Analysis of the advantage given by bunkers

BunkerAdvantage.ipynb

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   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# functions for running the experiment\n",
      "\n",
      "import roller\n",
      "\n",
      "def roll_till_end(a_army, d_army, bunker):\n",
      "    while a_army > 1 and d_army > 0:\n",
      "        a_army, d_army = roller.roll_once(a_army, d_army, bunker=bunker)\n",
      "        \n",
      "    return a_army, d_army\n",
      "\n",
      "def run_trials(trials, d_army_range, bunker):\n",
      "    a_army_initial = 1000  # chosen to be large enough to kill all def\n",
      "    results = {}\n",
      "    for d_army in xrange(*d_army_range):\n",
      "        results[d_army] = []\n",
      "        for i in xrange(trials):\n",
      "            a_alive, d_alive = roll_till_end(a_army_initial, d_army, bunker=bunker)\n",
      "            a_needed = a_army_initial - a_alive\n",
      "            results[d_army].append(a_needed)\n",
      "    return results"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# run the experiment for bunker and no bunker\n",
      "bunker = run_trials(10000, (5, 50, 5), True)\n",
      "no_bunker = run_trials(10000, (5, 50, 5), False)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pandas as pd\n",
      "\n",
      "def side_by_side(*objs, **kwds):\n",
      "    from pandas.core.common import adjoin\n",
      "    space = kwds.get('space', 4)\n",
      "    reprs = [repr(obj).split('\\n') for obj in objs]\n",
      "    print adjoin(space, *reprs)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "df_bunker = pd.DataFrame(bunker)\n",
      "df_no = pd.DataFrame(no_bunker)\n",
      "side_by_side(df_bunker.mean(), df_no.mean())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "5      8.0346     5      4.0073 \n",
        "10    16.2056     10     8.2825 \n",
        "15    24.4279     15    12.4920 \n",
        "20    32.7623     20    16.8635 \n",
        "25    40.9279     25    20.9976 \n",
        "30    49.4057     30    25.3942 \n",
        "35    57.5252     35    29.6516 \n",
        "40    65.6782     40    33.8682 \n",
        "45    73.8800     45    38.1472 \n",
        "dtype: float64    dtype: float64\n"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "df_bunker.mean().plot(kind='bar', label='bunker')\n",
      "df_no.mean().plot(kind='bar', color='red', label='no bunker')\n",
      "legend(loc='best')\n",
      "xlabel('defenders')\n",
      "ylabel('attackers')\n",
      "title('Attackers to take a country')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 24,
       "text": [
        "<matplotlib.text.Text at 0x4cf0c50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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BAwZI9Iodg/qptiktD6C8TJSHinybcc7x4YcfYvv27Th58iSOHz+OF154oUXXjX/yySdY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\nY4d8DzqhWAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x4cb6150>"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Difference between Bunker/No Bunker\n",
      "-----------------------------------"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "difference = df_bunker.mean() - df_no.mean()\n",
      "difference"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 27,
       "text": [
        "5      4.0273\n",
        "10     7.9231\n",
        "15    11.9359\n",
        "20    15.8988\n",
        "25    19.9303\n",
        "30    24.0115\n",
        "35    27.8736\n",
        "40    31.8100\n",
        "45    35.7328\n",
        "dtype: float64"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "difference.plot()\n",
      "xlim([0, None])\n",
      "title('# Attackers needed to defeat bunker - # to defeat no bunker')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 29,
       "text": [
        "<matplotlib.text.Text at 0x4ce8950>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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n6uC0xV8IUX0uXYLHHtNOmt6tG3z/PfTrp3cq5yY9fyGEwxQVQWwsPPUUDByo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\nbkB6/rpKS4PHH4e9e7W5+/f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       "text": [
        "<matplotlib.figure.Figure at 0x3723f50>"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy import stats\n",
      "slope, intercept, r_value, p_value, std_err = stats.linregress(difference.index, difference)\n",
      "slope"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 32,
       "text": [
        "0.79490266666666676"
       ]
      }
     ],
     "prompt_number": 32
    }
   ],
   "metadata": {}
  }
 ]
}

roller.py

import random

def dieroll(n):
    """Roll an n-sided die and return result"""
    return int(random.random() * n) + 1

def roll_once(
    a_army, d_army, a_dice=None, d_dice=None, firepower=False, ambush=False,
    double_casualties=False, bunker=False, atkrad=False, dfndrad=False
):
    # bail if the attacker or defender doesn't have enough guys to roll
    if a_army < 2 or d_army < 1:
        return (a_army, d_army)
    
    a_dice_requested = a_dice
    d_dice_requested = d_dice

    # figure out how many dice are allowed
    a_dice_modifier = 0
    if firepower:
        a_dice_modifier += 1
    if atkrad:
        a_dice_modifier -= 1
    a_dice = min(a_army - 1, 3) + a_dice_modifier
    if a_dice == 0:
        return (a_army, d_army)
    
    d_dice_modifier = 0
    if bunker:
        d_dice_modifier += 1
    if dfndrad:
        d_dice_modifier -= 1
    d_dice = min(d_army, 2) + d_dice_modifier
    if d_dice == 0:
        return (a_army, d_army)

    # if the user has requested an allowable amount of dice, set it
    if 0 < a_dice_requested <= a_dice:
        a_dice = a_dice_requested
    if 0 < d_dice_requested <= d_dice:
        d_dice = d_dice_requested

    # roll the dice
    a_rolls = sorted([dieroll(6) for i in xrange(a_dice)])
    d_rolls = sorted([dieroll(6) for i in xrange(d_dice)])

    # figure out the number of casualties.  Should be equal to the minimum
    # amount of dice rolled.  However, defender casualties are capped at 2 b/c
    # the bonus die from the bunker doesn't count toward their possible losses.
    num_casualties = min( a_dice, min(d_dice, 2) )
    for i in xrange(num_casualties):
        if ambush:
            a_wins = a_rolls[-1] >= d_rolls[-1]
        else:
            a_wins = a_rolls[-1] > d_rolls[-1]

        if a_wins:
            if double_casualties:
                d_army -= 2
            else:
                d_army -= 1
        else:
            a_army -= 1

        a_rolls.pop()
        d_rolls.pop()
        
    return (a_army, d_army)