ipynb/Riddler Battle Royale.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Riddler Battle Royale\n",
    "\n",
    "\n",
    "\n",
    "> [538's *The Riddler* Asks](http://fivethirtyeight.com/features/the-battle-for-riddler-nation-round-2/): *In a distant, war-torn land, there are 10 castles. There are two warlords: you and your archenemy, with whom you’re competing to collect the most victory points. Each castle has its own strategic value for a would-be conqueror. Specifically, the castles are worth 1, 2, 3, …, 9, and 10 victory points. You and your enemy each have 100 soldiers to distribute, any way you like, to fight at any of the 10 castles. Whoever sends more soldiers to a given castle conquers that castle and wins its victory points. If you each send the same number of troops, you split the points. You don’t know what distribution of forces your enemy has chosen until the battles begin. Whoever wins the most points wins the war. Submit a plan distributing your 100 soldiers among the 10 castles.*\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load some useful modules\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import csv\n",
    "import random\n",
    "from collections import Counter\n",
    "from statistics import mean"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's play with this and see if we can find a good solution. Some implementation choices:\n",
    "* A `Plan` will be a tuple of 10 soldier counts (one for each castle).\n",
    "* `castles` will hold the indexes of the castles. Note that index 0 is castle 1 (worth 1 point) and index 9 is castle 10 (worth 10 points).\n",
    "* `half` is half the total number of points; if you get more than this you win.\n",
    "* `plans` will hold a set of plans that were submitted in the previous contest.\n",
    "* `play(A, B)` gives the single game reward for Plan A against Plan B: 1 if A wins, 0 if A loses, and 1/2 for a tie.\n",
    "* `reward(a, b, payoff)` returns payoff, payoff/2, or 0, depending on whether `a` is bigger than `b`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "Plan    = tuple      \n",
    "castles = range(10)\n",
    "half    = 55/2     \n",
    "plans   = {Plan(map(int, row[:10])) \n",
    "           for row in csv.reader(open('battle_royale.csv'))}\n",
    "\n",
    "def play(A, B): \n",
    "    \"Play Plan A against Plan B and return a reward (0, 1/2, or 1).\"\n",
    "    A_points = sum(reward(A[c], B[c], c + 1) for c in castles)\n",
    "    return reward(A_points, half) \n",
    "\n",
    "def reward(a, b, payoff=1): return (payoff if a > b else payoff / 2 if a == b else 0) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some tests:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "assert reward(6, 5, 9) == 9  # 6 soldiers defeat 5, winning all 9 of the castle's points\n",
    "assert reward(6, 6, 8) == 4  # A tie on an 8-point castle is worth 4 points\n",
    "assert reward(6, 7, 7) == 0  # No points for a loss\n",
    "assert reward(30, 25)  == 1  # 30 victory points beats 25\n",
    "\n",
    "assert len(plans) == 1202\n",
    "\n",
    "assert play((26, 5, 5, 5, 6, 7, 26, 0,  0, 0),\n",
    "            (25, 0, 0, 0, 0, 0, 0, 25, 25, 25)) == 1 # A wins game\n",
    "\n",
