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Ghost.ipynb

@@ -15,7 +15,7 @@
     "- **Words**: I will read a standard online word list, `enable1`, and make a set of all the words of sufficient length.\n",
     "- **Fragment**: a fragment is a `str` of letters, such as `'gho'`.\n",
     "- **Beginning**: each word has a set of valid beginnings: for `ghost` it is `{'', g, gh, gho, ghos, ghost}`.  \"Prefix\" is a synonym of \"beginning\".\n",
-    "- **Vocabulary**: `Vocabulary(words)` is an object with: a set of all the `words`, and a set of all the valid `fragments` (beginnings) of the words.\n",
+    "- **Vocabulary**: A `Vocabulary` object holds a set of all the `words` in a dictionary, as well as all the valid `fragments` (beginnings) of the words.\n",
     "- **Player**: The first player will be called player `0`; the second player `1`. \n",
     "- **Play**: A play is a new fragment formed by adding one letter to the end of the existing fragment.\n",
     "- **Legal Play**: A play that is a valid prefix of some word. `enable1.legal_plays('gho') = {'ghos, 'ghou'}`.\n",
@@ -30,7 +30,7 @@
    "source": [
     "# Vocabulary: Words, Fragments, Legal Plays, and `enable1`\n",
     "\n",
-    "`Vocabulary(text)` takes a collection of words as input, stores the words as a set, and also stores all the legal fragments of those words (that is, the beginnings). `legal_plays(fragments)` gives a set of all plays that can be formed by adding a letter to create a legal word fragment (where 'fragment' includes complete words). I also define the function `words` to split any string into component words."
+    "`Vocabulary(words)` takes a collection of words as input, stores the words as a set, and also stores all the legal fragments of those words. `legal_plays(fragments)` gives a set of all plays that can be formed by adding a letter to create a legal word fragment. I also define the function `words` to split any string into component words."
    ]
   },
   {
@@ -65,9 +65,7 @@
   {
    "cell_type": "code",
    "execution_count": 2,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -89,9 +87,7 @@
   {
    "cell_type": "code",
    "execution_count": 3,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -129,9 +125,7 @@
   {
    "cell_type": "code",
    "execution_count": 5,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "enable1 = Vocabulary(words(open('enable1.txt').read()))"
@@ -141,15 +135,13 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Here I explore `enable1`:"
+    "Let's explore `enable1`:"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 6,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -169,9 +161,7 @@
   {
    "cell_type": "code",
    "execution_count": 7,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -191,9 +181,7 @@
   {
    "cell_type": "code",
    "execution_count": 8,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -213,9 +201,7 @@
   {
    "cell_type": "code",
    "execution_count": 9,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -263,21 +249,19 @@
     "Who wins a game if both players play rationally?  To answer that, consider the general situation at some point\n",
     "during the game where\n",
     "a player is presented with a fragment. That player can win if either:\n",
-    "- The fragment is a word (meaning the other player formed the word, and lost).\n",
-    "- The fragment is not a legal fragment (meaning the other player made a mistake, and lost).\n",
+    "- The fragment is a complete word (meaning the other player just formed the word, and thereby lost).\n",
+    "- The fragment is not a legal fragment (meaning the other player made a mistake, and thereby lost).\n",
     "- At least one of the legal plays  in this position puts the opponent in a position from which they *cannot* win.\n",
     "\n",
     "The function `win(vocab, fragment)` implements this. It returns a winning fragment if there is one, otherwise `False`. In particular, it returns `fragment` if the current player has already won (because `fragment` is\n",
-    "a word or illegal fragment), and it returns one of the legal plays if the play leads to a position from\n",
