premature.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise: some premature optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting roll.py\n"
     ]
    }
   ],
   "source": [
    "%%file roll.py\n",
    "\"\"\"\n",
    "rolls a slightly biased (100-sided) die\n",
    "\"\"\"\n",
    "\n",
    "import random\n",
    "import numpy as np\n",
    "import numpy.random as npr\n",
    "\n",
    "def win(x):\n",
    "    '''\n",
    "    a simple win/loss: where win if (100 > x > 50)\n",
    "    '''\n",
    "    return int(bool(100 > x > 50))\n",
    "\n",
    "\n",
    "def die():\n",
    "    '''     \n",
    "    a simple win/loss: where win if (100 > random(1,100) > 50)\n",
    "    '''         \n",
    "    return win(random.randint(1,100))\n",
    "\n",
    "\n",
    "_win = np.vectorize(win)\n",
    "\n",
    "\n",
    "def dice(N=1):\n",
    "    '''\n",
    "    a simple win/loss: where win if (100 > random(1,100,N) > 50)\n",
    "    '''\n",
    "    return _win(npr.randint(1,100,N))\n",
    "\n",
    "\n",
    "def many_die(N=1):\n",
    "    '''roll simple (biased) win/loss N times'''\n",
    "    rolls = []\n",
    "    for i in range(N):\n",
    "        rolls.append(die())\n",
    "    return rolls\n",
    "\n",
    "\n",
    "# EOF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting strategy.py\n"
     ]
    }
   ],
   "source": [
    "%%file strategy.py\n",
    "\"\"\"\n",
    "betting strategies\n",
    "\n",
    "forked from: http://pythonprogramming.net/dashboard/#tab_montecarloyo\n",
    "\"\"\"\n",
    "\n",
    "import roll\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "def trajectory(N=1):\n",
    "    \"\"\"convert dice rolls True/False to +1/-1\"\"\"\n",
    "    results = np.empty(N+1)\n",
    "    results[0] = 0\n",
    "    results[1:] = np.asarray(roll.dice(N), int)\n",
    "    record = results[1:]\n",
    "    record[record == 0] = -1\n",
    "    return results\n",
    "\n",
    "\n",
    "def clip(x):\n",
    "    \"\"\"clip all values to zero upon first non-positive value\"\"\"\n",
    "    x[x <= 0] = 0\n",
    "    x[np.logical_not(np.logical_and.accumulate(x))] = 0\n",
    "    return x\n",
    "\n",
    "\n",
    "def vsimple(funds, initial_wager, wager_count, *args):\n",
    "    '''Simple (numpy) bettor, betting the same amount each time.'''\n",
    "    wager = initial_wager\n",
    "    return clip(funds + (wager * np.cumsum(trajectory(wager_count))))\n",
    "\n",
    "\n",
    "def vmartingale(funds, initial_wager, wager_count, wscale=1, lscale=1):\n",
    "    wager = float(initial_wager)\n",
    "\n",
    "    history = trajectory(wager_count)\n",
    "    won = history.copy()\n",
    "    won[1:] = history[:-1] > -1  # also treat '0' as 'win'\n",
    "\n",
    "    # upon losing, double the bet\n",
    "    # upon winning, bet the initial\n",
    "    # can't bet more than you have\n",
    "    for i,w in enumerate(won[1:]):\n",
    "        n = i+1\n",
    "        if w:\n",
    "            won[n] = 1\n",
    "            continue\n",
    "        scale = wscale if history[i] == 1 else lscale\n",
    "        won[n] = min(scale * won[i], funds/wager + sum(history[:n] * won[:n]))\n",
    "    '''# calculation looks something like this...\n",
    "    history = [0, 1, 1,-1,-1, 1, 1,-1,-1,-1]\n",
    "        won = [0, 1, 1, 1, 0, 0, 1, 1, 0, 0]\n",
    "        bet = [0, 1, 1, 1, 2, 4, 1, 1, 2, 4]\n",
    "      value = [0, 1, 1,-1,-2, 4, 1,-1,-2,-4]\n",
    "    '''\n",
    "    return clip(funds + (wager * np.cumsum(history * won)))\n",
    "\n",
    "\n",
    "def simple(funds, initial_wager, wager_count, *args):\n",
    "    '''\n",
    "    Simple bettor, betting the same amount each time.\n",
    "    '''\n",
    "    value = funds\n",
    "    wager = initial_wager\n",
    "    wager_count = int(wager_count)\n",
    "    history = [funds] + [0]*(wager_count)\n",
    "\n",
    "    currentWager = 1\n",
    "\n",
    "    while currentWager <= wager_count:\n",
    "        if roll.die():\n",
    "            value += wager\n",
    "            history[currentWager] = value\n",
    "        else:\n",
    "            value -= wager\n",
    "            if value <= 0:\n",
    "                break\n",
    "            history[currentWager] = value\n",
    "        currentWager += 1\n",
    "\n",
    "    return history\n",
    "\n",
    "\n",
    "def martingale(funds, initial_wager, wager_count, wscale=1, lscale=1):\n",
    "    '''martingale bettor, \"doubling-down\" (actually, \"*scaling-down\")'''\n",
    "    value = funds\n",
    "    wager = initial_wager\n",
    "    wager_count = int(wager_count)\n",
    "    history = [funds] + [0]*(wager_count)\n",
    "\n",
    "    currentWager = 1\n",
    "\n",
    "    # since we'll be betting based on previous bet outcome #\n",
    "    previousWager = 'win'\n",
    "\n",
    "    # since we'll be doubling #\n",
    "    previousWagerAmount = initial_wager\n",
    "\n",
    "    while currentWager <= wager_count:\n",
    "        if previousWager == 'win':\n",
    "            if roll.die():\n",
    "                value += wager\n",
    "                history[currentWager] = value\n",
    "            else:\n",
    "                value -= wager\n",
    "                if value <= 0:\n",
    "                    break\n",
    "                history[currentWager] = value\n",
    "                previousWager = 'loss'\n",
    "                previousWagerAmount = wager\n",
    "        elif previousWager == 'loss':\n",
    "            if roll.die():\n",
    "                wager = previousWagerAmount * wscale\n",
    "                if (value - wager) < 0:\n",
    "                    wager = value\n",
    "                value += wager\n",
    "                history[currentWager] = value\n",
    "                wager = initial_wager\n",
    "                previousWager = 'win'\n",
    "            else:\n",
    "                wager = previousWagerAmount * lscale\n",
    "                if (value - wager) < 0:\n",
    "                    wager = value\n",
    "                value -= wager\n",
    "                if value <= 0:\n",
    "                    break\n",
    "                history[currentWager] = value\n",
    "                previousWager = 'loss'\n",
    "                previousWagerAmount = wager\n",
    "\n",
    "        currentWager += 1\n",
    "\n",
    "    return history\n",
    "\n",
    "\n",
    "def dAlembert(funds, initial_wager, wager_count, *args):\n",
    "    '''d'Alembert bettor'''\n",
    "    value = funds\n",
    "    wager = initial_wager\n",
    "    wager_count = int(wager_count)\n",
    "    history = [funds] + [0]*(wager_count)\n",
    "\n",
    "    currentWager = 1\n",
    "\n",
    "    # since we'll be betting based on previous bet outcome #\n",
    "    previousWager = 'win'\n",
    "\n",
    "    # since we'll be doubling #\n",
    "    previousWagerAmount = initial_wager\n",
    "\n",
    "    while currentWager <= wager_count:\n",
    "        if previousWager == 'win':\n",
