKK8DP1psCozzWT+jJ8PPoZe0vHEbIkFWEhS1IRFrIkFWEhS1IRFrIkFWEhS1IRFrIkFWEhS1IRFrIkFWEhS1IRFrIkFWEhS1IRFrIkFWEhS1IRFrIkFWEhS1IRFrIkFWEhS1IRFrIkFWEhS1IRFrIkFWEhS1IRFrIkFWEhS1IRa/oOIGm6zWzbddzy7PYtPSWZfo6QJakIR8gFDY84JK0OjpAlqQgLWZKKsJAlqQgLWZKKsJAlqQgLWZKKsJAlqQgLWZKKsJAlqQgLWZKKsJAlqQgLWZKKsJAlqQgLWZKKsJAlqQgLWZKKsJAlqQgLWZKKsJAlqQgLWZKKsJAlqQgLWZKKsJAlqQgLWZKKsJAlqYg1fQeQtLLMbNv1jHWz27f0kGT6WMg9G3XwSlqdnLKQpCIsZEkqwkKWpCIsZEkqwkKWpCIsZEkqwkKWpCIsZEkqwkKWpCIsZEkqwkKWpCIsZEkqwkKWpCIsZEkqwkKWpCIsZEkqwkKWpCIsZEkqwkKWpCIsZEkqwkKWpCIsZEkqwkKWpCLW9B1gtZnZtqvvCNKyGz7uZ7dv6SlJbY6QJakIC1mSirCQJakIC1mSirCQJakIC1mSirCQJakIC1mSirCQJakIC1mSirCQJakIC1mSirCQJakIC1mSirCQJakIC1mSirCQJakIC1mSirCQJakIC1mSirCQJakIP3W6Y37KtPRMo54XOzav7SFJLY6QJakIC1mSirCQJakIC1mSirCQJakIC1mSirCQJakIC1mSirCQJakIC1mSirCQJakIC1mSirCQJakIC1mSirCQJakIC1mSivAN6peQb0YvTW7fg09wzcBzaHb7lh7T9MMRsiQVYSFLUhEWsiQVYSFLUhEWsiQVYSFLUhEWsiQVYSFLUhEWsiQVYSFLUhG+dPok+FJpqTvDz6/V8FJqR8iSVISFLElFWMiSVISFLElFWMiSVISFLElFeNrbAnmKm9SvUc/BlXYqnCNkSSrCQpakIpyymMfwBy5KUtcsZElTa6W9vNopC0kqYlWOkBdyxsS1Fy1DEElLaiHP7cqj6MjMhe8c8Sjw1QnvayPw2ITX7YN5u2Xebk1bXpi+zIvJ+4LMPPtEOy2qkE9GROzJzJcvy50tAfN2y7zdmra8MH2Zu8jrHLIkFWEhS1IRy1nIH1rG+1oK5u2Webs1bXlh+jIved5lm0OWJI3nlIUkFWEhS1IRnRdyRGyOiPsi4ssRsa3r+5tERPxpRByKiHsG1p0VEZ+PiPvbr2f2mXFQRJwfEbsj4kBE7I+I97TrS2aOiNMi4vaIuKvN++vt+hdGxG1t3k9ExHP6zjooIk6JiDsi4uZ2uWzeiJiNiH0RcWdE7GnXlTweACJiQ0TcGBH3tsfxq6rmjYiXtI/r3OXJiHhvF3k7LeSIOAX4Q+AqYBPw1ojY1OV9TmgHsHlo3Tbglsx8MXBLu1zFUeDazLwQeCXwrvZxrZr5W8BrMvNi4BJgc0S8Evht4PfavIeBd/SYcZT3AAcGlqvn/dHMvGTg3NiqxwPA7wN/lZkvBS6meZxL5s3M+9rH9RLgMuCbwKfoIm9mdnYBXgX89cDydcB1Xd7nSWSdAe4ZWL4POLf9/lzgvr4zjsn+GeB105AZOB34IvAKmlc5rRl1rPR9Ac5rn2SvAW4GonjeWWDj0LqSxwOwHvgK7UkF1fMOZfwx4J+7ytv1lMXzga8NLB9s102D78rMhwHar8/rOc9IETEDXArcRuHM7Z//dwKHgM8DDwCPZ+bRdpdqx8YHgfcB/9sufye18ybwNxGxNyLe2a6rejxcADwK/Fk7JfThiFhL3byD3gJc336/5Hm7LuQYsc7z7JZIRKwDPgm8NzOf7DvPOJn5dDZ/8p0HXA5cOGq35U01WkS8ATiUmXsHV4/YtUTe1qsz82U004Pviogf6jvQGGuAlwF/lJmXAkcoMj0xTvs/gzcCN3R1H10X8kHg/IHl84CHOr7PpfJIRJwL0H491HOe40TEs2nK+C8yc2e7unRmgMx8HLiVZu57Q0TMveNgpWPj1cAbI2IW+DjNtMUHqZuXzHyo/XqIZn7zcuoeDweBg5l5W7t8I01BV8075yrgi5n5SLu85Hm7LuQvAC9u/zv9HJrh/k0d3+dSuQnY2n6/lWaetoSICOAjwIHM/MDAppKZI+LsiNjQfv9c4LU0/8TZDby53a1M3sy8LjPPy8wZmmP27zLzbRTNGxFrI+KMue9p5jnvoejxkJlfB74WES9pV10JfImieQe8lf+froAu8i7DJPjrgX+jmTP85b4n5efJeD3wMPA/NL+930EzZ3gLcH/79ay+cw7kvYLmz+W7gTvby+urZga+H7ijzXsP8P52/QXA7cCXaf4MPLXvrCOy/whwc+W8ba672sv+uedZ1eOhzXYJsKc9Jj4NnFk87+nAfwLfMbBuyfP60mlJKsJX6klSERayJBVhIUtSERayJBVhIUtSERayJBVhIUtSEf8H5TzeL6zRx2oAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for player in team: \n",
    "    repeated_hist(player, bins=range(70))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that none of the players have a distribution that looks like a normal distribution: `SC` is skewed to one side (the mean is 5 points to the right of the peak); the three next players have bimodal distributions; and `BE` is too flat on top. \n",
    "\n",
    "Now we define the team score to be the sum of the *k* = 5 players, and display this new distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "repeated_hist(Team, bins=range(60, 170))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sure enough, this looks very much like a normal distribution. The **Central Limit Theorem** appears to hold in this case. But I have to say: \"Central Limit\" is not a very evocative name, so I propose we re-name this as the **Strength in Numbers Theorem**, to indicate the fact that if you have a lot of numbers, you tend to get the expected result."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "\n",
    "# Appendix: Continuous Sample Spaces\n",
    "\n",
    "Everything up to here has been about discrete, finite sample spaces, where we can *enumerate* all the possible outcomes. \n",
    "\n",
    "But a reader asked about *continuous* sample spaces, such as the space of real numbers. The principles are the same: probability is still the ratio of the favorable cases to all the cases, but now instead of *counting* cases, we have to (in general) compute integrals to compare the sizes of cases. \n",