+    "a word or illegal fragment), and it returns one of the legal plays if that play leads to a position from\n",
     "which the opponent *cannot* `win`."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 11,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "def win(vocab, fragment=''):\n",
@@ -301,9 +285,7 @@
   {
    "cell_type": "code",
    "execution_count": 12,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -324,9 +306,7 @@
   {
    "cell_type": "code",
    "execution_count": 13,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -340,16 +320,14 @@
     }
    ],
    "source": [
-    "# 'g' is a winning play (but 'c' wuld be a loser)\n",
+    "# 'g' is a winning play (but 'c' would be a loser)\n",
     "win(Vocabulary(words('cat camel goat gerbil'))) "
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 14,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -363,16 +341,14 @@
     }
    ],
    "source": [
-    "# No winning play; dommed to 'camel' or 'gar'\n",
+    "# No winning play; doomed to 'camel' or 'gar'\n",
     "win(Vocabulary(words('cat camel goat gecko gerbil gar'))) "
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 15,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -386,7 +362,7 @@
     }
    ],
    "source": [
-    "# 'g' wins because 'ga' can be answered with 'gan'\n",
+    "# 'g' wins because 'ga' can be answered with 'gan' and 'ge' with 'ge'\n",
     "win(Vocabulary(words('cat camel goat gecko gerbil gar gannet'))) "
    ]
   },
@@ -402,9 +378,7 @@
   {
    "cell_type": "code",
    "execution_count": 16,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -434,22 +408,12 @@
   {
    "cell_type": "code",
    "execution_count": 17,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "CPU times: user 6.35 ms, sys: 179 µs, total: 6.53 ms\n",
-      "Wall time: 7.14 ms\n"
-     ]
-    },
     {
      "data": {
       "text/plain": [
-       "'h'"
+       "'n'"
       ]
      },
      "execution_count": 17,
@@ -460,7 +424,7 @@
    "source": [
     "enable1_4 = Vocabulary(enable1.words, 4)\n",
     "\n",
-    "%time win(enable1_4)"
+    "win(enable1_4)"
    ]
   },
   {
@@ -482,9 +446,7 @@
   {
    "cell_type": "code",
    "execution_count": 18,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "import random\n",
@@ -495,22 +457,20 @@
     "\n",
     "def ask(name):\n",
     "    \"Return a strategy that asks for the next letter.\"\n",
-    "    return (lambda _, fragment: input('Player {}, given \"{}\", plays? '.format(name, fragment)))"
+    "    return lambda _, fragment: input('Player ' + name + ' given \"' + fragment + '\" plays? ')"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Here is a function to play a game. You give it a vocabulary, two (or potentially more) strategies, and optionally a `verbose` keyword to say if you want a line printed for each play or not."
+    "Here is a function to play a game. You give it a vocabulary, two (or possibly more) strategies, and optionally a `verbose` keyword to say if you want a line printed for each play or not."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 19,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "from itertools import cycle\n",
@@ -533,14 +493,12 @@
   {
    "cell_type": "code",
    "execution_count": 20,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "(1, 'llama')"
+       "(1, 'odyssey')"
       ]
      },
      "execution_count": 20,
@@ -555,33 +513,31 @@
   {
    "cell_type": "code",
    "execution_count": 21,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "[(1, 'dreck'),\n",
-       " (1, 'mho'),\n",
+       "[(1, 'truancies'),\n",
+       " (1, 'xebec'),\n",
+       " (1, 'ods'),\n",
+       " (1, 'vying'),\n",
+       " (1, 'ewe'),\n",
+       " (1, 'bwana'),\n",
+       " (1, 'vying'),\n",
+       " (1, 'knell'),\n",
+       " (1, 'zloty'),\n",
+       " (1, 'flirt'),\n",
+       " (1, 'zlote'),\n",
        " (1, 'bwana'),\n",
-       " (1, 'aal'),\n",
        " (1, 'gjetost'),\n",
-       " (1, 'oquassa'),\n",
-       " (1, 'oquassa'),\n",
-       " (1, 'yperite'),\n",
-       " (1, 'yperite'),\n",
-       " (1, 'plica'),\n",
-       " (1, 'wrest'),\n",
-       " (1, 'qursh'),\n",
-       " (1, 'aal'),\n",
