montecarlo_demo.ipynb

{
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  {
   "cell_type": "markdown",
   "id": "45e51a6c-5fae-41fc-a5f9-32f0b93df6ee",
   "metadata": {},
   "source": [
    "# Scenarios"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "0da5d35b-ac52-4a2f-aff3-702af201757a",
   "metadata": {},
   "outputs": [],
   "source": [
    "from montecarlo import Die, Game, Analyzer"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bccef2e7-03b4-4e8c-9741-3ef84380b80b",
   "metadata": {},
   "source": [
    "## Scenario 1: A 2-headed coin"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64043aee-0c5b-4a35-839a-b5bc773518f4",
   "metadata": {},
   "source": [
    "---\n",
    "Create a fair coin (with faces H and T) and one unfair coin, in which one of the faces has a weight of 5 and the others 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8ed8522e-5962-4091-b0d3-ad8df2fb3c31",
   "metadata": {},
   "outputs": [],
   "source": [
    "fair = Die(['H', 'T'])\n",
    "unfair = Die(['H','T'])\n",
    "unfair.change_weight('H', 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "0ad3ba50-8373-4998-a79c-d646b5dccd55",
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Weight</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>H</th>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>T</th>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Weight\n",
       "H     1.0\n",
       "T     1.0"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fair.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "92f89d4e-2a0c-4b30-9a85-5e78792d7e00",
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Weight</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>H</th>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>T</th>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "   Weight\n",
       "H     5.0\n",
       "T     1.0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unfair.show()"
   ]
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  {
   "cell_type": "markdown",
   "id": "e55806c8-6b39-4fd3-84c0-b7a2bd3650bf",
   "metadata": {},
   "source": [
    "---\n",
    "Play a game of 1000 flips of three coins with all fair dice."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "28bac68b-e57e-4f2e-8fe2-0585277c04dc",
   "metadata": {},
   "outputs": [
    {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Die</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Roll</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>T</td>\n",
       "      <td>H</td>\n",
       "      <td>T</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>H</td>\n",
       "      <td>T</td>\n",
       "      <td>T</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>T</td>\n",
       "      <td>H</td>\n",
       "      <td>T</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>T</td>\n",
       "      <td>H</td>\n",
       "      <td>H</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>H</td>\n",
       "      <td>H</td>\n",
       "      <td>H</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>995</th>\n",
       "      <td>H</td>\n",
       "      <td>T</td>\n",
       "      <td>H</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>996</th>\n",
       "      <td>H</td>\n",
       "      <td>H</td>\n",
       "      <td>T</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>997</th>\n",
       "      <td>T</td>\n",
       "      <td>T</td>\n",
       "      <td>T</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>998</th>\n",
       "      <td>T</td>\n",
       "      <td>T</td>\n",
       "      <td>H</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>999</th>\n",
       "      <td>T</td>\n",
       "      <td>H</td>\n",
       "      <td>H</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1000 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "Die   0  1  2\n",
       "Roll         \n",
       "0     T  H  T\n",
       "1     H  T  T\n",
       "2     T  H  T\n",
       "3     T  H  H\n",
       "4     H  H  H\n",
       "...  .. .. ..\n",
       "995   H  T  H\n",
       "996   H  H  T\n",
       "997   T  T  T\n",
       "998   T  T  H\n",
       "999   T  H  H\n",
       "\n",
       "[1000 rows x 3 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fair_game = Game([fair, fair, fair])\n",
    "fair_game.play(1000)\n",
    "fair_game.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3ddca71-67c3-4898-b0e1-0b253f6f5885",
   "metadata": {},
   "source": [
    "---\n",
    "Play a game of 1000 flips with two unfair dice and one fair die."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b9db76b7-e7c7-4949-ada9-8c106381e115",
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Die</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Roll</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>H</td>\n",
       "      <td>H</td>\n",
       "      <td>H</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>H</td>\n",
       "      <td>H</td>\n",
       "      <td>H</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>T</td>\n",
       "      <td>H</td>\n",
       "      <td>T</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>H</td>\n",
       "      <td>H</td>\n",
       "      <td>T</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>H</td>\n",
       "      <td>H</td>\n",
       "      <td>T</td>\n",
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       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>995</th>\n",
       "      <td>H</td>\n",
       "      <td>T</td>\n",
       "      <td>H</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>996</th>\n",
       "      <td>H</td>\n",
       "      <td>H</td>\n",