    "assert play((26, 5, 5, 5, 6, 7, 26, 0,  0, 0),\n",
    "            (0, 25, 0, 0, 0, 0, 0, 25, 25, 25)) == 0 # B wins game\n",
    "\n",
    "assert play((25, 5, 5, 5, 6, 7, 26, 0,  0, 0),\n",
    "            (25, 0, 0, 0, 0, 0, 0, 25, 25, 25)) == 1/2 # Tie game"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's run a tournament, playing each plan against every other, and returning a list of `[(plan, mean_game_points),...]`.  I will also define `show` to pretty-print these results and display a histogram:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def tournament(plans):\n",
    "    \"Play each plan against each other; return a sorted list of [(plan: mean_points)]\"\n",
    "    rankdict = {A: mean_points(A, plans) for A in plans}\n",
    "    return Counter(rankdict).most_common()\n",
    "\n",
    "def mean_points(A, opponents): \n",
    "    \"Mean points for A playing against all opponents (but not against itself).\"\n",
    "    return mean(play(A, B) for B in opponents if B is not A)\n",
    "\n",
    "def show(rankings, n=10): \n",
    "    \"Pretty-print the n best plans, and display a histogram of all plans.\"\n",
    "    print('Top', n, 'of', len(rankings), 'plans:')\n",
    "    for (plan, points) in rankings[:n]:\n",
    "        print(pplan(plan), pct(points))\n",
    "    plt.hist([s for (p, s) in rankings], bins=20)\n",
    "    \n",
    "def pct(x): return '{:6.1%}'.format(x)\n",
    "def pplan(plan): return '(' + ', '.join('{:2}'.format(c) for c in plan) + ')'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[((0, 25, 0, 0, 0, 0, 0, 25, 25, 25), 1),\n",
       " ((26, 5, 5, 5, 6, 7, 26, 0, 0, 0), 0.5),\n",
       " ((25, 0, 0, 0, 0, 0, 0, 25, 25, 25), 0)]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# This is what the result of a tournament looks like:\n",
    "tournament({(26, 5, 5, 5, 6, 7, 26, 0,  0, 0),\n",
    "            (25, 0, 0, 0, 0, 0, 0, 25, 25, 25),\n",
    "            (0, 25, 0, 0, 0, 0, 0, 25, 25, 25)})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Top 10 of 1202 plans:\n",
      "( 0,  3,  4,  7, 16, 24,  4, 34,  4,  4)  85.6%\n",
      "( 5,  7,  9, 11, 15, 21, 25,  2,  2,  3)  84.1%\n",
      "( 3,  5,  8, 10, 13,  1, 26, 30,  2,  2)  83.3%\n",
      "( 2,  2,  6, 12,  2, 18, 24, 30,  2,  2)  83.3%\n",
      "( 2,  8,  2,  2, 10, 18, 26, 26,  3,  3)  83.2%\n",
      "( 3,  6,  7,  9, 11,  2, 27, 31,  2,  2)  83.2%\n",
      "( 1,  1,  1,  5, 11, 16, 28, 29,  3,  5)  82.8%\n",
      "( 1,  3,  1,  1, 17, 20, 21, 30,  3,  3)  82.6%\n",
      "( 3,  6, 10, 12, 16, 21, 26,  2,  2,  2)  82.4%\n",
      "( 6,  6,  6, 11, 20, 21, 21,  3,  3,  3)  82.2%\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b2c3a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A tournament with all 1202 plans:\n",
    "rankings = tournament(plans)\n",
    "show(rankings)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It looks like there are a few really bad plans in there.  Let's just keep the top 1000 plans (out of 1202), and re-run the rankings:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Top 10 of 1000 plans:\n",
      "( 0,  3,  4,  7, 16, 24,  4, 34,  4,  4)  87.4%\n",
      "( 5,  5,  5,  5,  5,  5, 27, 30,  6,  7)  84.8%\n",