    "            if wager == initial_wager:\n",
    "                pass\n",
    "            else:\n",
    "                wager -= initial_wager\n",
    "            if roll.die():\n",
    "                value += wager\n",
    "                history[currentWager] = value\n",
    "            else:\n",
    "                value -= wager\n",
    "                if value <= 0:\n",
    "                    break\n",
    "                history[currentWager] = value\n",
    "                previousWager = 'loss'\n",
    "                previousWagerAmount = wager\n",
    "        elif previousWager == 'loss':\n",
    "            wager = previousWagerAmount + initial_wager\n",
    "            if (value - wager) < 0:\n",
    "                wager = value\n",
    "            if roll.die():\n",
    "                value += wager\n",
    "                history[currentWager] = value\n",
    "                previousWager = 'win'\n",
    "            else:\n",
    "                value -= wager\n",
    "                if value <= 0:\n",
    "                    break\n",
    "                history[currentWager] = value\n",
    "                previousWager = 'loss'\n",
    "                previousWagerAmount = wager\n",
    "\n",
    "        currentWager += 1\n",
    "\n",
    "    return history\n",
    "\n",
    "\n",
    "# for vector monte carlo\n",
    "''' # could be nice, but history has different lengths\n",
    "v_simple = np.vectorize(simple)\n",
    "v_martingale = np.vectorize(martingale)\n",
    "v_dAlembert = np.vectorize(dAlembert)\n",
    "'''\n",
    "\n",
    "# EOF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting trials.py\n"
     ]
    }
   ],
   "source": [
    "%%file trials.py\n",
    "\"\"\"\n",
    "monte carlo trials for betting strategies, and measures of success\n",
    "\"\"\"\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "def monte(bettor, initial_funds, initial_bet, number_bets, number_players, W,L):\n",
    "    \"monte carlo run for a betting strategy\"\n",
    "    history = []\n",
    "    while len(history) < number_players:\n",
    "        history.append(bettor(initial_funds, initial_bet, number_bets, W,L))\n",
    "    return np.array(history)\n",
    "\n",
    "\n",
    "def alive(history, number_players):\n",
    "    \"find the percentage of players that are not broke\"\n",
    "    return 100. * sum(np.asarray(history, bool).T[-1])/number_players\n",
    "\n",
    "\n",
    "def gains(history, number_players, initial_funds):\n",
    "    \"find the percentage of players that have profited\"\n",
    "    return 100. * sum(history.T[-1] > initial_funds)/number_players\n",
    "\n",
    "\n",
    "def profit(history, number_players, initial_funds):\n",
    "    \"find the total profit\"\n",
    "    return np.max(history.T[-1]) - initial_funds\n",
    "\n",
    "\n",
    "def margin(history, number_players, initial_funds):\n",
    "    \"find the percentage the return on investment is over the initial funds\"\n",
    "    initial = number_players * initial_funds\n",
    "    return 100.* (sum(history.T[-1]) - initial)/initial\n",
    "\n",
    "\n",
    "# EOF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting use_trials2.py\n"
     ]
    }
   ],
   "source": [
    "%%file use_trials2.py\n",
    "\"\"\"\n",
    "usage testing of trials\n",
    "\"\"\"\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pylab as mpl\n",
    "import trials\n",
    "import time\n",
    "\n",
    "def plot_trajectories(bettor, initial_funds, initial_bet, number_bets, number_players, W,L):\n",
    "    \"plot the Monte Carlo trajectories of a 100-sided die for the selected strategy\"\n",
    "    history = trials.monte(bettor, initial_funds, initial_bet, number_bets, number_players, W,L)\n",
    "    mpl.plot(history.T)\n",
    "    mpl.plot(initial_funds * np.ones(number_bets+1), lw=2)\n",
    "\n",
    "    print \"survived: {}%\".format(trials.alive(history, number_players))\n",
    "    print \"profited: {}%\".format(trials.gains(history, number_players, initial_funds))\n",
    "    funds = trials.margin(history, number_players, initial_funds)\n",
    "    funds = np.mean(funds)*initial_funds\n",
    "    win = funds >= 0\n",
    "    print \"ave profit: {}${:.2f}\".format('' if win else '-', funds if win else -funds)\n",
    "    funds = trials.profit(history, number_players, initial_funds)\n",
    "    win = funds >= 0\n",
    "    print \"max profit: {}${:.2f}\".format('' if win else '-', funds if win else -funds)\n",
    "    return \n",
    "\n",
    "\n",
    "def use_monte():\n",
    "    import strategy\n",
    "    initial_funds = 10000\n",
    "    initial_bet = 100\n",
    "    number_bets = 1000\n",
    "    number_players = 100\n",
    "    bettor = strategy.martingale\n",
    "    W = L = 2.0\n",
    "\n",
    "    return trials.monte(bettor, initial_funds, initial_bet, number_bets, number_players, W,L)\n",
    "\n",
    "\n",
    "def use_vmonte():\n",
    "    import strategy\n",
    "    initial_funds = 10000\n",
    "    initial_bet = 100\n",
    "    number_bets = 1000\n",
    "    number_players = 100\n",
    "    bettor = strategy.vmartingale\n",
    "    W = L = 2.0\n",
    "\n",
    "    return trials.monte(bettor, initial_funds, initial_bet, number_bets, number_players, W,L)\n",
    "\n",
    "\n",
    "def use_trials():\n",
    "    import strategy\n",
    "    initial_funds = 10000\n",
    "    initial_bet = 100\n",
    "    number_bets = 1000\n",
    "    number_players = 100\n",
    "    bettor = strategy.martingale\n",
    "    W = L = 2.0\n",
    "\n",
    "    plot_trajectories(bettor, initial_funds, initial_bet, number_bets, number_players, W,L)\n",
    "    mpl.show()\n",
    "\n",
    "\n",
    "def use_vtrials():\n",
    "    import strategy\n",
    "    initial_funds = 10000\n",
    "    initial_bet = 100\n",
    "    number_bets = 1000\n",
    "    number_players = 100\n",
    "    bettor = strategy.vmartingale\n",
    "    W = L = 2.0\n",
    "\n",
    "    plot_trajectories(bettor, initial_funds, initial_bet, number_bets, number_players, W,L)\n",
    "    mpl.show()\n",
    "    \n",
    "\n",
    "# EOF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import random\n",
    "np.random.seed(123)\n",
    "random.seed(123)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "survived: 13.0%\n",
      "profited: 13.0%\n",
      "ave profit: -$243900.00\n",
      "max profit: $52200.00\n"
     ]
    },
    {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109be4ad0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "use_trials()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.random.seed(123)\n",
    "random.seed(123)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "survived: 13.0%\n",
      "profited: 13.0%\n",
      "ave profit: -$243900.00\n",
      "max profit: $52200.00\n"
     ]
    },
    {
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       "RQkllFBCCatFiSxKKKGEEkpYLUpkUUIJJZRQwmrx/2BfoXBGYJiuAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10aa65fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "use_trials()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.random.seed(123)\n",