       "      <td>T</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>997</th>\n",
       "      <td>H</td>\n",
       "      <td>H</td>\n",
       "      <td>H</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>998</th>\n",
       "      <td>H</td>\n",
       "      <td>T</td>\n",
       "      <td>T</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>999</th>\n",
       "      <td>T</td>\n",
       "      <td>H</td>\n",
       "      <td>H</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1000 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "Die   0  1  2\n",
       "Roll         \n",
       "0     H  H  H\n",
       "1     H  H  H\n",
       "2     T  H  T\n",
       "3     H  H  T\n",
       "4     H  H  T\n",
       "...  .. .. ..\n",
       "995   H  T  H\n",
       "996   H  H  T\n",
       "997   H  H  H\n",
       "998   H  T  T\n",
       "999   T  H  H\n",
       "\n",
       "[1000 rows x 3 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unfair_game = Game([unfair, unfair, fair])\n",
    "unfair_game.play(1000)\n",
    "unfair_game.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb11fcc9-1901-4ce9-84b7-2472fe08576f",
   "metadata": {},
   "source": [
    "---\n",
    "For each game, use an Analyzer object to determine the relative frequency of jackpots – getting either all Hs or all Ts."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "4bc890e7-d6a7-4846-b2e1-69a07d155c98",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Relative frequency of jackpots for the fair game: 0.255\n",
      "Relative frequency of jackpots for the unfair game: 0.334\n"
     ]
    }
   ],
   "source": [
    "fair_analyzer = Analyzer(fair_game)\n",
    "unfair_analyzer = Analyzer(unfair_game)\n",
    "\n",
    "fair_frq = fair_analyzer.jackpot() / 1000\n",
    "unfair_frq = unfair_analyzer.jackpot() / 1000\n",
    "\n",
    "print('Relative frequency of jackpots for the fair game:', fair_frq)\n",
    "print('Relative frequency of jackpots for the unfair game:', unfair_frq)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0889f637-c61c-474c-b042-e9918fba3bcb",
   "metadata": {},
   "source": [
    "---\n",
    "Show your results, comparing the two relative frequencies, in a simple bar chart."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "bda63b1a-925b-45f7-93f5-9880616f8389",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.bar(['Fair', 'Unfair'],[fair_frq, unfair_frq]);\n",
    "plt.title('Relative frequency of jackpots');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57d36d79-cb13-4d9a-abad-14091b451640",
   "metadata": {},
   "source": [
    "## Scenario 2: A 6-sided die"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc0fffa5-02e0-479b-9569-d9360d88c5a7",
   "metadata": {},
   "source": [
    "---\n",
    "Create a fair die and two unfair dice, all of six sides with the faces 1 through 6. One unfair die (Type 1) will weight 6 five times more than the others (i.e. it has weight of 5 and the others a weight of 1 each). The other unfair die (Type 2) will  weight 1 five times more than the others."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "60da9954-bb80-43e7-b619-fab8ef32b1cf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Weight</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Weight\n",
       "1     1.0\n",
       "2     1.0\n",
       "3     1.0\n",
       "4     1.0\n",
       "5     1.0\n",
       "6     1.0"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fair = Die([1, 2, 3, 4, 5, 6])\n",
    "fair.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "d67ded27-a2a3-443f-a2d1-f767b3ba32ca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Weight</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Weight\n",
       "1     1.0\n",
       "2     1.0\n",
       "3     1.0\n",
       "4     1.0\n",
       "5     1.0\n",
       "6     5.0"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unfair1 = Die([1, 2, 3, 4, 5, 6])\n",
    "unfair1.change_weight(6, 5)\n",
    "unfair1.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "000a69fa-c418-4029-8089-5639972768c7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Weight</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Weight\n",
       "1     5.0\n",
       "2     1.0\n",
       "3     1.0\n",
       "4     1.0\n",
       "5     1.0\n",
       "6     1.0"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unfair2 = Die([1, 2, 3, 4, 5, 6])\n",
    "unfair2.change_weight(1, 5)\n",
    "unfair2.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "47d82211-0957-4e8c-9e8a-2944d8a157a3",
   "metadata": {},
   "source": [
    "---\n",
    "Play a game of 10000 rolls with 5 fair dice. \n",
    "\n",
    "Play a game of 10000 rolls with 2 unfair dice of type 1, 1 unfair die of type 2, and the rest fair dice."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "383c558c-f5fd-42c9-8f3e-6f8cc9edf525",
   "metadata": {},
   "outputs": [],
   "source": [
    "fair_game = Game([fair, fair, fair, fair, fair])\n",
    "fair_game.play(10000)\n",
    "\n",
    "unfair_game = Game([unfair1, unfair1, unfair2, fair, fair])\n",
    "unfair_game.play(10000)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e31d163-7987-4b11-8203-86ab892b0eee",
   "metadata": {},
   "source": [
    "---\n",
    "For each game, use an Analyzer object to determine the relative frequency of jackpots and show your results, comparing the two relative frequencies, in a simple bar chart."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "a63b6b69-80f7-4662-813e-04f84deee8bb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Relative frequency of jackpots for the fair game: 0.006\n",
      "Relative frequency of jackpots for the unfair game: 0.005\n"