      "( 5,  5,  5,  5,  5,  5, 30, 30,  5,  5)  84.2%\n",
      "( 3,  3,  5,  5,  7,  7, 30, 30,  5,  5)  84.1%\n",
      "( 1,  2,  3,  4,  6, 16, 25, 33,  4,  6)  82.5%\n",
      "( 2,  2,  2,  5,  5, 26, 26, 26,  3,  3)  82.4%\n",
      "( 1,  1,  1,  5, 11, 16, 28, 29,  3,  5)  82.0%\n",
      "( 0,  1,  3,  3, 11, 18, 25, 33,  3,  3)  82.0%\n",
      "( 5,  7,  9, 11, 15, 21, 25,  2,  2,  3)  81.7%\n",
      "( 0,  0,  5,  5, 25,  3, 25,  3, 31,  3)  81.5%\n"
     ]
    },
    {
     "data": {
      "image/png": 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2qRnXCOs/2fIs4B9nUtnjjVJnAYcNpw8D7q6qWefTKHWeAFwGUFW7ge1JfnxfK5124G+U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\nJDXCwJekRvw/BVQV7pgMVw8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113439358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plans = {A for (A, _) in rankings[:1000]}\n",
    "rankings = tournament(plans)\n",
    "show(rankings)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The top 10 plans are still winning over 80%, and the top plan remains `(0, 3, 4, 7, 16, 24, 4, 34, 4, 4)`. This is an interesting plan: it places most of the soldiers on castles 4+5+6+8, which totals only 23 points, so it needs to pick up 5 more points from the other castles (that have mostly 4 soldiers attacking each one). Is this a good strategy? Where should we optiomally allocate soldiers? \n",
    "\n",
    "To gain some insight, I'll create a plot with 10 curves, one for each castle. Each curve maps the number of soldiers sent to the castle (on the x-axis) to the expected points won (against the 1000 plans) on the y-axis:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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rfUIR+Mrf3R1c8RlEAeOAKcCrmqZFAjuEEFd5VbK2ZPdume8/MlL6CkJD21si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\ngYGBgYEBRmdgYGBgYIDRGRgYGBgYAP8PHSppLKx/0zUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10adc7160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plotter(plans, X=range(41)):\n",
    "    X = list(X)\n",
    "    def mean_reward(c, s): return mean(reward(s, p[c], c+1) for p in plans)\n",
    "    for c in range(10):\n",
    "        plt.plot(X, [mean_reward(c, s) for s in X], '.-')\n",
    "    plt.xlabel('Number of soldiers (on each of the ten castles)')\n",
    "    plt.ylabel('Expected points won')\n",
    "    plt.grid()\n",
    "        \n",
    "plotter(plans)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For example, this says that for castle 10 (the orange line at top), there is a big gain in expected return as we increase from 0 to 4 soldiers, and after that the gains are relatively less steep. This plot is interesting, but I can't see how to directly read off a best plan from it.\n",
    "\n",
    "## Hillclimbing\n",
    "\n",
    "Instead I'll see if I can improve the existing plans, using a simple *hillclimbing* strategy: Take a Plan A, and change it by randomly moving some soldiers from one castle to another. If that yields more `mean_points`, then keep the updated plan, otherwise discard it. Repeat."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def hillclimb(A, plans=plans, steps=1000):\n",
    "    \"Try to improve Plan A, repeat `steps` times; return new plan and total.\"\n",