    "random.seed(123)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "survived: 15.0%\n",
      "profited: 14.0%\n",
      "ave profit: -$263500.00\n",
      "max profit: $54000.00\n"
     ]
    },
    {
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       "TkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10aa65ed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "use_vtrials()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 loops, best of 3: 96.6 ms per loop\n",
      "10 loops, best of 3: 2.5 s per loop\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(123)\n",
    "random.seed(123)\n",
    "%timeit -n 10 use_monte()\n",
    "\n",
    "np.random.seed(123)\n",
    "random.seed(123)\n",
    "%timeit -n 10 use_vmonte()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000 loops, best of 3: 538 µs per loop\n",
      "100 loops, best of 3: 2.16 ms per loop\n",
      "         1018 function calls in 0.001 seconds\n",
      "\n",
      "   Ordered by: standard name\n",
      "\n",
      "   ncalls  tottime  percall  cumtime  percall filename:lineno(function)\n",
      "        1    0.000    0.000    0.001    0.001 <string>:1(<module>)\n",
      "        1    0.000    0.000    0.001    0.001 function_base.py:1672(__call__)\n",
      "        1    0.000    0.000    0.000    0.000 function_base.py:1702(_get_ufunc_and_otypes)\n",
      "        1    0.000    0.000    0.001    0.001 function_base.py:1758(_vectorize_call)\n",
      "        2    0.000    0.000    0.000    0.000 numeric.py:394(asarray)\n",
      "        1    0.000    0.000    0.001    0.001 roll.py:26(dice)\n",
      "     1001    0.000    0.000    0.000    0.000 roll.py:9(win)\n",
      "        1    0.000    0.000    0.000    0.000 {isinstance}\n",
      "        1    0.000    0.000    0.000    0.000 {len}\n",
      "        1    0.000    0.000    0.000    0.000 {method 'disable' of '_lsprof.Profiler' objects}\n",
      "        1    0.000    0.000    0.000    0.000 {method 'join' of 'str' objects}\n",
      "        1    0.000    0.000    0.000    0.000 {method 'randint' of 'mtrand.RandomState' objects}\n",
      "        4    0.000    0.000    0.000    0.000 {numpy.core.multiarray.array}\n",
      "        1    0.000    0.000    0.000    0.000 {numpy.core.umath.frompyfunc}\n",
      "\n",
      "\n",
      "         6004 function calls in 0.003 seconds\n",
      "\n",
      "   Ordered by: standard name\n",
      "\n",
      "   ncalls  tottime  percall  cumtime  percall filename:lineno(function)\n",
      "        1    0.000    0.000    0.003    0.003 <string>:1(<module>)\n",
      "     1000    0.001    0.000    0.001    0.000 random.py:175(randrange)\n",
      "     1000    0.000    0.000    0.002    0.000 random.py:238(randint)\n",
      "     1000    0.001    0.000    0.003    0.000 roll.py:16(die)\n",
      "        1    0.000    0.000    0.003    0.003 roll.py:33(many_die)\n",
      "     1000    0.001    0.000    0.001    0.000 roll.py:9(win)\n",
      "     1000    0.000    0.000    0.000    0.000 {method 'append' of 'list' objects}\n",
      "        1    0.000    0.000    0.000    0.000 {method 'disable' of '_lsprof.Profiler' objects}\n",
      "     1000    0.000    0.000    0.000    0.000 {method 'random' of '_random.Random' objects}\n",
      "        1    0.000    0.000    0.000    0.000 {range}\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import profiling\n",
    "import roll\n",
    "\n",
    "%timeit roll.dice(1000)\n",
    "%timeit roll.many_die(1000)\n",
    "\n",
    "profiling.profile('roll.dice(1000)')\n",
    "profiling.profile('roll.many_die(1000)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting profile_strategy.py\n"
     ]
    }
   ],
   "source": [
    "%%file profile_strategy.py\n",
    "\"\"\"\n",
    "betting strategies\n",
    "\n",
    "forked from: http://pythonprogramming.net/dashboard/#tab_montecarloyo\n",
    "\"\"\"\n",
    "\n",
    "import roll\n",
    "import numpy as np\n",
    "import random\n",
    "\n",
    "\n",
    "@profile\n",
    "def trajectory(N=1):\n",
    "    \"\"\"convert dice rolls True/False to +1/-1\"\"\"\n",
    "    results = np.empty(N+1)\n",
    "    results[0] = 0\n",
    "    results[1:] = np.asarray(roll.dice(N), int)\n",
    "    record = results[1:]\n",
    "    record[record == 0] = -1\n",
    "    return results\n",
    "\n",
    "\n",
    "@profile\n",
    "def clip(x):\n",
    "    \"\"\"clip all values to zero upon first non-positive value\"\"\"\n",
    "    x[x <= 0] = 0\n",
    "    x[np.logical_not(np.logical_and.accumulate(x))] = 0\n",
    "    return x\n",
    "\n",
    "\n",
    "@profile\n",
    "def vsimple(funds, initial_wager, wager_count, *args):\n",
    "    '''Simple (numpy) bettor, betting the same amount each time.'''\n",
    "    wager = initial_wager\n",
    "    return clip(funds + (wager * np.cumsum(trajectory(wager_count))))\n",
    "\n",
    "\n",
    "@profile\n",
    "def vmartingale(funds, initial_wager, wager_count, wscale=1, lscale=1):\n",
    "    wager = float(initial_wager)\n",
    "\n",
    "    history = trajectory(wager_count)\n",
    "    won = history.copy()\n",
    "    won[1:] = history[:-1] > -1  # also treat '0' as 'win'\n",
    "\n",
    "    # upon losing, double the bet\n",
    "    # upon winning, bet the initial\n",
    "    # can't bet more than you have\n",
    "    for i,w in enumerate(won[1:]):\n",
    "        n = i+1\n",
    "        if w:\n",
    "            won[n] = 1\n",
    "            continue\n",
    "        scale = wscale if history[i] == 1 else lscale\n",
    "        won[n] = min(scale * won[i], funds/wager + sum(history[:n] * won[:n]))\n",
    "    '''# calculation looks something like this...\n",
    "    history = [0, 1, 1,-1,-1, 1, 1,-1,-1,-1]\n",
    "        won = [0, 1, 1, 1, 0, 0, 1, 1, 0, 0]\n",
    "        bet = [0, 1, 1, 1, 2, 4, 1, 1, 2, 4]\n",
    "      value = [0, 1, 1,-1,-2, 4, 1,-1,-2,-4]\n",
    "    '''\n",
    "    return clip(funds + (wager * np.cumsum(history * won)))\n",
    "\n",
    "\n",
    "@profile\n",
    "def simple(funds, initial_wager, wager_count, *args):\n",
    "    '''\n",
    "    Simple bettor, betting the same amount each time.\n",
    "    '''\n",
    "    value = funds\n",
    "    wager = initial_wager\n",
    "    wager_count = int(wager_count)\n",
    "    history = [funds] + [0]*(wager_count)\n",
    "\n",
    "    currentWager = 1\n",
    "\n",
    "    while currentWager <= wager_count:\n",
    "        if roll.die():\n",
    "            value += wager\n",
    "            history[currentWager] = value\n",
    "        else:\n",
    "            value -= wager\n",
    "            if value <= 0:\n",
    "                break\n",
    "            history[currentWager] = value\n",
    "        currentWager += 1\n",
    "\n",
    "    return history\n",
    "\n",
    "\n",
    "@profile\n",
    "def martingale(funds, initial_wager, wager_count, wscale=1, lscale=1):\n",