-       " (1, 'aas'),\n",
-       " (1, 'tweak'),\n",
-       " (1, 'uintahite'),\n",
-       " (1, 'uintahite'),\n",
-       " (1, 'hmm'),\n",
-       " (1, 'uintahite'),\n",
-       " (1, 'jnana')]"
+       " (1, 'pliancies'),\n",
+       " (1, 'flounce'),\n",
+       " (1, 'ufologist'),\n",
+       " (1, 'flour'),\n",
+       " (1, 'dweeb'),\n",
+       " (1, 'flirt'),\n",
+       " (1, 'ignatia')]"
       ]
      },
      "execution_count": 21,
@@ -598,14 +554,12 @@
   {
    "cell_type": "code",
    "execution_count": 22,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "(0, 'hugs')"
+       "(0, 'nyctalopia')"
       ]
      },
      "execution_count": 22,
@@ -620,23 +574,22 @@
   {
    "cell_type": "code",
    "execution_count": 23,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Player 0, given \"\", plays? d\n",
-      "Player 0, given \"dr\", plays? dri\n",
-      "Player 0, given \"drif\", plays? drift\n"
+      "Player P given \"\" plays? d\n",
+      "Player P given \"dw\" plays? dwa\n",
+      "Player P given \"dwar\" plays? dwarv\n",
+      "Player P given \"dwarve\" plays? dwarves\n"
      ]
     },
     {
      "data": {
       "text/plain": [
-       "(1, 'drift')"
+       "(1, 'dwarves')"
       ]
      },
      "execution_count": 23,
@@ -645,7 +598,7 @@
     }
    ],
    "source": [
-    "play(enable1, ask(0), rational)"
+    "play(enable1, ask('P'), rational)"
    ]
   },
   {
@@ -665,9 +618,7 @@
   {
    "cell_type": "code",
    "execution_count": 24,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "import textwrap \n",
@@ -717,9 +668,7 @@
   {
    "cell_type": "code",
    "execution_count": 25,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "name": "stdout",
@@ -745,16 +694,14 @@
   {
    "cell_type": "code",
    "execution_count": 26,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
       "Outcomes (7) for player 0:\n",
-      "Winners (7): nays nene ngultrum nirvanic nolo null nyctalopia\n"
+      "Winners (7): naan nene ngultrum nirvanic nolo null nyctalopia\n"
      ]
     }
    ],
@@ -778,21 +725,19 @@
   {
    "cell_type": "code",
    "execution_count": 27,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
       "Outcomes (55) for player 1:\n",
-      "Winners (55): aah aal aargh aas bwana cwm drake dreck drift droit\n",
-      "druse dry ewe fjeld fjord gjetost hmm ihram jnana kwashiorkor llama\n",
-      "mho nth oquassa praam prequel prill pro prurigo pry qua quell quiff\n",
-      "quondam qursh rhamnus rheum rhizoid rho rhumb rhyolitic sjambok\n",
-      "tchotchke uhlan vroom wrang wrest wrick wrong wrung wry xanthic\n",
-      "xanthin yperite zucchetto\n"
+      "Winners (55): aah aal aargh aas bwana cwm drave dreck drink droit\n",
+      "druid dry ewe fjeld fjord gjetost hmm ihram jnana kwashiorkor llano\n",
+      "mho nth oquassa prawn prequel prill pro prurigo pry qua quell quiff\n",
+      "quomodo qursh rhamnus rheum rhizoid rho rhumb rhyolitic squoosh\n",
+      "tchotchke uhlan vying wrath wrest wrist wrong wrung wry xanthic\n",
+      "xanthin yttrium zucchetto\n"
      ]
     }
    ],
@@ -812,26 +757,24 @@
   {
    "cell_type": "code",
    "execution_count": 28,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
       "Outcomes (85) for player 1:\n",
-      "Losers (4): hybrid hyphen hyte ngultrum\n",
+      "Losers (4): hybris hyphen hyte ngultrum\n",
       "Winners (81): aquiculture aquifer aquilegia aquiver bwana cnidarian\n",
-      "drake dreck drift droit druse drywall eschatologies eschatology\n",
-      "escheat eserine eskar esophagus esplanade esquire esquiring essay\n",
+      "drave dreck drink droit druid dryness eschatologies eschatology\n",
+      "escheat eserine esker esophagus esplanade esquire esquiring essay\n",
       "estuarine estuary esurience fjeld fjord gjetost hyaenic hydatid hyena\n",
       "hyenine hyenoid hygeist hying hylozoism hylozoist hymen hyoid hypha\n",
-      "hyraces hyrax hyson ihram jnana kwashiorkor llama mbira ngwee oquassa\n",
-      "plaza plethoric plica plonk pluck plyer quaff quell quiff quondam\n",
-      "qursh rhamnus rheum rhizoid rhomb rhumb rhyolitic sjambok tchotchke\n",
