Expected number of draws - simple case and then for any number of aces for fun

acesimulation.ipynb

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  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyMmtNKXOsly/nD2g+OorT2P",
      "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/ab6847b7d9ef335a6870a54e1009665d/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": 17,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "OKysGLXGxnwE",
        "outputId": "3f2696d6-3e92-4515-e9b3-e98b2632f810"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Single case - 10000 iterations\n",
            "  Average steps: 7.031, Std. Dev: 3.739\n",
            "Full case - 10000 iterations\n",
            "  Average steps: 10.570, Std. Dev: 8.226\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 = 10_000\n",
        "\n",
        "game_configs = {\n",
        "    \"single\": {\n",
        "        \"number_of_games\": number_of_repeats,\n",
        "        \"deck_size\": 13,\n",
        "        \"ace_count\": 1\n",
        "    },\n",
        "    \"full\": {\n",
        "        \"number_of_games\": number_of_repeats,\n",
        "        \"deck_size\": 52,\n",
        "        \"ace_count\": 4\n",
        "    }\n",
        "}\n",
        "\n",
        "for game_name, game_config in game_configs.items():\n",
        "  avg, stdev = play_the_game(**game_config)\n",
        "  print(f\"{game_name.capitalize()} case - {game_config['number_of_games']} iterations\")\n",
        "  print(f\"  Average steps: {avg:.3f}, Std. Dev: {stdev:.3f}\")"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# more fun - get the average for the full deck for every possible number of A's\n",
        "# and plot it:\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "\n",
        "full_config = game_configs[\"full\"]\n",
        "\n",
        "\n",
        "def actual(ace_count, deck_size):\n",
        "  return (deck_size + 1) / (ace_count + 1)\n",
        "\n",
        "\n",
        "res = {}\n",
        "for ace_count in range(1, full_config[\"deck_size\"] + 1):\n",
        "  full_config[\"ace_count\"] = ace_count\n",
        "  avg, stdev = play_the_game(**full_config)\n",
        "  res[ace_count] = (avg, stdev, actual(ace_count, full_config['deck_size']))\n",
        "\n",
        "\n",
        "\n",
        "plt.errorbar(res.keys(),\n",
        " [x[0] for x in res.values()],\n",
        "  yerr=[x[1] for x in res.values()], fmt=\".\", label=\"Sim\")\n",
        "plt.plot(res.keys(), [x[2] for x in res.values()],\"--.k\", label=\"Actual\")\n",
        "plt.xlabel(\"Number of Aces in Deck\")\n",
        "plt.ylabel(\"Average Draws\")\n",
        "plt.title(f\"Average Draw to First Ace ({full_config['number_of_games']} games)\")\n",
        "plt.grid()\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "VhHYW_K8rOnp",
        "outputId": "0784db6c-c2c3-4fc0-d557-646b45fb031d"
      },
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}