    "Here we will cover a simple example, which we first solve approximately by simulation, and then exactly by calculation.\n",
    "\n",
    "## The Hot New Game Show Problem: Simulation\n",
    "\n",
    "Oliver Roeder posed [this problem](http://fivethirtyeight.com/features/can-you-win-this-hot-new-game-show/) in the 538 *Riddler* blog:\n",
    "\n",
    ">Two players go on a hot new game show called *Higher Number Wins.* The two go into separate booths, and each presses a button, and a random number between zero and one appears on a screen. (At this point, neither knows the other’s number, but they do know the numbers are chosen from a standard uniform distribution.) They can choose to keep that first number, or to press the button again to discard the first number and get a second random number, which they must keep. Then, they come out of their booths and see the final number for each player on the wall. The lavish grand prize — a case full of gold bullion — is awarded to the player who kept the higher number. Which number is the optimal cutoff for players to discard their first number and choose another? Put another way, within which range should they choose to keep the first number, and within which range should they reject it and try their luck with a second number?\n",
    "\n",
    "We'll use this notation:\n",
    "- **A,** **B:** the two players.\n",
    "-  $A$, $B$: the cutoff values they choose: the lower bound of the range of first numbers they will accept.\n",
    "- $a$, $b$: the actual random numbers that appear on the screen.\n",
    "\n",
    "For example, if player **A** chooses a cutoff of $A$ = 0.6, that means that **A** would accept any first number greater than 0.6, and reject any number below that cutoff. The question is: What cutoff, $A$, should player **A** choose to maximize the chance of winning, that is, maximize P($a$ > $b$)?\n",
    "\n",
    "First, simulate the number that a player with a given cutoff gets (note that `random.random()` returns a float sampled uniformly from the interval [0..1]):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "import itertools\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "number = random.random\n",
    "\n",
    "def strategy(cutoff):\n",
    "    \"Play the game with given cutoff, returning the first or second random number.\"\n",
    "    first = number()\n",
    "    return first if first > cutoff else number()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.23132261507622254"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "strategy(.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now compare the numbers returned with a cutoff of $A$ versus a cutoff of $B$, and repeat for a large number of trials; this gives us an estimate of the probability that cutoff $A$ is better than cutoff $B$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Pwin(A, B, trials=20000):\n",
    "    \"The probability that cutoff A wins against cutoff B.\"\n",
    "    return mean(strategy(A) > strategy(B) \n",
    "                for _ in range(trials))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5616"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Pwin(0.6, 0.9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now define a function, `top`, that considers a collection of possible cutoffs, estimate the probability for each cutoff playing against each other cutoff, and returns a list with the `N` top cutoffs (the ones that defeated the most number of opponent cutoffs), and the number of opponents they defeat: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def top(N, cutoffs):\n",
    "    \"Return the N best cutoffs and the number of opponent cutoffs they beat.\"\n",
    "    winners = Counter(A if Pwin(A, B) > 0.5 else B\n",
    "                      for (A, B) in itertools.combinations(cutoffs, 2))\n",
