{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Inspired by comment from https://www.quantamagazine.org/20160313-mathematicians-discover-prime-conspiracy/\n", "\n", "\"Soundararajan was drawn to study consecutive primes after hearing a lecture at Stanford by the mathematician Tadashi Tokieda, of the University of Cambridge, in which he mentioned a counterintuitive property of coin-tossing: If Alice tosses a coin until she sees a head followed by a tail, and Bob tosses a coin until he sees two heads in a row, then on average, Alice will require four tosses while Bob will require six tosses (try this at home!), even though head-tail and head-head have an equal chance of appearing after two coin tosses.\"" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from random import random" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def flip():\n", " \"flip a coin and return 'H'eads or 'T'ails\"\n", " if random() >= 0.5:\n", " return \"H\"\n", " return \"T\"\n", "\n", "def flips(n):\n", " \"flip a coin n times. return a string describing the sequence\"\n", " return ''.join([flip() for i in range(n)])\n", "\n", "def find_in_flips(seq,n):\n", " \"how many flips did it take to find a particular sequence\"\n", " cur_flips = flips(n)\n", " try:\n", " x = cur_flips.index(seq)\n", " return x + len(seq)\n", " except ValueError:\n", " return n + len(seq)\n", "\n", "def run_game(seq,num_tries,max_flips):\n", " game_results = np.zeros(num_tries)\n", " for i in range(num_tries):\n", " game_results[i] = find_in_flips(seq,max_flips)\n", " return game_results" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "num_games=10000\n", "games = [run_game(x+y,num_games,50) for x in ['H','T'] for y in ['H','T']]\n", "labels = [x+y for x in ['H','T'] for y in ['H','T']]\n", "plt.figure(figsize=[16,4])\n", "values,bases,patches = plt.hist(games,bins=int(np.max(games)),label=labels,histtype = 'step')\n", "plt.xlim(1,20)\n", "l = plt.legend()" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cumulative = np.cumsum(values,axis=1)\n", "cumulative_bases = bases[:-1]\n", "plt.figure(figsize=[16,4])\n", "plt.plot(cumulative_bases, cumulative.T)\n", "x = plt.xlim(1,20)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[5.957, 3.9889, 4.0215, 6.0563]" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "[g.mean() for g in games]" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.4" } }, "nbformat": 4, "nbformat_minor": 1 }