    "    m = mean_points(A, plans)\n",
    "    for _ in range(steps):\n",
    "        B = mutate(A)\n",
    "        m, A = max((m, A), \n",
    "                   (mean_points(B, plans), B))\n",
    "    return A, m\n",
    "\n",
    "def mutate(plan):\n",
    "    \"Return a new plan that is a slight mutation.\"\n",
    "    plan = list(plan) # So we can modify it.\n",
    "    i, j = random.sample(castles, 2)\n",
    "    plan[i], plan[j] = random_split(plan[i] + plan[j])\n",
    "    return Plan(plan)\n",
    "\n",
    "def random_split(n):\n",
    "    \"Split the integer n into two integers that sum to n.\"\n",
    "    r = random.randint(0, n)\n",
    "    return r, n - r"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see how well this works. Remember, the best plan so far had a score of `87.4%`. Can we improve on that?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((0, 3, 4, 15, 7, 21, 3, 31, 3, 13), 0.916)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hillclimb((0, 3, 4, 7, 16, 24, 4, 34, 4, 4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We got an improvement. Let's see what happens if we start with other plans:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((0, 5, 5, 12, 7, 22, 3, 31, 3, 12), 0.912)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hillclimb((10, 10, 10, 10, 10, 10, 10, 10, 10, 10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((1, 3, 4, 14, 7, 21, 3, 31, 4, 12), 0.9105)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hillclimb((0, 1, 2, 3, 4, 18, 18, 18, 18, 18))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((0, 5, 5, 15, 7, 21, 3, 31, 6, 7), 0.9065)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hillclimb((2, 3, 5, 5, 5, 20, 20, 20, 10, 10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((0, 2, 6, 7, 18, 1, 26, 2, 32, 6), 0.8855)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hillclimb((0, 0, 5, 5, 25, 3, 25, 3, 31, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What if we hillclimb 20 times longer?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((0, 5, 6, 14, 9, 21, 3, 31, 3, 8), 0.9065)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hillclimb((0, 3, 4, 7, 16, 24, 4, 34, 4, 4), steps=20000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Opponent modeling\n",
    "\n",
    "To have a chance of winning the second round of this contest, we have to predict what the other entries will be like. Nobody knows for sure, but I can hypothesize that the entries will be slightly better than the first round, and try to approximate that by hillclimbing from each of the first-round plans for a small number of steps:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def hillclimbers(plans, steps=100):\n",
    "    \"Return a sorted list of [(improved_plan, mean_points), ...]\"\n",
    "    pairs = {hillclimb(plan, plans, steps) for plan in plans}\n",
    "    return sorted(pairs, key=lambda pair: pair[1], reverse=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[((29, 19, 2, 10, 6, 5, 3, 1, 25, 0), 1),\n",
       " ((11, 9, 18, 3, 1, 11, 0, 27, 0, 0), 1),\n",
       " ((0, 25, 0, 0, 0, 0, 0, 25, 25, 25), 1)]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# For example:\n",