    "    return winners.most_common(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0.6200000000000001, 45),\n",
       " (0.5800000000000001, 44),\n",
       " (0.6100000000000001, 44),\n",
       " (0.55, 43),\n",
       " (0.5900000000000001, 43),\n",
       " (0.53, 41),\n",
       " (0.54, 41),\n",
       " (0.5700000000000001, 41),\n",
       " (0.6300000000000001, 41),\n",
       " (0.6400000000000001, 41)]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "top(10, np.arange(0.5, 1.0, 0.01))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We get a good idea of the top cutoffs, but they are close to each other, so we can't quite be sure which is best, only that the best is somewhere around 0.60. We could get a better estimate by increasing the number of trials, but that would consume more time.\n",
    "\n",
    "## The Hot New Game Show Problem: Exact Calculation\n",
    "\n",
    "More promising is the possibility of making `Pwin(A, B)` an exact calculation. But before we get to `Pwin(A, B)`, let's solve a simpler problem: assume that both players **A** and **B** have chosen a cutoff, and have each received a number above the cutoff. What is the probability that **A** gets the higher number? We'll call this `Phigher(A, B)`. We can think of this as a two-dimensional sample space of points in the ($a$, $b$) plane, where$a$ ranges from the cutoff $A$ to 1 and $b$ ranges from the cutoff B to 1. Here is a diagram of that two-dimensional sample space, with the cutoffs $A$=0.5 and $B$=0.6:\n",
    "\n",
    "<img src=\"http://norvig.com/ipython/probability2da.jpg\" width=413>\n",
    "\n",
    "The total area of the sample space is 0.5 &times; 0.4 = 0.20, and in general it is (1 - $A$) &middot; (1 - $B$). What about the favorable cases, where **A** beats **B**? That corresponds to the shaded triangle below:\n",
    "\n",
    "<img src=\"http://norvig.com/ipython/probability2d.jpg\" width=413>\n",
    "\n",
    "The area of a triangle is 1/2 the base times the height, or in this case, 0.4<sup>2</sup> / 2 = 0.08, and in general, (1 - $B$)<sup>2</sup> / 2. So in general we have:\n",
    "\n",
    "    Phigher(A, B) = favorable / total\n",
    "    favorable     = ((1 - B) ** 2) / 2 \n",
    "    total         = (1 - A) * (1 - B)\n",
    "    Phigher(A, B) = (((1 - B) ** 2) / 2) / ((1 - A) * (1 - B))\n",
    "    Phigher(A, B) = (1 - B) / (2 * (1 - A))\n",
    "    \n",
    "And in this specific case we have:\n",
    "\n",
    "     A = 0.5; B = 0.6\n",
    "     favorable         = 0.4 ** 2 / 2 = 0.08\n",
    "     total             = 0.5 * 0.4    = 0.20\n",
    "     Phigher(0.5, 0.6) = 0.08 / 0.20  = 0.4\n",
    "\n",
    "But note that this only works when the cutoff $A$ &le; $B$; when $A$ > $B$, we need to reverse things. That gives us the code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Phigher(A, B):\n",
    "    \"Probability that a uniform sample from [A..1] is higher than one from [B..1].\"\n",
    "    if A <= B:\n",
    "        return (1 - B) / (2 * (1 - A))\n",
    "    else:\n",
    "        return 1 - Phigher(B, A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Phigher(0.5, 0.6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We're now ready to tackle the full game. There are four cases to consider, depending on whether **A** and **B** gets a first number that is above or below their cutoff choices:\n",
    "\n",
    "| first $a$ | first $b$ | P($a$, $b$) | P(A wins│ $a$, $b$) |  Comment |\n",
    "|:-----:|:-----:| ----------- | ------------- | ------------ |\n",
    "|$a$ > $A$ | $b$ > $B$ | (1 - $A$) &middot; (1 - $B$) | Phigher(*A*, $B$) | Both above cutoff; both keep first numbers |\n",
    "|$a$ < $A$ | $b$ < $B$ | $A$ &middot; $B$ | Phigher(0, 0)  | Both below cutoff, both get new numbers from [0..1] |\n",
    "|$a$ > $A$ | $b$ < $B$ | (1 - $A$) &middot;  $B$ | Phigher($A$, 0) | **A** keeps number; **B** gets new number from [0..1] |\n",
    "|$a$ < $A$ | $b$ > $B$ | $A$ &middot; (1 - $B$) | Phigher(0, $B$) | **A** gets new number from [0..1]; **B** keeps number |\n",