    "    '''martingale bettor, \"doubling-down\" (actually, \"*scaling-down\")'''\n",
    "    value = funds\n",
    "    wager = initial_wager\n",
    "    wager_count = int(wager_count)\n",
    "    history = [funds] + [0]*(wager_count)\n",
    "\n",
    "    currentWager = 1\n",
    "\n",
    "    # since we'll be betting based on previous bet outcome #\n",
    "    previousWager = 'win'\n",
    "\n",
    "    # since we'll be doubling #\n",
    "    previousWagerAmount = initial_wager\n",
    "\n",
    "    while currentWager <= wager_count:\n",
    "        if previousWager == 'win':\n",
    "            if roll.die():\n",
    "                value += wager\n",
    "                history[currentWager] = value\n",
    "            else:\n",
    "                value -= wager\n",
    "                if value <= 0:\n",
    "                    break\n",
    "                history[currentWager] = value\n",
    "                previousWager = 'loss'\n",
    "                previousWagerAmount = wager\n",
    "        elif previousWager == 'loss':\n",
    "            if roll.die():\n",
    "                wager = previousWagerAmount * wscale\n",
    "                if (value - wager) < 0:\n",
    "                    wager = value\n",
    "                value += wager\n",
    "                history[currentWager] = value\n",
    "                wager = initial_wager\n",
    "                previousWager = 'win'\n",
    "            else:\n",
    "                wager = previousWagerAmount * lscale\n",
    "                if (value - wager) < 0:\n",
    "                    wager = value\n",
    "                value -= wager\n",
    "                if value <= 0:\n",
    "                    break\n",
    "                history[currentWager] = value\n",
    "                previousWager = 'loss'\n",
    "                previousWagerAmount = wager\n",
    "\n",
    "        currentWager += 1\n",
    "\n",
    "    return history\n",
    "\n",
    "\n",
    "\n",
    "def run_trajectory(initial_funds, initial_bets, number_bets, *args, **kwds):\n",
    "    \"plot the rolls of a 100-sided die for all strategies\"\n",
    "    bettors = (simple, martingale, vsimple, vmartingale)\n",
    "    for bettor in bettors:\n",
    "        np.random.seed(123)\n",
    "        random.seed(123)\n",
    "        _ = bettor(initial_funds, initial_bets, number_bets, *args, **kwds)\n",
    "    return\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    initial_funds = 10000\n",
    "    initial_bet = 100\n",
    "    number_bets = 1000\n",
    "    W = L = 2\n",
    "\n",
    "    run_trajectory(initial_funds, initial_bet, number_bets, W,L)\n",
    "\n",
    "\n",
    "# EOF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wrote profile results to profile_strategy.py.lprof\n",
      "Timer unit: 1e-06 s\n",
      "\n",
      "Total time: 0.002013 s\n",
      "File: profile_strategy.py\n",
      "Function: trajectory at line 12\n",
      "\n",
      "Line #      Hits         Time  Per Hit   % Time  Line Contents\n",
      "==============================================================\n",
      "    12                                           @profile\n",
      "    13                                           def trajectory(N=1):\n",
      "    14                                               \"\"\"convert dice rolls True/False to +1/-1\"\"\"\n",
      "    15         2           13      6.5      0.6      results = np.empty(N+1)\n",
      "    16         2            5      2.5      0.2      results[0] = 0\n",
      "    17         2         1926    963.0     95.7      results[1:] = np.asarray(roll.dice(N), int)\n",
      "    18         2            2      1.0      0.1      record = results[1:]\n",
      "    19         2           67     33.5      3.3      record[record == 0] = -1\n",
      "    20         2            0      0.0      0.0      return results\n",
      "\n",
      "Total time: 5.8e-05 s\n",
      "File: profile_strategy.py\n",
      "Function: clip at line 23\n",
      "\n",
      "Line #      Hits         Time  Per Hit   % Time  Line Contents\n",
      "==============================================================\n",
      "    23                                           @profile\n",
      "    24                                           def clip(x):\n",
      "    25                                               \"\"\"clip all values to zero upon first non-positive value\"\"\"\n",
      "    26         2           18      9.0     31.0      x[x <= 0] = 0\n",
      "    27         2           39     19.5     67.2      x[np.logical_not(np.logical_and.accumulate(x))] = 0\n",
      "    28         2            1      0.5      1.7      return x\n",
      "\n",
      "Total time: 0.00113 s\n",
      "File: profile_strategy.py\n",
      "Function: vsimple at line 31\n",
      "\n",
      "Line #      Hits         Time  Per Hit   % Time  Line Contents\n",
      "==============================================================\n",
      "    31                                           @profile\n",
      "    32                                           def vsimple(funds, initial_wager, wager_count, *args):\n",
      "    33                                               '''Simple (numpy) bettor, betting the same amount each time.'''\n",
      "    34         1            0      0.0      0.0      wager = initial_wager\n",
      "    35         1         1130   1130.0    100.0      return clip(funds + (wager * np.cumsum(trajectory(wager_count))))\n",
      "\n",
      "Total time: 0.027562 s\n",
      "File: profile_strategy.py\n",
      "Function: vmartingale at line 38\n",
      "\n",
      "Line #      Hits         Time  Per Hit   % Time  Line Contents\n",
      "==============================================================\n",
      "    38                                           @profile\n",
      "    39                                           def vmartingale(funds, initial_wager, wager_count, wscale=1, lscale=1):\n",
      "    40         1            1      1.0      0.0      wager = float(initial_wager)\n",
      "    41                                           \n",
      "    42         1          977    977.0      3.5      history = trajectory(wager_count)\n",
      "    43         1            2      2.0      0.0      won = history.copy()\n",
      "    44         1           18     18.0      0.1      won[1:] = history[:-1] > -1  # also treat '0' as 'win'\n",
      "    45                                           \n",
      "    46                                               # upon losing, double the bet\n",
      "    47                                               # upon winning, bet the initial\n",
      "    48                                               # can't bet more than you have\n",
      "    49      1001          592      0.6      2.1      for i,w in enumerate(won[1:]):\n",
      "    50      1000          466      0.5      1.7          n = i+1\n",
      "    51      1000          449      0.4      1.6          if w:\n",
