Lecture 01 - Dice Game.ipynb

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              {
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                "name": "stdout",
                "text": [
                  "New data (n=1): [(2, 3)]\n",
                  "All datapoints: [(4, 1), (5, 4), (1, 3), (1, 6), (2, 3)]\n"
                ]
              },
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                  "text/plain": "<Figure size 1500x400 with 2 Axes>",
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\n"
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "48dmT-b06Qs8"
      },
      "source": [
        "# The dice game\n",
        "\n",
        "Below are some simulations for one of the lab exercises. Sometimes, we can't easily find an answer to a probability problem using theory. This notebook shows how we can find some answers using simulation.\n",
        "\n",
        "First, we need to import some libraries."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cXCsLonp6Qs_"
      },
      "source": [
        "import numpy as np  # Math\n",
        "import random       # Randomness\n",
        "import matplotlib.pylab as plt  # Plotting\n",
        "import ipywidgets as widgets    # Interactive stuff"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Zn0OqFJo6QtS"
      },
      "source": [
        "The first thing to do is to define a set of outcomes."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dz6lG5DSPslG",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "3862ef61-b43d-4d1c-cff1-3e1a1512fa0c"
      },
      "source": [
        "outcomes = list()\n",
        "for die1 in range(1, 6+1):\n",
        "  for die2 in range(1, 6+1):\n",
        "    outcomes.append((die1, die2))\n",
        "print(\"%i outcomes: %s\" % (len(outcomes), outcomes))"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "36 outcomes: [(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ae1s8Lb3Mp90"
      },
      "source": [
        "Let's pick a few pairs of die outcomes and show the game outcome."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YDFkgFAxP-0T",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c759d3d1-2c24-4a5f-b364-cb32fcff5771"
      },
      "source": [
        "def peach_wins(outcome):\n",
        "  die1, die2 = outcome\n",
        "  diff = abs( die1 - die2 )\n",
        "  if diff <= 2:\n",
        "    return True\n",
        "  else:\n",
        "    return False\n",
        "\n",
        "for outcome in random.choices(outcomes, k=5):\n",
        "  print(\"Outcome drawn: %s\" % repr(outcome))\n",
        "  if peach_wins(outcome):\n",
        "    print(\"  -> Peach wins!\")\n",
        "  else:\n",
        "    print(\"  -> Yoshi wins!\")\n",
        "  print()"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Outcome drawn: (2, 4)\n",
            "  -> Peach wins!\n",
            "\n",
            "Outcome drawn: (1, 5)\n",
            "  -> Yoshi wins!\n",
            "\n",
            "Outcome drawn: (4, 2)\n",
            "  -> Peach wins!\n",
            "\n",
            "Outcome drawn: (1, 1)\n",
            "  -> Peach wins!\n",
            "\n",
            "Outcome drawn: (5, 2)\n",
            "  -> Yoshi wins!\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p4V0AJYzMRku"
      },
      "source": [
        "We can simulate this just like before."
      ]
    },
    {
      "cell_type": "code",
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        "id": "DPBEL7KJQ7GG",
        "colab": {
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      "source": [
        "data = list()\n",
        "\n",
        "def throw_dice(n_throws):\n",
        "  # Throw the dice\n",
        "  new_data = random.choices(outcomes, k=n_throws)\n",
        "  data.extend(new_data)\n",
        "  print(\"New data (n=%i): %s\" % (len(new_data), new_data))\n",
        "  if len(data) < 50:\n",
        "    print(\"All datapoints:\", data)\n",
        "  else:\n",
        "    print(\"Last data points: ...\", data[-50:])\n",
        "  # Define the figures\n",
        "  fig = plt.figure(figsize=(15, 4), dpi=100)\n",
        "  ax = fig.subplots(1, 2)\n",
        "  ax[0].set_ylabel(\"# games\")\n",
        "  n = np.sum([peach_wins(outcome) for outcome in data])\n",
        "  m = np.sum([not peach_wins(outcome) for outcome in data])\n",
        "  ax[0].set_xlabel(\"Diff. for games (Yoshi wins: %i, Peach wins: %i)\" %(m, n))\n",
        "  ax[1].set_xlabel(\"# games (total of %i)\" % len(data))\n",
        "  ax[1].set_ylabel('Probability')\n",
        "  # Plot data\n",
        "  diff_counts = np.zeros(6)\n",
        "  for outcome in data:\n",
        "    diff_counts[abs(outcome[0]-outcome[1])] += 1\n",
        "  new_diff_counts = np.zeros(6)\n",
        "  for outcome in new_data:\n",
        "    new_diff_counts[abs(outcome[0]-outcome[1])] += 1\n",
        "  games = np.arange(1, len(data)+1)\n",
        "  ax[1].plot(games, np.cumsum([peach_wins(outcome) for outcome in data])/games,\n",
        "              color='pink', label=\"Prob. of Peach winning\", linewidth=2)\n",
        "  ax[1].plot(games, np.cumsum([not peach_wins(outcome) for outcome in data])/games,\n",
        "              color='green', alpha=.6, label=\"Prob. of Yoshi winning\", linewidth=2)\n",
        "  # ax[1].plot(x, np.ones(x.shape)/n_outcomes, 'g--', alpha=.5, label=\"Theoretical prob.\")\n",
        "  labels = [\"%i\" % i for i in range(6)]\n",
        "  colours = ['pink', 'pink', 'pink', 'green', 'green', 'green']\n",
        "  old_diff_counts = diff_counts-new_diff_counts\n",
        "  ax[0].bar(labels, new_diff_counts, bottom=old_diff_counts, align='center', color=colours, alpha=.7)#, edgecolor='gray')\n",
        "  ax[0].bar(labels, old_diff_counts, align='center', color=colours)#, edgecolor='gray')\n",
        "  ax[0].bar(labels, old_diff_counts+new_diff_counts, align='center', color='none', edgecolor='gray')\n",
        "  # Adjust graphs and commit to screen\n",
        "  a = list(ax[0].axis())\n",
        "  a[2] = 0\n",
        "  a[3] = max(np.max(diff_counts)+10, 25)\n",
        "  ax[0].axis(tuple(a))\n",
        "  a = list(ax[1].axis())\n",
        "  a[2] = 0\n",
        "  a[3] = 1\n",
        "  ax[1].axis(tuple(a))\n",
        "  ax[1].legend(loc='upper right')\n",
        "  plt.show()\n",
        "  #fig.show()\n",
        "\n",
        "widgets.interact_manual.opts['manual_name'] = 'Throw dice!'\n",
        "interact_plot = widgets.interact_manual(throw_dice, n_throws=widgets.IntSlider(min=1, max=100, step=1, value=1));\n",
        "output = interact_plot.widget.children[-1] # This should prevent flickering\n",
        "output.layout.height = '400px'"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "interactive(children=(IntSlider(value=1, description='n_throws', min=1), Button(description='Throw dice!', sty…"
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              "version_major": 2,
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    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mZQUef9VN4eI"
      },
      "source": [
        "Does this prove that the French had it right in 1789?"
      ]
    }
  ]
}