    "\n",
    "For example, the first row of this table says that the event of both first numbers being above their respective cutoffs has probability (1 - $A$) &middot; (1 - $B$), and if this does occur, then the probability of **A** winning is Phigher(*A*, $B$).\n",
    "We're ready to replace the old simulation-based `Pwin` with a new calculation-based version:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Pwin(A, B):\n",
    "    \"With what probability does cutoff A win against cutoff B?\"\n",
    "    return ((1-A) * (1-B) * Phigher(A, B)  # both above cutoff; both keep 1st number\n",
    "            + A * B       * Phigher(0, 0)  # both below cutoff; both get new numbers\n",
    "            + (1-A) * B   * Phigher(A, 0)  # A above, B below; B gets new number\n",
    "            + A * (1-B)   * Phigher(0, B)) # A below, B above; A gets new number"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.495"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Pwin(0.5, 0.6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`Pwin` relies on a lot of algebra. Let's define a few tests to check for obvious errors:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'ok'"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def test():\n",
    "    assert Phigher(0.5, 0.5) == Phigher(0.75, 0.75) == Phigher(0, 0) == 0.5\n",
    "    assert Pwin(0.5, 0.5) == Pwin(0.75, 0.75) == 0.5\n",
    "    assert Phigher(.6, .5) == 0.6\n",
    "    assert Phigher(.5, .6) == 0.4\n",
    "    return 'ok'\n",
    "\n",
    "test()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's repeat the calculation with our new, exact `Pwin`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0.6200000000000001, 49),\n",
       " (0.6100000000000001, 48),\n",
       " (0.6000000000000001, 47),\n",
       " (0.5900000000000001, 46),\n",
       " (0.6300000000000001, 45),\n",
       " (0.5800000000000001, 44),\n",
       " (0.5700000000000001, 43),\n",
       " (0.6400000000000001, 42),\n",
       " (0.56, 41),\n",
       " (0.55, 40)]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "top(10, np.arange(0.5, 1.0, 0.01))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is good to see that the simulation and the exact calculation are in rough agreement; that gives me more confidence in both of them. We see here that 0.62 defeats all the other cutoffs (there are 50 cutoffs and it defeated the 49 others), and 0.61 defeats all cutoffs except 0.62. The great thing about the exact calculation code is that it runs fast, regardless of how much accuracy we want. We can zero in on the range around 0.6:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0.6180000000000001, 199),\n",
       " (0.6170000000000001, 198),\n",
       " (0.6160000000000001, 197),\n",
       " (0.6190000000000001, 196),\n",
       " (0.6150000000000001, 195),\n",
       " (0.6140000000000001, 194),\n",
       " (0.6130000000000001, 193),\n",
       " (0.6200000000000001, 192),\n",
       " (0.6120000000000001, 191),\n",
       " (0.6110000000000001, 190)]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "top(10, np.arange(0.5, 0.7, 0.001))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This says 0.618 is best. We can get even more accuracy:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0.6180340000000297, 2000),\n",
       " (0.6180330000000297, 1999),\n",
       " (0.6180320000000297, 1998),\n",
       " (0.6180350000000298, 1997),\n",
       " (0.6180310000000296, 1996),\n",
       " (0.6180300000000296, 1995),\n",
       " (0.6180290000000296, 1994),\n",
       " (0.6180360000000298, 1993),\n",
       " (0.6180280000000296, 1992),\n",
       " (0.6180270000000295, 1991)]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "top(10, np.arange(0.617, 0.619, 0.000001))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So 0.618034 is best. Does that number [look familiar](https://en.wikipedia.org/wiki/Golden_ratio)? Can we prove that it is what I think it is?\n",