      "    52       491          278      0.6      1.0              won[n] = 1\n",
      "    53       491          192      0.4      0.7              continue\n",
      "    54       509          492      1.0      1.8          scale = wscale if history[i] == 1 else lscale\n",
      "    55       509        24050     47.2     87.3          won[n] = min(scale * won[i], funds/wager + sum(history[:n] * won[:n]))\n",
      "    56                                               '''# calculation looks something like this...\n",
      "    57                                               history = [0, 1, 1,-1,-1, 1, 1,-1,-1,-1]\n",
      "    58                                                   won = [0, 1, 1, 1, 0, 0, 1, 1, 0, 0]\n",
      "    59                                                   bet = [0, 1, 1, 1, 2, 4, 1, 1, 2, 4]\n",
      "    60                                                 value = [0, 1, 1,-1,-2, 4, 1,-1,-2,-4]\n",
      "    61                                               '''\n",
      "    62         1           45     45.0      0.2      return clip(funds + (wager * np.cumsum(history * won)))\n",
      "\n",
      "Total time: 0.007904 s\n",
      "File: profile_strategy.py\n",
      "Function: simple at line 65\n",
      "\n",
      "Line #      Hits         Time  Per Hit   % Time  Line Contents\n",
      "==============================================================\n",
      "    65                                           @profile\n",
      "    66                                           def simple(funds, initial_wager, wager_count, *args):\n",
      "    67                                               '''\n",
      "    68                                               Simple bettor, betting the same amount each time.\n",
      "    69                                               '''\n",
      "    70         1            4      4.0      0.1      value = funds\n",
      "    71         1            1      1.0      0.0      wager = initial_wager\n",
      "    72         1            1      1.0      0.0      wager_count = int(wager_count)\n",
      "    73         1            9      9.0      0.1      history = [funds] + [0]*(wager_count)\n",
      "    74                                           \n",
      "    75         1            0      0.0      0.0      currentWager = 1\n",
      "    76                                           \n",
      "    77      1001          401      0.4      5.1      while currentWager <= wager_count:\n",
      "    78      1000         5832      5.8     73.8          if roll.die():\n",
      "    79       468          211      0.5      2.7              value += wager\n",
      "    80       468          226      0.5      2.9              history[currentWager] = value\n",
      "    81                                                   else:\n",
      "    82       532          262      0.5      3.3              value -= wager\n",
      "    83       532          242      0.5      3.1              if value <= 0:\n",
      "    84                                                           break\n",
      "    85       532          262      0.5      3.3              history[currentWager] = value\n",
      "    86      1000          453      0.5      5.7          currentWager += 1\n",
      "    87                                           \n",
      "    88         1            0      0.0      0.0      return history\n",
      "\n",
      "Total time: 0.000205 s\n",
      "File: profile_strategy.py\n",
      "Function: martingale at line 91\n",
      "\n",
      "Line #      Hits         Time  Per Hit   % Time  Line Contents\n",
      "==============================================================\n",
      "    91                                           @profile\n",
      "    92                                           def martingale(funds, initial_wager, wager_count, wscale=1, lscale=1):\n",
      "    93                                               '''martingale bettor, \"doubling-down\" (actually, \"*scaling-down\")'''\n",
      "    94         1            0      0.0      0.0      value = funds\n",
      "    95         1            1      1.0      0.5      wager = initial_wager\n",
      "    96         1            1      1.0      0.5      wager_count = int(wager_count)\n",
      "    97         1           12     12.0      5.9      history = [funds] + [0]*(wager_count)\n",
      "    98                                           \n",
      "    99         1            0      0.0      0.0      currentWager = 1\n",
      "   100                                           \n",
      "   101                                               # since we'll be betting based on previous bet outcome #\n",
      "   102         1            0      0.0      0.0      previousWager = 'win'\n",
      "   103                                           \n",
      "   104                                               # since we'll be doubling #\n",
      "   105         1            0      0.0      0.0      previousWagerAmount = initial_wager\n",
      "   106                                           \n",
      "   107        16            9      0.6      4.4      while currentWager <= wager_count:\n",
      "   108        16           10      0.6      4.9          if previousWager == 'win':\n",
      "   109         4           27      6.8     13.2              if roll.die():\n",
      "   110                                                           value += wager\n",
      "   111                                                           history[currentWager] = value\n",
      "   112                                                       else:\n",
      "   113         4            3      0.8      1.5                  value -= wager\n",
      "   114         4            2      0.5      1.0                  if value <= 0:\n",
      "   115                                                               break\n",
      "   116         4            3      0.8      1.5                  history[currentWager] = value\n",
      "   117         4            2      0.5      1.0                  previousWager = 'loss'\n",
      "   118         4            3      0.8      1.5                  previousWagerAmount = wager\n",
      "   119        12            7      0.6      3.4          elif previousWager == 'loss':\n",
      "   120        12           75      6.2     36.6              if roll.die():\n",
      "   121         3            3      1.0      1.5                  wager = previousWagerAmount * wscale\n",
      "   122         3            2      0.7      1.0                  if (value - wager) < 0:\n",
      "   123                                                               wager = value\n",
      "   124         3            0      0.0      0.0                  value += wager\n",
      "   125         3            0      0.0      0.0                  history[currentWager] = value\n",
      "   126         3            0      0.0      0.0                  wager = initial_wager\n",
