AceSimulation.ipynb

acesimulation.ipynb

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  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyNpUfJvEk6DhpancL0mxIlz",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/heathhenley/20ede25bd68b3e0a70dbd3869f427768/acesimulation.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "OKysGLXGxnwE",
        "outputId": "c6df11fc-e946-454c-8437-676d21dde456"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Single suit case - 50000 iterations\n",
            "  Average steps: 6.990, Std. Dev: 3.742\n",
            "Full deck case - 50000 iterations\n",
            "  Average steps: 10.574, Std. Dev: 8.244\n"
          ]
        }
      ],
      "source": [
        "from typing import List, Tuple\n",
        "\n",
        "import random\n",
        "\n",
        "\n",
        "def strategy_random(deck: List[str], target: str = 'A') -> int:\n",
        "  \"\"\" Returns number of guesses needed to find the ace \"\"\"\n",
        "  steps = 1\n",
        "  while True:\n",
        "    flip_idx = random.randint(0, len(deck)-1)\n",
        "    if deck[flip_idx] == target:\n",
        "      break\n",
        "    deck.pop(flip_idx)\n",
        "    steps += 1\n",
        "  return steps\n",
        "\n",
        "\n",
        "def stats(x_sum, x2_sum, n) -> Tuple[float, float]:\n",
        "  x_bar = x_sum / n\n",
        "  x2_bar = x2_sum / n\n",
        "  return (x_bar, (x2_bar - x_bar**2)**0.5)\n",
        "\n",
        "\n",
        "def play_the_game(\n",
        "    number_of_games: int = 1, deck_size: int = 13, ace_count: int = 1\n",
        "  ) -> Tuple[float, float]:\n",
        "\n",
        "  total_steps = 0\n",
        "  steps_sqrd_total = 0\n",
        "  for _ in range(number_of_games):\n",
        "    # make a deck and shuffle it\n",
        "    deck = list(\"A\" * ace_count + (deck_size - ace_count) * \"X\")\n",
        "    random.shuffle(deck)\n",
        "    # play the game - find the ace\n",
        "    steps = strategy_random(deck)\n",
        "    # stats\n",
        "    total_steps += steps\n",
        "    steps_sqrd_total += steps * steps\n",
        "  return stats(total_steps, steps_sqrd_total, number_of_games)\n",
        "\n",
        "\n",
        "# Play the game and see what we get to check our results\n",
        "number_of_repeats = 50_000\n",
        "\n",
        "# Single\n",
        "avg, stdev = play_the_game(\n",
        "    number_of_games=number_of_repeats,\n",
        "    deck_size = 13,\n",
        "    ace_count = 1\n",
        "  )\n",
        "print(f\"Single suit case - {number_of_repeats} iterations\")\n",
        "print(f\"  Average steps: {avg:.3f}, Std. Dev: {stdev:.3f}\")\n",
        "\n",
        "# Full deck\n",
        "avg, stdev = play_the_game(\n",
        "    number_of_games=number_of_repeats,\n",
        "    deck_size = 52,\n",
        "    ace_count = 4\n",
        "  )\n",
        "print(f\"Full deck case - {number_of_repeats} iterations\")\n",
        "print(f\"  Average steps: {avg:.3f}, Std. Dev: {stdev:.3f}\")\n",
        "\n"
      ]
    }
  ]
}