MotyHall.ipynb

motyhall.ipynb

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    "colab": {
      "name": "MotyHall.ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyP2/8afzWAYzQKv2IBT4mg9",
      "include_colab_link": true
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    "kernelspec": {
      "name": "python3",
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    "language_info": {
      "name": "python"
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
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      "source": [
        "<a href=\"https://colab.research.google.com/gist/Ziul/3d9009cd89ab331472250bc04f04d5e5/motyhall.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
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    {
      "cell_type": "markdown",
      "source": [
        "# Honty Hall Example\n",
        "\n",
        "Let's create a example to check if the Monty Hall Paradox really works"
      ],
      "metadata": {
        "id": "ryou3nXAU8rY"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "7nJ_tmPkU4eW"
      },
      "outputs": [],
      "source": [
        "from random import choice\n",
        "from string import ascii_lowercase as _keys_"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def monty_hall(doors_left:int = 2, total:int = int(1e5), start_doors:int = len(_keys_)) -> float:\n",
        "    \"\"\"\n",
        "    Repeat the Monty Hall example several times to check probabilities\n",
        "\n",
        "    Args:\n",
        "        total (int): How many times to repeat the experiment. Default: int(1e5)\n",
        "        doors_left (int): Total of doors left in the end. Default: 2.\n",
        "        start_doors (int): Initial amount of doors. Max: 26. Default: 26\n",
        "    Returns:\n",
        "        rate (float): Success rate\n",
        "    \"\"\"\n",
        "    # all available doors\n",
        "    keys = _keys_[:start_doors]\n",
        "\n",
        "    hits = 0 # how many times the player wons\n",
        "\n",
        "    for _ in range(total):\n",
        "        # set all ports\n",
        "        ports = dict.fromkeys(keys, False)\n",
        "        # set the correct answer\n",
        "        answer = choice(keys)\n",
        "        ports[answer] = True\n",
        "        # player choose the first door\n",
        "        user_choice = choice(keys)\n",
        "\n",
        "        while len(ports.keys()) > doors_left:\n",
        "            # remove a port not winner\n",
        "            del ports[choice(list(ports.keys() - answer))]\n",
        "            # player choose another random door different from the actual\n",
        "            user_choice = choice(list(ports.keys() - user_choice))\n",
        "        if answer == user_choice:\n",
        "            # player wons\n",
        "            hits +=1\n",
        "    # returns success rate\n",
        "    return hits/total"
      ],
      "metadata": {
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      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "monty_hall(doors_left=2, start_doors =3)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Wy6o-BAxVXu2",
        "outputId": "bcbe09d8-4cbc-4ea3-b226-504e0bfbc595"
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      "execution_count": 3,
      "outputs": [
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          "output_type": "execute_result",
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              "0.49996"
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          "metadata": {},
          "execution_count": 3
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    {
      "cell_type": "code",
      "source": [
        "monty_hall(doors_left=2, start_doors = 10)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
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        "id": "1VuyZ6QEVgfH",
        "outputId": "441a10f7-3198-40af-ba76-245247f36dbf"
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      "execution_count": 4,
      "outputs": [
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          "metadata": {},
          "execution_count": 4
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    {
      "cell_type": "code",
      "source": [
        "monty_hall(doors_left=3)"
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      "outputs": [
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              "0.3377"
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          "metadata": {},
          "execution_count": 5
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