    "hillclimbers({(26, 5, 5, 5, 6, 7, 26, 0,  0, 0),\n",
    "              (25, 0, 0, 0, 0, 0, 0, 25, 25, 25),\n",
    "              (0, 25, 0, 0, 0, 0, 0, 25, 25, 25)})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I will define `plans2` (and `rankings2`) to be my estimate of the entries for round 2:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 6min 11s, sys: 3.21 s, total: 6min 14s\n",
      "Wall time: 6min 17s\n",
      "Top 10 of 1000 plans:\n",
      "( 1,  4,  5, 15,  6, 21,  3, 31,  3, 11)  90.8%\n",
      "( 0,  3,  5, 14,  7, 21,  3, 30,  4, 13)  90.6%\n",
      "( 0,  4,  6, 15,  9, 21,  4, 31,  5,  5)  90.2%\n",
      "( 2,  4,  3, 13,  5, 22,  3, 32,  4, 12)  90.1%\n",
      "( 0,  3,  5, 15,  8, 21,  4, 32,  6,  6)  90.0%\n",
      "( 0,  3,  5, 15,  6, 24,  3, 31,  5,  8)  90.0%\n",
      "( 0,  3,  6, 13,  6, 21,  5, 30,  4, 12)  90.0%\n",
      "( 3,  4,  5, 15,  7, 21,  2, 31,  6,  6)  89.9%\n",
      "( 2,  3,  3, 13,  6, 21,  3, 30,  5, 14)  89.8%\n",
      "( 0,  2,  2, 12,  2, 23,  4, 31,  3, 21)  89.8%\n"
     ]
    },
    {
     "data": {
      "image/png": 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Agao6F7gb2Dd9MyVJQ5rmBu6PV9X93fL3gMPAbuAS4ObubTcDl07bSEnSsAaZ80+yB/gp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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113a56908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%time rankings2 = hillclimbers(plans)\n",
    "plans2 = {A for (A, _) in rankings2}\n",
    "show(rankings2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Even though we only took 100 steps, the `plans2` plans are greatly improved: Almost all of them defeat 75% or more of the first-round `plans`. The top 10 plans are all very  similar, targeting castles 4+6+8+10 (for 28 points), but reserving 20 or soldiers to spread among the other castles. Let's look more carefully at every 40th plan, plus the last one:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "( 1,  4,  5, 15,  6, 21,  3, 31,  3, 11)  90.8%\n",
      "( 0,  6,  3, 13,  3, 22,  2, 32,  4, 15)  88.9%\n",
      "( 1,  3,  6, 13,  9, 22,  1, 30,  4, 11)  88.3%\n",
      "( 2,  2,  1, 13,  3, 21,  2, 32,  3, 21)  87.9%\n",
      "( 0,  2,  5,  5, 15,  2, 28, 31,  5,  7)  87.6%\n",
      "( 2,  2,  4, 14,  9,  1, 27, 30,  6,  5)  87.3%\n",
      "( 3,  2,  3, 12,  3, 28,  3, 32,  6,  8)  87.0%\n",
      "( 1,  3,  2,  5, 18,  3, 26,  3, 33,  6)  86.7%\n",
      "( 0,  4,  4,  6, 15,  3, 29, 30,  5,  4)  86.5%\n",
      "( 5,  5,  4,  5, 13, 22,  2, 29,  3, 12)  86.2%\n",
      "( 5,  6,  5,  6, 16, 24, 26,  1,  5,  6)  85.9%\n",
      "( 0,  2,  5, 15,  8,  3, 20, 36,  6,  5)  85.7%\n",
      "( 5,  1,  6, 12,  2, 24,  5, 32,  4,  9)  85.4%\n",
      "( 2,  5,  8, 16, 11,  3,  2, 36,  5, 12)  85.1%\n",
      "( 2,  7,  3, 15, 14,  2,  3, 31,  9, 12)  84.8%\n",
      "( 6,  5,  8,  6,  7, 22, 30,  3,  7,  6)  84.6%\n",
      "( 5,  3,  3,  5,  3, 21, 26, 26,  3,  5)  84.4%\n",
      "( 0,  2,  4, 13,  2, 22, 17, 33,  2,  5)  84.0%\n",
      "( 0,  7, 12,  6,  8, 21,  2, 29, 12,  3)  83.5%\n",
      "( 5,  5,  4, 13, 18,  2, 26,  2,  6, 19)  83.0%\n",
      "( 5,  6,  3, 15, 17, 24,  4,  2,  5, 19)  82.5%\n",
      "( 5,  6,  5,  9,  6, 22, 34,  1,  7,  5)  81.8%\n",