-      "uhlan vroom wrang wrest wrick wrong wrung wryly xanthic xanthin\n",
-      "yperite zucchetto\n"
+      "hyraces hyrax hyson ihram jnana kwashiorkor llano mbira ngwee oquassa\n",
+      "plaza plethoric plica plonk pluck plyer quaff quell quiff quomodo\n",
+      "qursh rhamnus rheum rhizoid rhomb rhumb rhyolitic squoosh tchotchke\n",
+      "uhlan vying wrath wrest wrist wrong wrung wryly xanthic xanthin\n",
+      "yttrium zucchetto\n"
      ]
     }
    ],
@@ -858,9 +801,7 @@
   {
    "cell_type": "code",
    "execution_count": 29,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "class SuperVocabulary(Vocabulary):\n",
@@ -886,21 +827,17 @@
   {
    "cell_type": "code",
    "execution_count": 30,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
-    "enable1s   = SuperVocabulary(enable1.words, 3)\n",
-    "enable1_4s = SuperVocabulary(enable1.words, 4)"
+    "enable1_3super = SuperVocabulary(enable1.words, 3)\n",
+    "enable1_4super = SuperVocabulary(enable1.words, 4)"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 31,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -932,20 +869,18 @@
    ],
    "source": [
     "# Example legal plays\n",
-    "enable1s.legal_plays('crop')"
+    "enable1_3super.legal_plays('crop')"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 32,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "'y'"
+       "'u'"
       ]
      },
      "execution_count": 32,
@@ -956,20 +891,18 @@
    "source": [
     "# Can the first player win in SuperGhost with 3-letter words?\n",
     "\n",
-    "win(enable1s)"
+    "win(enable1_3super)"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 33,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "'y'"
+       "'u'"
       ]
      },
      "execution_count": 33,
@@ -980,7 +913,7 @@
    "source": [
     "# How about with a 4-letter limit?\n",
     "\n",
-    "win(enable1_4s)"
+    "win(enable1_4super)"
    ]
   },
   {
@@ -993,24 +926,22 @@
   {
    "cell_type": "code",
    "execution_count": 34,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Player 0, given \"\", plays? q\n",
-      "Player 0, given \"mq\", plays? mqu\n",
-      "Player 0, given \"umqu\", plays? umqua\n",
-      "Player 0, given \"cumqua\", plays? cumquat\n"
+      "Player P given \"\" plays? q\n",
+      "Player P given \"cq\" plays? cqu\n",
+      "Player P given \"cque\" plays? acque\n",
+      "Player P given \"acques\" plays? acquest\n"
      ]
     },
     {
      "data": {
       "text/plain": [
-       "(1, 'cumquat')"
+       "(1, 'acquest')"
       ]
      },
      "execution_count": 34,
@@ -1019,7 +950,7 @@
     }
    ],
    "source": [
-    "play(enable1s, ask(0), rational)"
+    "play(enable1_3super, ask('P'), rational)"
    ]
   },
   {
@@ -1047,9 +978,7 @@
     "        \n",
     "    def legal_plays(self, fragment):\n",
     "        \"All plays that form a valid infix; optionally reverse fragment first.\"\n",
-    "        def all4(frag, L): \n",
-    "            return (frag + L, frag[::-1] + L, \n",
-    "                    L + frag, L + frag[::-1])\n",
+    "        def all4(f, L): return (f + L, f[::-1] + L, L + f, L + f[::-1])\n",
     "        return {p for L in alphabet for p in all4(fragment, L)} & self.fragments"
    ]
   },
@@ -1061,16 +990,14 @@
    },
    "outputs": [],
    "source": [
-    "enable1sd   = SuperDuperVocabulary(enable1.words)\n",
-    "enable1_4sd = SuperDuperVocabulary(enable1.words, 4)"
+    "enable1_3duper = SuperDuperVocabulary(enable1.words)\n",
+    "enable1_4duper = SuperDuperVocabulary(enable1.words, 4)"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 37,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -1108,22 +1035,20 @@
    ],
    "source": [
     "# Example legal plays\n",
-    "enable1sd.legal_plays('crop')"
+    "enable1_3duper.legal_plays('crop')"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Now we should check who wins. But I'm impateint: I tried `win(enable1sd)`, waited a minute, and it still hadn't returned, so I interrupted that computation and threw in a `lru_cache` decorator; which stops `win` from wasting time repeating the same computation over and over. This brings the time down to about 2 seconds."
