{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# General Monty Hall Game Simulation \n", "\n", "### Descriptions are available at [metalearner.org](https://metalearner.org/2016/05/05/monty-hall-simulation/)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# -*- coding: utf-8 -*-\n", "# Author: Ehsan M. Kermani, ehsanmo1367@gmail.com\n", "# Website: metalearner.org\n", "\n", "\"\"\"\n", "Monty Hall Game Simulation [[http://en.wikipedia.org/wiki/Monty_Hall_problem]]\n", "\"\"\"\n", "\n", "import numpy as np\n", "from numpy.random import RandomState\n", "from random import sample\n", "from mpl_toolkits.mplot3d import Axes3D\n", "from matplotlib import cm\n", "from matplotlib.ticker import LinearLocator, FormatStrFormatter\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "\n", "\n", "class MontyHall(object):\n", " \"\"\"\n", " Creates simulation game object\n", "\n", " Parameters:\n", " ----------\n", " n_games: int Number of games\n", " n_bins: int Number of bins\n", " n_discards: int Number of discard options, between 1, n_bins-2\n", " switch: boolean Switch or not\n", " seed: int Seed number\n", " \"\"\"\n", "\n", " def __init__(self, n_games, n_bins, n_discards, switch=False, seed=123):\n", " self.n_games = n_games\n", " self.n_bins = n_bins\n", " if 1 <= n_discards <= n_bins-2:\n", " self.n_discards = n_discards\n", " else:\n", " raise ValueError(\"n_discards must be between 1 and n_bins-2\")\n", " self.switch = switch\n", " self.seed = seed\n", "\n", " def set_prize(self):\n", " \"\"\" Set prize randomly for each game with fixed RandomState \"\"\"\n", " prng = RandomState(self.seed)\n", " return prng.randint(0, self.n_bins, self.n_games)\n", "\n", " def player_first_choice(self):\n", " \"\"\" Player first choice in each game with fixed\n", " RandomState to get same numbers in different calls\n", " \"\"\"\n", " prng = RandomState(2 * self.seed)\n", " return prng.randint(0, self.n_bins, self.n_games)\n", "\n", " def player_final_choice(self):\n", " \"\"\" Player final choice after discarding some options by host\"\"\"\n", " if not self.switch:\n", " return self.player_first_choice()\n", " else:\n", " opts = list(range(self.n_bins))\n", " arr = np.vstack([self.player_first_choice(), self.host_discard()])\n", " final = self._col_choice(opts, arr, 1)\n", " return final\n", "\n", " def host_discard(self):\n", " \"\"\" Host choice for removing n_discards bins\"\"\"\n", " if self.switch:\n", " opts = list(range(self.n_bins))\n", " arr = np.vstack([self.set_prize(), self.player_first_choice()])\n", " disc = self._col_choice(opts, arr, self.n_discards)\n", " return disc\n", "\n", " def _col_choice(self, opts, arr, n_disc):\n", " \"\"\" Possible choices per game\"\"\"\n", " try:\n", " res = np.apply_along_axis(\n", " lambda x:\n", " sample([v for i, v in enumerate(opts)\n", " if i not in set(x)], n_disc),\n", " axis=0,\n", " arr=arr)\n", " return res\n", " except:\n", " print(self.n_discards, 'must be less than', self.n_bins - 1)\n", "\n", " def score(self):\n", " \"\"\" Calculate the number of wins\"\"\"\n", " return np.sum(self.player_final_choice() == self.set_prize())\n", "\n", " def proba(self):\n", " \"\"\" Compute the winning probability\"\"\"\n", " return self.score() / self.n_games\n", "\n", " def __str__(self):\n", " if not self.switch:\n", " return 'Probability of winning if not switching: %.4f' \\\n", " % self.proba()\n", " else:\n", " return 'Probability of winning if switching: %.4f' \\\n", " % self.proba()\n", "\n", "if __name__ == '__main__':\n", "\n", " def simulation_proba(n_games, n_bins, n_discards, switch):\n", " \"\"\" Compute simulation probability of n_games with n_bins\n", " and n_discards