      "( 4,  3,  7, 17, 17, 22,  3,  3,  5, 19)  81.0%\n",
      "( 0,  1,  2, 11, 12, 13, 28, 27,  2,  4)  80.4%\n",
      "( 5,  6, 13, 16, 15, 26,  2,  4,  7,  6)  78.9%\n",
      "( 0,  0,  1, 13,  0,  1, 24, 21, 36,  4)  70.3%\n"
     ]
    }
   ],
   "source": [
    "for (p, m) in rankings2[::40] + [rankings2[-1]]:\n",
    "    print(pplan(p), pct(m))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see a wider variety in plans as we go farther down the rankings. Now for the plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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lZWXceuutrFixAgCj0Uhqamq9C7szpg9XmTtXS8+xbJkWeutsWVDm0dhEiqJE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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113b38a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plotter(plans2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that many castles (e.g. 9 (green), 8 (blue), 7 (black), 6 (yellowish)) have two plateaus. Castle 7 (black) has a plateau at 3.5 points for 6 to 20 soldiers (suggesting that 6 soldiers is a good investment and 20 soldiers a bad investment), and then another plateau at 7 points for everything above 30 soldiers.\n",
    "\n",
    "Now that we have an estimate of the opponents, we can use `hillclimbers` to try to find a plan that does well against all the others:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 5min 40s, sys: 1 s, total: 5min 41s\n",
      "Wall time: 5min 42s\n",
      "Top 10 of 1000 plans:\n",
      "( 3,  8, 10, 18, 21,  3,  5,  6, 10, 16)  99.9%\n",
      "( 1,  9, 10, 17, 21,  6,  4,  6,  9, 17)  99.9%\n",
      "( 1,  8, 10, 18, 21,  4,  4,  6, 11, 17)  99.9%\n",
      "( 0, 10, 10, 17, 20,  4,  5,  6,  7, 21)  99.9%\n",
      "( 2, 11,  1, 16, 18,  7,  6,  6,  8, 25)  99.8%\n",
      "( 1,  8, 11, 19, 20,  4,  6,  5,  7, 19)  99.8%\n",
      "( 0,  1, 11, 15, 18,  7,  6,  5, 13, 24)  99.8%\n",
      "( 2, 10,  1, 17, 18,  9,  5,  6,  8, 24)  99.8%\n",
      "( 1,  9, 10, 17, 19,  4,  6,  6,  9, 19)  99.8%\n",
      "( 0,  2, 11, 18, 21,  4,  6,  8,  8, 22)  99.8%\n"
     ]
    },
    {
     "data": {
      "image/png": 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kuQN4Abh12CIlSaPlxVwkLQv3/Bfed5K+6ilJWoEMf0lqkOEvSQ0y/CUtmr/Ps3J5wFfS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\nPqzoGSj/xk4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113d16588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%time rankings3 = hillclimbers(plans2)\n",
    "show(rankings3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can try even harder to improve the champ:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((3, 9, 10, 17, 21, 3, 5, 6, 7, 19), 1)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "champ, _ = rankings3[0]\n",
    "hillclimb(champ, plans2, 10000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are some champion plans from previous runs of this notebook:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "champs = {\n",
    " (0, 1, 3, 16, 20, 3, 4, 5, 32, 16),\n",
    " (0, 1, 9, 16, 15, 24, 5, 5, 8, 17),\n",
    " (0, 1, 9, 16, 16, 24, 5, 5, 7, 17),\n",
    " (0, 2, 9, 16, 15, 24, 5, 5, 8, 16),\n",
    " (0, 2, 9, 16, 15, 25, 5, 4, 7, 17),\n",