+    "Now we should check who wins. But I'm impateint: I tried `win(enable1_3duper)`, waited a minute, and it still hadn't returned, so I interrupted that computation and threw in a `lru_cache` decorator; which stops `win` from wasting time repeating the same computation over and over. This brings the time down to about 2 seconds."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 38,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "from functools import lru_cache\n",
@@ -1143,14 +1068,12 @@
   {
    "cell_type": "code",
    "execution_count": 39,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "'y'"
+       "'p'"
       ]
      },
      "execution_count": 39,
@@ -1159,20 +1082,18 @@
     }
    ],
    "source": [
-    "win(enable1sd)"
+    "win(enable1_3duper)"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 40,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "'y'"
+       "'p'"
       ]
      },
      "execution_count": 40,
@@ -1181,7 +1102,7 @@
     }
    ],
    "source": [
-    "win(enable1_4sd)"
+    "win(enable1_4duper)"
    ]
   },
   {
@@ -1194,30 +1115,28 @@
   {
    "cell_type": "code",
    "execution_count": 41,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Player 0, given \"\", plays \"y\".\n",
-      "Player 1, given \"y\", plays \"zy\".\n",
-      "Player 0, given \"zy\", plays \"izy\".\n",
-      "Player 1, given \"izy\", plays \"mizy\".\n",
-      "Player 0, given \"mizy\", plays \"mizyg\".\n",
-      "Player 1, given \"mizyg\", plays \"emizyg\".\n",
-      "Player 0, given \"emizyg\", plays \"emizygo\".\n",
-      "Player 1, given \"emizygo\", plays \"emizygou\".\n",
-      "Player 0, given \"emizygou\", plays \"hemizygou\".\n",
-      "Player 1, given \"hemizygou\", plays \"hemizygous\".\n"
+      "Player 0, given \"\", plays \"p\".\n",
+      "Player 1, given \"p\", plays \"pr\".\n",
+      "Player 0, given \"pr\", plays \"lpr\".\n",
+      "Player 1, given \"lpr\", plays \"rple\".\n",
+      "Player 0, given \"rple\", plays \"rplex\".\n",
+      "Player 1, given \"rplex\", plays \"rplexe\".\n",
+      "Player 0, given \"rplexe\", plays \"urplexe\".\n",
+      "Player 1, given \"urplexe\", plays \"urplexes\".\n",
+      "Player 0, given \"urplexes\", plays \"ourplexes\".\n",
+      "Player 1, given \"ourplexes\", plays \"fourplexes\".\n"
      ]
     },
     {
      "data": {
       "text/plain": [
-       "(0, 'hemizygous')"
+       "(0, 'fourplexes')"
       ]
      },
      "execution_count": 41,
@@ -1226,7 +1145,7 @@
     }
    ],
    "source": [
-    "play(enable1sd, rational, rational, verbose=True)"
+    "play(enable1_3duper, rational, rational, verbose=True)"
    ]
   },
   {
@@ -1239,9 +1158,7 @@
   {
    "cell_type": "code",
    "execution_count": 42,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -1256,7 +1173,7 @@
    ],
    "source": [
     "[len(v.fragments) \n",
-    " for v in [enable1, enable1_4, enable1s, enable1_4s, enable1sd, enable1_4sd]]"
+    " for v in [enable1, enable1_4, enable1_3super, enable1_4super, enable1_3duper, enable1_4duper]]"
    ]
   },
   {
@@ -1268,7 +1185,7 @@
     "Here's a summary of what we have learned. (*Note:* the bold **qursh**  means it is a losing word):\n",
     "\n",
     "| Variant \t| Shortest \t| Winner \t| First Player Forced Outcomes | 2nd  Outcomes | Fragments\n",
-    "|----\t|---:\t    |---\t    |---                    |--- |---:\n",
+    "|:----:\t|:---:\t    |:---:\t    |:---:                    |:---: |---:\n",
     "| Ghost | 3 \t    | Second \t| qaid qiviut qoph **qursh** qurush qwerty  | 55 words | 387,878\n",
     "| Ghost | 4 \t    | First \t| naan nene ngultrum nirvanic nolo null nyctalopia | 85 words | 387,844\n",
     "| Super | 3\t| First \t| ? | ? | 1,076,434\n",
@@ -1306,7 +1223,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.0"
+   "version": "3.5.3"
   }
  },
  "nbformat": 4,