Yahtzee simulation, based on a question on facebook: in 5 dice yahtzee game, what is the chance of getting a yahtzee (5 similar dice), ignoring all other options (straight, etc)

yahtzee.ipynb

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   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Task: in 5 dice yahtzee game, what is the chance of getting a yahtzee (5 similar dice), ignoring all other options (straight, etc)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from random import randrange\n",
      "from collections import Counter\n",
      "import operator"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def throw(num_dices = 5):\n",
      "    \"\"\"Performs a throw with up to 5 dices\"\"\"\n",
      "    thrown = []\n",
      "    for i in range(num_dices):\n",
      "        thrown.append(randrange(6)+1)\n",
      "    return thrown"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def most_common(dices):\n",
      "    \"\"\"\n",
      "    Returns the dices that are most common\n",
      "    In case of a draw, returns the lowest number\n",
      "    \"\"\"\n",
      "    counts = Counter(dices)\n",
      "    keep = max(counts.iteritems(), key=operator.itemgetter(1))[0]\n",
      "    return [keep] * counts[keep]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def roll_dice():\n",
      "    \"\"\"\n",
      "    Roles the dice three times \n",
      "    Keeps the most frequent dice after each throw\n",
      "    Returns the most frequent dices after the final throw\n",
      "    \"\"\"\n",
      "    dices = []\n",
      "    for i in range(3):\n",
      "        dices.extend(throw(5-len(dices)))\n",
      "        # select most frequent\n",
      "        dices = most_common(dices)\n",
      "    return dices"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def game():\n",
      "    \"\"\"\n",
      "    Plays a game of up to 15 rolls\n",
      "    Tests whether yahtzee is reached\n",
      "    \"\"\"\n",
      "    win = False\n",
      "    for i in range(15):\n",
      "        dices = roll_dice()\n",
      "        # test for 5 (similar) dices returned\n",
      "        if len(dices) == 5:\n",
      "            win = True\n",
      "    return win"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Below is the code that does the actual playing."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "games = 100000\n",
      "wins = 0\n",
      "for i in range(games):\n",
      "    if game():\n",
      "        wins += 1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print \"Games played: %i. Games with yahztee: %i. Frequency: %f%%\" %(games, wins, 100*wins/float(games))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Games played: 100000. Games with yahztee: 50893. Frequency: 50.893000%\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here we only check the chance for a Yahtzee for a set of three rolls."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rolls = 100000\n",
      "roll_wins = 0\n",
      "for i in range(rolls):\n",
      "    if len(roll_dice()) == 5:\n",
      "        roll_wins += 1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print \"Rolls (three each): %i. Rolls with yahztee: %i. Frequency: %f%%\" %(rolls, roll_wins, 100*roll_wins/float(rolls))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Rolls (three each): 100000. Rolls with yahztee: 4582. Frequency: 4.582000%\n"
       ]
      }
     ],
     "prompt_number": 9
    }
   ],
   "metadata": {}
  }
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