    "\n",
    "To understand the strategic possibilities, it is helpful to draw a 3D plot of `Pwin(A, B)` for values of $A$ and $B$ between 0 and 1:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits.mplot3d.axes3d import Axes3D\n",
    "\n",
    "def map2(fn, A, B):\n",
    "    \"Map fn to corresponding elements of 2D arrays A and B.\"\n",
    "    return [[fn(a, b) for (a, b) in zip(Arow, Brow)]\n",
    "            for (Arow, Brow) in zip(A, B)]\n",
    "\n",
    "def plot3d(fn):\n",
    "    fig = plt.figure(figsize=(10,10))\n",
    "    ax = fig.add_subplot(111, projection='3d')\n",
    "    x = y = np.arange(0, 1.0, 0.05)\n",
    "    X, Y = np.meshgrid(x, y)\n",
    "    Z = np.array(map2(fn, X, Y))\n",
    "    ax.plot_surface(X, Y, Z)\n",
    "    ax.set_xlabel('A')\n",
    "    ax.set_ylabel('B')\n",
    "    ax.set_zlabel('Pwin(A, B)')\n",
    "    \n",
    "plot3d(Pwin)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What does this [Pringle of Probability](http://fivethirtyeight.com/features/should-you-shoot-free-throws-underhand/) show us? The highest win percentage for **A**, the peak of the surface, occurs when $A$ is around 0.5 and $B$ is 0 or 1. We can confirm that, finding the maximum `Pwin(A, B)` for many different cutoff values of `A` and `B`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "cutoffs = (set(np.arange(0.00,    1.00,    0.01)) | \n",
    "           set(np.arange(0.500,   0.700,   0.001)) | \n",
    "           set(np.arange(0.61803, 0.61804, 0.000001)))\n",
    "\n",
    "def Pwin_summary(A, B): return (Pwin(A, B), 'A:', A, 'B:', B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.625, 'A:', 0.5, 'B:', 0.0)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max(Pwin_summary(A, B) for A in cutoffs for B in cutoffs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So **A** could win 62.5% of the time if only **B** would chose a cutoff of 0. But, unfortunately for **A**, a rational player **B** is not going to do that. We can ask what happens if the game is changed so that player **A** has to declare a cutoff first, and then player **B** gets to respond with a cutoff, with full knowledge of **A**'s choice. In other words, what cutoff should **A** choose to maximize `Pwin(A, B)`, given that **B** is going to take that knowledge and pick a cutoff that minimizes `Pwin(A, B)`? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.5, 'A:', 0.6180340000000001, 'B:', 0.6180340000000001)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max(min(Pwin_summary(A, B) for B in cutoffs)\n",
    "    for A in cutoffs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And what if we run it the other way around, where **B** chooses a cutoff first, and then **A** responds?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.5, 'A:', 0.6180340000000001, 'B:', 0.6180340000000001)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "min(max(Pwin_summary(A, B) for A in cutoffs)\n",
    "    for B in cutoffs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In both cases, the rational choice for both players is a cutoff of 0.618034, which corresponds to the  \"saddle point\" in the middle of the plot. This is a *stable equilibrium*; consider fixing $B$ = 0.618034, \n",
    "and notice that if $A$ changes to any other value, we slip off the saddle to the right or left, resulting in a worse win probability for **A**. Similarly, if we fix $A$ = 0.618034, then if $B$ changes to another value, we ride up the saddle to a higher win percentage for **A**, which is worse for **B**. So neither player will want to move from the saddle point.\n",
    "\n",
    "The moral for continuous spaces is the same as for discrete spaces: be careful about defining your sample space; measure carefully, and let your code take care of the rest."
   ]
  }
 ],
 "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": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}