    " (0, 3, 4, 7, 16, 24, 4, 34, 4, 4),\n",
    " (0, 3, 5, 6, 20, 4, 4, 33, 8, 17),\n",
    " (0, 4, 5, 7, 20, 4, 4, 33, 7, 16),\n",
    " (0, 4, 6, 7, 19, 4, 4, 31, 8, 17),\n",
    " (0, 4, 12, 18, 21, 7, 6, 4, 8, 20),\n",
    " (0, 4, 12, 19, 25, 4, 5, 6, 8, 17),\n",
    " (0, 5, 6, 7, 18, 4, 5, 32, 7, 16),\n",
    " (0, 5, 7, 3, 18, 4, 4, 34, 8, 17),\n",
    " (1, 2, 9, 16, 15, 24, 5, 4, 7, 17),\n",
    " (1, 2, 9, 16, 15, 24, 5, 4, 8, 16),\n",
    " (1, 2, 11, 16, 15, 24, 5, 4, 7, 15),\n",
    " (1, 3, 14, 18, 24, 4, 5, 6, 8, 17),\n",
    " (1, 6, 3, 16, 16, 24, 5, 5, 7, 17),\n",
    " (2, 3, 7, 16, 16, 25, 5, 5, 8, 13),\n",
    " (2, 3, 8, 16, 12, 25, 5, 4, 8, 17),\n",
    " (2, 3, 8, 16, 15, 24, 5, 4, 7, 16),\n",
    " (2, 3, 8, 16, 15, 25, 4, 5, 8, 14),\n",
    " (2, 3, 8, 16, 16, 24, 5, 5, 8, 13),\n",
    " (2, 3, 9, 15, 12, 25, 4, 5, 8, 17),\n",
    " (2, 3, 9, 16, 12, 24, 5, 5, 8, 16),\n",
    " (2, 4, 12, 18, 24, 4, 6, 5, 8, 17),\n",
    " (3, 3, 7, 16, 16, 24, 5, 5, 8, 13),\n",
    " (3, 3, 8, 16, 12, 25, 4, 4, 8, 17),\n",
    " (3, 3, 8, 16, 15, 25, 5, 4, 7, 14),\n",
    " (3, 4, 12, 18, 23, 4, 6, 5, 8, 17),\n",
    " (3, 4, 15, 18, 23, 4, 5, 6, 8, 14),\n",
    " (3, 5, 7, 16, 5, 4, 5, 34, 7, 14),\n",
    " (3, 6, 13, 17, 23, 4, 6, 5, 8, 15),\n",
    " (4, 3, 12, 18, 23, 4, 5, 6, 8, 17),\n",
    " (4, 5, 3, 15, 11, 23, 5, 5, 10, 19),\n",
    " (4, 6, 3, 16, 14, 25, 5, 5, 8, 14),\n",
    " (4, 6, 3, 16, 16, 24, 5, 5, 7, 14),\n",
    " (4, 6, 3, 16, 16, 24, 5, 5, 8, 13),\n",
    " (5, 3, 12, 17, 23, 4, 5, 6, 8, 17),\n",
    " (5, 5, 3, 16, 12, 25, 4, 5, 8, 17),\n",
    " (5, 6, 3, 16, 16, 24, 5, 5, 7, 13),\n",
    " (5, 6, 7, 3, 21, 4, 27, 5, 8, 14),\n",
    " (5, 6, 8, 3, 18, 4, 27, 5, 8, 16),\n",
    " (5, 6, 8, 3, 20, 4, 27, 5, 8, 14),\n",
    " (5, 6, 8, 3, 21, 4, 27, 5, 8, 13)}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can evaluate each of them against the original `plans`, against the improved `plans2`, against their fellow champs, and against all of those put together:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Plan                                      plans plans2 champs  all\n",
      "( 0,  5,  7,  3, 18,  4,  4, 34,  8, 17)  85.5%  96.0%  68.5%  90.2%\n",
      "( 0,  4,  6,  7, 19,  4,  4, 31,  8, 17)  84.7%  95.0%  63.0%  89.2%\n",
      "( 0,  1,  3, 16, 20,  3,  4,  5, 32, 16)  85.6%  95.2%  31.5%  89.0%\n",
      "( 0,  3,  5,  6, 20,  4,  4, 33,  8, 17)  84.1%  95.2%  60.9%  89.0%\n",
      "( 0,  5,  6,  7, 18,  4,  5, 32,  7, 16)  84.3%  96.3%  28.3%  88.9%\n",
      "( 3,  5,  7, 16,  5,  4,  5, 34,  7, 14)  85.2%  95.7%  18.5%  88.8%\n",
      "( 5,  6,  8,  3, 18,  4, 27,  5,  8, 16)  81.8%  96.4%  64.1%  88.6%\n",
      "( 0,  4,  5,  7, 20,  4,  4, 33,  7, 16)  84.7%  95.0%  18.5%  88.2%\n",
      "( 5,  6,  8,  3, 20,  4, 27,  5,  8, 14)  82.0%  96.2%  48.9%  88.2%\n",
      "( 0,  1,  9, 16, 15, 24,  5,  5,  8, 17)  78.2%  98.6%  72.8%  88.0%\n",
      "( 5,  6,  7,  3, 21,  4, 27,  5,  8, 14)  81.8%  96.0%  51.1%  88.0%\n",
      "( 0,  1,  9, 16, 16, 24,  5,  5,  7, 17)  79.1%  98.5%  46.7%  87.8%\n",
      "( 5,  6,  8,  3, 21,  4, 27,  5,  8, 13)  82.0%  95.2%  45.7%  87.6%\n",
      "( 2,  3,  9, 15, 12, 25,  4,  5,  8, 17)  78.5%  97.9%  58.7%  87.5%\n",