options\n", " \"\"\"\n", " g = MontyHall(n_games=n_games, n_bins=n_bins, n_discards=n_discards,\n", " switch=switch)\n", " return g.proba()\n", "\n", " def simulation_2dplot(n_games, max_bins, n_discards=1, switch=True):\n", " \"\"\" Simulation 2D plot \"\"\"\n", " X = np.array(range(n_discards+2, max_bins))\n", " Y = np.array([simulation_proba(n_games, b, n_discards, switch)\n", " for b in X])\n", " plt.plot(X, Y, linestyle='-', color='b', lw=2)\n", " plt.xlabel('Number of Bins')\n", " if switch:\n", " plt.ylabel('Winning Probability after switching')\n", " else:\n", " plt.ylabel('Winning Probability if not switching')\n", " plt.title(\"Monty Hall Simulation with %d games and %d discards\"\n", " % (n_games, n_discards))\n", " plt.ylim(0.0, 1.0)\n", " # save must be before show\n", " plt.savefig('simulation_2dplot.png', dpi=300)\n", " plt.show()\n", "\n", " def simulation_3dplot(n_games, max_bins, max_discards, switch):\n", " \"\"\" Simulation 3D plot\"\"\"\n", " X = np.array(range(3, max_bins))\n", " Y = np.array(range(1, max_discards))\n", " X_grid, Y_grid = np.meshgrid(X, Y)\n", " triu_idx = np.triu_indices(n=max_discards-1)\n", " X_grid_utri, Y_grid_utri = X_grid[triu_idx], Y_grid[triu_idx]\n", "\n", " vect_simulation_proba = np.vectorize(simulation_proba)\n", " Z = vect_simulation_proba(n_games, X_grid_utri, Y_grid_utri, switch)\n", " nZ = np.zeros((max_discards-1, max_discards-1))\n", " nZ[triu_idx] = Z\n", "\n", " fig = plt.figure(figsize=(8, 6))\n", " ax = fig.gca(projection='3d')\n", " surf = ax.plot_surface(X_grid, Y_grid, nZ, rstride=1, cstride=1,\n", " cmap=cm.coolwarm, linewidth=0,\n", " antialiased=False)\n", " ax.set_zlim = (0.0, 1.0)\n", " ax.set_xlabel('Number of Bins')\n", " ax.set_ylabel('Number of Discards')\n", " if switch:\n", " ax.set_zlabel('Winning probability after switching')\n", " else:\n", " ax.set_zlabel('Winning probability if not switching')\n", " ax.zaxis.set_major_locator(LinearLocator(5))\n", " ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))\n", " ax.set_title('Monty Hall Probability Surface for %d games' % n_games)\n", "\n", " fig.colorbar(surf, shrink=0.5, aspect=5)\n", "\n", " fig.savefig('3d_simulation.png', dpi=300) # save must be before show\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.66413999999999995" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "simulation_proba(100000, 3, 1, switch=True)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.33585999999999999" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "simulation_proba(100000, 3, 1, switch=False)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.37542999999999999" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "simulation_proba(100000, 4, 1, switch=True)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.75002999999999997" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "simulation_proba(100000, 4, 2, switch=True)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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KKnO4HLgQuDvLawFwYj4faGZmpS9XcJgQ3j+Z5TWfxpuZNWFJVysdDFwJtEZTcPw+yzLH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\nDjWtq3v3IDjmmCC49NIg+Pn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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "simulation_2dplot(1000, 101, 1, switch=True)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "simulation_2dplot(1000, 101, 20, switch=True)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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4//336devH0uXLlUM4O9//3vOOOMM5b24zh588EHcbrcSQXE6nbzwwgurtT8r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\ngQCAwMBAnDhxgq/wX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