      "   127         3            1      0.3      0.5                  previousWager = 'win'\n",
      "   128                                                       else:\n",
      "   129         9            6      0.7      2.9                  wager = previousWagerAmount * lscale\n",
      "   130         9            4      0.4      2.0                  if (value - wager) < 0:\n",
      "   131         1            0      0.0      0.0                      wager = value\n",
      "   132         9            4      0.4      2.0                  value -= wager\n",
      "   133         9            5      0.6      2.4                  if value <= 0:\n",
      "   134         1            1      1.0      0.5                      break\n",
      "   135         8            4      0.5      2.0                  history[currentWager] = value\n",
      "   136         8            4      0.5      2.0                  previousWager = 'loss'\n",
      "   137         8            5      0.6      2.4                  previousWagerAmount = wager\n",
      "   138                                           \n",
      "   139        15           10      0.7      4.9          currentWager += 1\n",
      "   140                                           \n",
      "   141         1            1      1.0      0.5      return history\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%%bash\n",
    "kernprof -lv profile_strategy.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting profile_strategy2.py\n"
     ]
    }
   ],
   "source": [
    "%%file profile_strategy2.py\n",
    "\"\"\"\n",
    "betting strategies\n",
    "\n",
    "forked from: http://pythonprogramming.net/dashboard/#tab_montecarloyo\n",
    "\"\"\"\n",
    "\n",
    "import roll\n",
    "import numpy as np\n",
    "import random\n",
    "\n",
    "\n",
    "#@profile\n",
    "def trajectory(N=1):\n",
    "    \"\"\"convert dice rolls True/False to +1/-1\"\"\"\n",
    "    results = np.empty(N+1)\n",
    "    results[0] = 0\n",
    "    results[1:] = np.asarray(roll.dice(N), int)\n",
    "    record = results[1:]\n",
    "    record[record == 0] = -1\n",
    "    return results\n",
    "\n",
    "\n",
    "#@profile\n",
    "def clip(x):\n",
    "    \"\"\"clip all values to zero upon first non-positive value\"\"\"\n",
    "    x[x <= 0] = 0\n",
    "    x[np.logical_not(np.logical_and.accumulate(x))] = 0\n",
    "    return x\n",
    "\n",
    "\n",
    "#@profile\n",
    "def vsimple(funds, initial_wager, wager_count, *args):\n",
    "    '''Simple (numpy) bettor, betting the same amount each time.'''\n",
    "    wager = initial_wager\n",
    "    return clip(funds + (wager * np.cumsum(trajectory(wager_count))))\n",
    "\n",
    "\n",
    "#@profile\n",
    "def vmartingale(funds, initial_wager, wager_count, wscale=1, lscale=1):\n",
    "    wager = float(initial_wager)\n",
    "\n",
    "    history = trajectory(wager_count)\n",
    "    won = history.copy()\n",
    "    won[1:] = history[:-1] > -1  # also treat '0' as 'win'\n",
    "\n",
    "    # upon losing, double the bet\n",
    "    # upon winning, bet the initial\n",
    "    # can't bet more than you have\n",
    "    for i,w in enumerate(won[1:]):\n",
    "        n = i+1\n",
    "        if w:\n",
    "            won[n] = 1\n",
    "            continue\n",
    "        scale = wscale if history[i] == 1 else lscale\n",
    "        won[n] = min(scale * won[i], funds/wager + sum(history[:n] * won[:n]))\n",
    "    '''# calculation looks something like this...\n",
    "    history = [0, 1, 1,-1,-1, 1, 1,-1,-1,-1]\n",
    "        won = [0, 1, 1, 1, 0, 0, 1, 1, 0, 0]\n",
    "        bet = [0, 1, 1, 1, 2, 4, 1, 1, 2, 4]\n",
    "      value = [0, 1, 1,-1,-2, 4, 1,-1,-2,-4]\n",
    "    '''\n",
    "    return clip(funds + (wager * np.cumsum(history * won)))\n",
    "\n",
    "\n",
    "@profile\n",
    "def simple(funds, initial_wager, wager_count, *args):\n",
    "    '''\n",
    "    Simple bettor, betting the same amount each time.\n",
    "    '''\n",
    "    value = funds\n",
    "    wager = initial_wager\n",
    "    wager_count = int(wager_count)\n",
    "    history = [funds] + [0]*(wager_count)\n",
    "    roll_die = roll.dice(wager_count+1)\n",
    "\n",
    "\n",
    "    currentWager = 1\n",
    "\n",
    "    while currentWager <= wager_count:\n",
    "        if roll_die[currentWager]:\n",
    "            value += wager\n",
    "            history[currentWager] = value\n",
    "        else:\n",
    "            value -= wager\n",
    "            if value <= 0:\n",
    "                break\n",
    "            history[currentWager] = value\n",
    "        currentWager += 1\n",
    "\n",
    "    return history\n",
    "\n",
    "\n",
    "@profile\n",
    "def martingale(funds, initial_wager, wager_count, wscale=1, lscale=1):\n",
    "    '''martingale bettor, \"doubling-down\" (actually, \"*scaling-down\")'''\n",
    "    value = funds\n",
    "    wager = initial_wager\n",
    "    wager_count = int(wager_count)\n",
    "    history = [funds] + [0]*(wager_count)\n",
    "    roll_die = roll.dice(wager_count+1)\n",
    "\n",
    "\n",
    "    currentWager = 1\n",
    "\n",
    "    # since we'll be betting based on previous bet outcome #\n",
    "    previousWager = 'win'\n",
    "\n",
    "    # since we'll be doubling #\n",
    "    previousWagerAmount = initial_wager\n",
    "\n",
    "    while currentWager <= wager_count:\n",
    "        if previousWager == 'win':\n",
    "            if roll_die[currentWager]:\n",
    "                value += wager\n",
    "                history[currentWager] = value\n",
    "            else:\n",
    "                value -= wager\n",
    "                if value <= 0:\n",
    "                    break\n",
    "                history[currentWager] = value\n",
    "                previousWager = 'loss'\n",
    "                previousWagerAmount = wager\n",
    "        elif previousWager == 'loss':\n",
    "            if roll_die[currentWager]:\n",
    "                wager = previousWagerAmount * wscale\n",
    "                if (value - wager) < 0:\n",
    "                    wager = value\n",
    "                value += wager\n",
    "                history[currentWager] = value\n",
    "                wager = initial_wager\n",
    "                previousWager = 'win'\n",
    "            else:\n",
    "                wager = previousWagerAmount * lscale\n",
    "                if (value - wager) < 0:\n",
    "                    wager = value\n",
    "                value -= wager\n",
    "                if value <= 0:\n",
    "                    break\n",
    "                history[currentWager] = value\n",
    "                previousWager = 'loss'\n",
    "                previousWagerAmount = wager\n",
    "\n",
    "        currentWager += 1\n",
    "\n",
    "    return history\n",
    "\n",
    "\n",
    "\n",
    "def run_trajectory(initial_funds, initial_bets, number_bets, *args, **kwds):\n",
    "    \"plot the rolls of a 100-sided die for all strategies\"\n",