      "( 4,  5,  3, 15, 11, 23,  5,  5, 10, 19)  76.8%  97.8%  97.8%  87.5%\n",
      "( 2,  3,  8, 16, 12, 25,  5,  4,  8, 17)  78.2%  98.1%  57.6%  87.5%\n",
      "( 2,  3,  8, 16, 15, 25,  4,  5,  8, 14)  79.7%  97.9%  31.5%  87.5%\n",
      "( 0,  2,  9, 16, 15, 24,  5,  5,  8, 16)  78.5%  98.2%  50.0%  87.4%\n",
      "( 2,  3,  7, 16, 16, 25,  5,  5,  8, 13)  79.3%  97.5%  44.6%  87.4%\n",
      "( 4,  6,  3, 16, 14, 25,  5,  5,  8, 14)  79.0%  97.4%  48.9%  87.3%\n",
      "( 5,  5,  3, 16, 12, 25,  4,  5,  8, 17)  78.1%  97.8%  60.9%  87.3%\n",
      "( 4,  6,  3, 16, 16, 24,  5,  5,  7, 14)  80.3%  97.2%  21.7%  87.3%\n",
      "( 2,  3,  8, 16, 15, 24,  5,  4,  7, 16)  80.2%  97.8%  10.9%  87.2%\n",
      "( 1,  2,  9, 16, 15, 24,  5,  4,  7, 17)  79.8%  97.8%  19.6%  87.2%\n",
      "( 0,  2,  9, 16, 15, 25,  5,  4,  7, 17)  79.1%  97.9%  31.5%  87.2%\n",
      "( 2,  3,  8, 16, 16, 24,  5,  5,  8, 13)  79.5%  97.5%  29.3%  87.2%\n",
      "( 2,  3,  9, 16, 12, 24,  5,  5,  8, 16)  78.0%  98.2%  45.7%  87.1%\n",
      "( 3,  3,  8, 16, 15, 25,  5,  4,  7, 14)  80.3%  97.6%   6.5%  87.1%\n",
      "( 1,  2,  9, 16, 15, 24,  5,  4,  8, 16)  79.2%  97.6%  27.2%  87.0%\n",
      "( 3,  3,  7, 16, 16, 24,  5,  5,  8, 13)  79.8%  97.1%  26.1%  87.0%\n",
      "( 4,  6,  3, 16, 16, 24,  5,  5,  8, 13)  80.0%  96.7%  28.3%  87.0%\n",
      "( 3,  3,  8, 16, 12, 25,  4,  4,  8, 17)  78.8%  97.8%  28.3%  87.0%\n",
      "( 5,  6,  3, 16, 16, 24,  5,  5,  7, 13)  80.9%  96.5%   8.7%  86.9%\n",
      "( 1,  2, 11, 16, 15, 24,  5,  4,  7, 15)  79.9%  97.2%   6.5%  86.7%\n",
      "( 1,  6,  3, 16, 16, 24,  5,  5,  7, 17)  75.2%  97.9%  41.3%  85.5%\n",
      "( 5,  3, 12, 17, 23,  4,  5,  6,  8, 17)  64.3%  99.5%  84.8%  82.0%\n",
      "( 4,  3, 12, 18, 23,  4,  5,  6,  8, 17)  64.0%  99.5%  88.0%  81.9%\n",
      "( 3,  4, 12, 18, 23,  4,  6,  5,  8, 17)  63.2%  99.5%  88.0%  81.5%\n",
      "( 2,  4, 12, 18, 24,  4,  6,  5,  8, 17)  63.0%  99.5%  91.3%  81.5%\n",
      "( 3,  4, 15, 18, 23,  4,  5,  6,  8, 14)  63.4%  99.5%  76.1%  81.3%\n",
      "( 3,  6, 13, 17, 23,  4,  6,  5,  8, 15)  63.2%  99.4%  78.3%  81.2%\n",
      "( 1,  3, 14, 18, 24,  4,  5,  6,  8, 17)  62.4%  99.5%  93.5%  81.2%\n",
      "( 0,  4, 12, 19, 25,  4,  5,  6,  8, 17)  62.1%  99.5%  95.7%  81.1%\n",
      "( 1,  9, 11, 17, 21,  6,  5,  4, 10, 16)  62.1% 100.0%  76.1%  80.9%\n",
      "( 0,  4, 12, 18, 21,  7,  6,  4,  8, 20)  61.4%  99.6% 100.0%  80.9%\n",
      "( 1,  7, 13, 17, 23,  6,  6,  5,  8, 14)  62.4%  99.5%  78.3%  80.9%\n",
      "( 0,  3,  4,  7, 16, 24,  4, 34,  4,  4)  87.4%  37.6%   0.0%  61.1%\n"
     ]
    }
   ],
   "source": [
    "def μ(plan, plans): return pct(mean_points(plan,plans))\n",
    "all = plans | plans2 | champs\n",
    "\n",
    "print('Plan                                      plans plans2 champs  all')\n",
    "for p in sorted(champs, key=lambda p: -mean_points(p, all)):\n",
    "    print(pplan(p), μ(p, plans), μ(p, plans2), μ(p, champs), μ(p, all))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Which plan is best? In the end, we don't know, because we don't know the pool we will be competing against."
   ]
  }
 ],
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