    "    bettors = (simple, martingale, vsimple, vmartingale)\n",
    "    for bettor in bettors:\n",
    "        np.random.seed(123)\n",
    "        random.seed(123)\n",
    "        _ = bettor(initial_funds, initial_bets, number_bets, *args, **kwds)\n",
    "    return\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    initial_funds = 10000\n",
    "    initial_bet = 100\n",
    "    number_bets = 1000\n",
    "    W = L = 2\n",
    "\n",
    "    run_trajectory(initial_funds, initial_bet, number_bets, W,L)\n",
    "\n",
    "\n",
    "# EOF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wrote profile results to profile_strategy2.py.lprof\n",
      "Timer unit: 1e-06 s\n",
      "\n",
      "Total time: 0.003621 s\n",
      "File: profile_strategy2.py\n",
      "Function: simple at line 65\n",
      "\n",
      "Line #      Hits         Time  Per Hit   % Time  Line Contents\n",
      "==============================================================\n",
      "    65                                           @profile\n",
      "    66                                           def simple(funds, initial_wager, wager_count, *args):\n",
      "    67                                               '''\n",
      "    68                                               Simple bettor, betting the same amount each time.\n",
      "    69                                               '''\n",
      "    70         1            3      3.0      0.1      value = funds\n",
      "    71         1            0      0.0      0.0      wager = initial_wager\n",
      "    72         1            1      1.0      0.0      wager_count = int(wager_count)\n",
      "    73         1           10     10.0      0.3      history = [funds] + [0]*(wager_count)\n",
      "    74         1          989    989.0     27.3      roll_die = roll.dice(wager_count+1)\n",
      "    75                                           \n",
      "    76                                           \n",
      "    77         1            0      0.0      0.0      currentWager = 1\n",
      "    78                                           \n",
      "    79      1001          428      0.4     11.8      while currentWager <= wager_count:\n",
      "    80      1000          531      0.5     14.7          if roll_die[currentWager]:\n",
      "    81       490          227      0.5      6.3              value += wager\n",
      "    82       490          231      0.5      6.4              history[currentWager] = value\n",
      "    83                                                   else:\n",
      "    84       510          229      0.4      6.3              value -= wager\n",
      "    85       510          257      0.5      7.1              if value <= 0:\n",
      "    86                                                           break\n",
      "    87       510          247      0.5      6.8              history[currentWager] = value\n",
      "    88      1000          467      0.5     12.9          currentWager += 1\n",
      "    89                                           \n",
      "    90         1            1      1.0      0.0      return history\n",
      "\n",
      "Total time: 0.001582 s\n",
      "File: profile_strategy2.py\n",
      "Function: martingale at line 93\n",
      "\n",
      "Line #      Hits         Time  Per Hit   % Time  Line Contents\n",
      "==============================================================\n",
      "    93                                           @profile\n",
      "    94                                           def martingale(funds, initial_wager, wager_count, wscale=1, lscale=1):\n",
      "    95                                               '''martingale bettor, \"doubling-down\" (actually, \"*scaling-down\")'''\n",
      "    96         1            0      0.0      0.0      value = funds\n",
      "    97         1            1      1.0      0.1      wager = initial_wager\n",
      "    98         1            1      1.0      0.1      wager_count = int(wager_count)\n",
      "    99         1            9      9.0      0.6      history = [funds] + [0]*(wager_count)\n",
      "   100         1          918    918.0     58.0      roll_die = roll.dice(wager_count+1)\n",
      "   101                                           \n",
      "   102                                           \n",
      "   103         1            1      1.0      0.1      currentWager = 1\n",
      "   104                                           \n",
      "   105                                               # since we'll be betting based on previous bet outcome #\n",
      "   106         1            1      1.0      0.1      previousWager = 'win'\n",
      "   107                                           \n",
      "   108                                               # since we'll be doubling #\n",
      "   109         1            1      1.0      0.1      previousWagerAmount = initial_wager\n",
      "   110                                           \n",
      "   111       123           57      0.5      3.6      while currentWager <= wager_count:\n",
      "   112       123           66      0.5      4.2          if previousWager == 'win':\n",
      "   113        62           41      0.7      2.6              if roll_die[currentWager]:\n",
      "   114        29           16      0.6      1.0                  value += wager\n",
      "   115        29           20      0.7      1.3                  history[currentWager] = value\n",
      "   116                                                       else:\n",
      "   117        33           17      0.5      1.1                  value -= wager\n",
      "   118        33           22      0.7      1.4                  if value <= 0:\n",
      "   119                                                               break\n",
      "   120        33           18      0.5      1.1                  history[currentWager] = value\n",
      "   121        33           16      0.5      1.0                  previousWager = 'loss'\n",
      "   122        33           17      0.5      1.1                  previousWagerAmount = wager\n",
      "   123        61           29      0.5      1.8          elif previousWager == 'loss':\n",
      "   124        61           36      0.6      2.3              if roll_die[currentWager]:\n",
      "   125        32           21      0.7      1.3                  wager = previousWagerAmount * wscale\n",
      "   126        32           22      0.7      1.4                  if (value - wager) < 0:\n",
      "   127                                                               wager = value\n",
      "   128        32           17      0.5      1.1                  value += wager\n",
      "   129        32           18      0.6      1.1                  history[currentWager] = value\n",
      "   130        32           16      0.5      1.0                  wager = initial_wager\n",
      "   131        32           14      0.4      0.9                  previousWager = 'win'\n",
      "   132                                                       else:\n",
      "   133        29           18      0.6      1.1                  wager = previousWagerAmount * lscale\n",
      "   134        29           16      0.6      1.0                  if (value - wager) < 0:\n",
      "   135         1            1      1.0      0.1                      wager = value\n",
      "   136        29           14      0.5      0.9                  value -= wager\n",
      "   137        29           15      0.5      0.9                  if value <= 0:\n",
      "   138         1            1      1.0      0.1                      break\n",
      "   139        28           18      0.6      1.1                  history[currentWager] = value\n",
      "   140        28           15      0.5      0.9                  previousWager = 'loss'\n",
      "   141        28           17      0.6      1.1                  previousWagerAmount = wager\n",
      "   142                                           \n",
      "   143       122           71      0.6      4.5          currentWager += 1\n",
      "   144                                           \n",
      "   145         1            1      1.0      0.1      return history\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%%bash\n",
    "kernprof -lv profile_strategy2.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting strategy.py\n"
     ]
    }
   ],
   "source": [
    "%%file strategy.py\n",
    "\"\"\"\n",
    "betting strategies\n",
    "\n",
    "forked from: http://pythonprogramming.net/dashboard/#tab_montecarloyo\n",
    "\"\"\"\n",
    "\n",
    "import roll\n",
    "\n",
    "\n",
    "def simple(funds, initial_wager, wager_count, *args):\n",
    "    '''\n",
    "    Simple bettor, betting the same amount each time.\n",
    "    '''\n",
    "    value = funds\n",
    "    wager = initial_wager\n",
    "    wager_count = int(wager_count)\n",
    "    history = [funds] + [0]*(wager_count)\n",
    "    roll_die = roll.dice(wager_count+1)\n",
    "\n",
    "\n",
    "    currentWager = 1\n",
    "\n",
    "    while currentWager <= wager_count:\n",
    "        if roll_die[currentWager]:\n",
    "            value += wager\n",
    "            history[currentWager] = value\n",
    "        else:\n",
    "            value -= wager\n",
    "            if value <= 0:\n",
    "                break\n",
    "            history[currentWager] = value\n",
    "        currentWager += 1\n",
    "\n",
    "    return history\n",
    "\n",
    "\n",
    "def martingale(funds, initial_wager, wager_count, wscale=1, lscale=1):\n",
    "    '''martingale bettor, \"doubling-down\" (actually, \"*scaling-down\")'''\n",
    "    value = funds\n",
    "    wager = initial_wager\n",
    "    wager_count = int(wager_count)\n",
    "    history = [funds] + [0]*(wager_count)\n",
    "    roll_die = roll.dice(wager_count+1)\n",
    "\n",
    "\n",
    "    currentWager = 1\n",
    "\n",
    "    # since we'll be betting based on previous bet outcome #\n",
    "    previousWager = 'win'\n",
    "\n",
    "    # since we'll be doubling #\n",
    "    previousWagerAmount = initial_wager\n",
    "\n",
    "    while currentWager <= wager_count:\n",
    "        if previousWager == 'win':\n",
    "            if roll_die[currentWager]:\n",
    "                value += wager\n",
    "                history[currentWager] = value\n",
    "            else:\n",
    "                value -= wager\n",
    "                if value <= 0:\n",
    "                    break\n",
    "                history[currentWager] = value\n",
    "                previousWager = 'loss'\n",
    "                previousWagerAmount = wager\n",
    "        elif previousWager == 'loss':\n",
    "            if roll_die[currentWager]:\n",
    "                wager = previousWagerAmount * wscale\n",
    "                if (value - wager) < 0:\n",
    "                    wager = value\n",
    "                value += wager\n",
    "                history[currentWager] = value\n",
    "                wager = initial_wager\n",
    "                previousWager = 'win'\n",
    "            else:\n",
    "                wager = previousWagerAmount * lscale\n",
    "                if (value - wager) < 0:\n",
    "                    wager = value\n",
    "                value -= wager\n",
    "                if value <= 0:\n",
    "                    break\n",
    "                history[currentWager] = value\n",
    "                previousWager = 'loss'\n",
    "                previousWagerAmount = wager\n",
    "\n",
    "        currentWager += 1\n",
    "\n",
    "    return history\n",
    "\n",
    "\n",
    "def dAlembert(funds, initial_wager, wager_count, *args):\n",
    "    '''d'Alembert bettor'''\n",
    "    value = funds\n",
    "    wager = initial_wager\n",
    "    wager_count = int(wager_count)\n",
    "    history = [funds] + [0]*(wager_count)\n",
    "    roll_die = roll.dice(wager_count+1)\n",
    "\n",
    "\n",
    "    currentWager = 1\n",
    "\n",
    "    # since we'll be betting based on previous bet outcome #\n",
    "    previousWager = 'win'\n",
    "\n",
    "    # since we'll be doubling #\n",
    "    previousWagerAmount = initial_wager\n",
    "\n",
    "    while currentWager <= wager_count:\n",
    "        if previousWager == 'win':\n",
    "            if wager == initial_wager:\n",
    "                pass\n",
    "            else:\n",
    "                wager -= initial_wager\n",
    "            if roll_die[currentWager]:\n",
    "                value += wager\n",
    "                history[currentWager] = value\n",
    "            else:\n",
    "                value -= wager\n",
    "                if value <= 0:\n",
    "                    break\n",
    "                history[currentWager] = value\n",
    "                previousWager = 'loss'\n",
    "                previousWagerAmount = wager\n",
    "        elif previousWager == 'loss':\n",
    "            wager = previousWagerAmount + initial_wager\n",
    "            if (value - wager) < 0:\n",
    "                wager = value\n",
    "            if roll_die[currentWager]:\n",
    "                value += wager\n",
    "                history[currentWager] = value\n",
    "                previousWager = 'win'\n",
    "            else:\n",
    "                value -= wager\n",
    "                if value <= 0:\n",
    "                    break\n",
    "                history[currentWager] = value\n",
    "                previousWager = 'loss'\n",
    "                previousWagerAmount = wager\n",
    "\n",
    "        currentWager += 1\n",
    "\n",
    "    return history\n",
    "\n",
    "\n",
    "# EOF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 loops, best of 3: 95.8 ms per loop\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(123)\n",
    "random.seed(123)\n",
    "import use_trials2\n",
    "%timeit -n 10 use_trials2.use_monte()"
   ]
  }
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