     ]
    }
   ],
   "source": [
    "fair_analyzer = Analyzer(fair_game)\n",
    "unfair_analyzer = Analyzer(unfair_game)\n",
    "\n",
    "fair_frq = fair_analyzer.jackpot() / 1000\n",
    "unfair_frq = unfair_analyzer.jackpot() / 1000\n",
    "\n",
    "print('Relative frequency of jackpots for the fair game:', fair_frq)\n",
    "print('Relative frequency of jackpots for the unfair game:', unfair_frq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "19a60b44-6c26-4c6a-86e1-e3cfe2fb0ef1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.bar(['Fair', 'Unfair'],[fair_frq, unfair_frq])\n",
    "plt.title('Relative frequency of jackpots');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c133c02-8fe3-4572-b312-af7b2bfbb6df",
   "metadata": {},
   "source": [
    "---\n",
    "Also compute 10 most frequent combinations of faces for each game. Plot each of these as bar charts."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "a5ae4256-b56c-45a8-bf58-2b54f8169765",
   "metadata": {},
   "outputs": [],
   "source": [
    "fair_analyzer.combo()\n",
    "unfair_analyzer.combo()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "a1fd80f9-ab8d-4026-b5a7-3a039a2e7299",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>Counts</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <td>190</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"6\" valign=\"top\">1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>6</th>\n",
       "      <td>156</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <td>153</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"3\" valign=\"top\">2</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <td>149</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <td>144</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <td>138</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>6</th>\n",
       "      <td>93</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <td>92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">1</th>\n",
       "      <th>2</th>\n",
       "      <th>2</th>\n",
       "      <th>4</th>\n",
       "      <th>6</th>\n",
       "      <td>91</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>4</th>\n",
       "      <th>6</th>\n",
       "      <td>90</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           Counts\n",
       "0 1 2 3 4        \n",
       "2 3 4 5 6     190\n",
       "1 2 3 4 6     156\n",
       "  3 4 5 6     153\n",
       "  2 4 5 6     149\n",
       "    3 4 5     144\n",
       "      5 6     138\n",
       "  1 3 4 6      93\n",
       "2 3 3 4 5      92\n",
       "1 2 2 4 6      91\n",
       "  1 2 4 6      90"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fair_analyzer.combos.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "ab329720-d573-4cef-86e7-5c8fe2f14d69",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>Counts</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"10\" valign=\"top\">1</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>6</th>\n",
       "      <th>6</th>\n",
       "      <td>211</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <th>4</th>\n",
       "      <th>6</th>\n",
       "      <th>6</th>\n",
       "      <td>203</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>6</th>\n",
       "      <td>198</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>6</th>\n",
       "      <td>192</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>6</th>\n",
       "      <td>182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"4\" valign=\"top\">2</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <td>178</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"3\" valign=\"top\">3</th>\n",
       "      <th>6</th>\n",
       "      <th>6</th>\n",
       "      <td>176</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <th>6</th>\n",
       "      <td>165</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <td>162</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <th>4</th>\n",
       "      <th>6</th>\n",
       "      <th>6</th>\n",
       "      <td>160</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           Counts\n",
       "0 1 2 3 4        \n",
       "1 3 4 6 6     211\n",
       "  2 4 6 6     203\n",
       "  3 5 6 6     198\n",
       "  2 5 6 6     192\n",
       "  4 5 6 6     182\n",
       "  2 4 5 6     178\n",
       "    3 6 6     176\n",
       "      4 6     165\n",
       "      5 6     162\n",
       "  1 4 6 6     160"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unfair_analyzer.combos.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "59384295-8f70-45dd-b2c5-ddcf538c33b0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fair_plot = fair_analyzer.combos.head(10).reset_index()\n",
    "fair_plot[\"labels\"] = fair_plot[0].astype(str) + fair_plot[1].astype(str) + fair_plot[2].astype(str) \\\n",
    "                + fair_plot[3].astype(str) + fair_plot[4].astype(str)\n",
    "fair_plot = fair_plot[['Counts', 'labels']]\n",
    "plt.bar(fair_plot['labels'],fair_plot['Counts'])\n",
    "plt.xticks(rotation='vertical');\n",
    "plt.title(\"Fair Game Plot\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "32863dcd-a9a6-4afe-81da-0b76d908e777",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "unfair_plot = unfair_analyzer.combos.head(10).reset_index()\n",
    "unfair_plot[\"labels\"] = unfair_plot[0].astype(str) + unfair_plot[1].astype(str) + unfair_plot[2].astype(str) \\\n",
    "                + unfair_plot[3].astype(str) + unfair_plot[4].astype(str)\n",
    "unfair_plot = unfair_plot[['Counts', 'labels']]\n",
    "plt.bar(unfair_plot['labels'],unfair_plot['Counts'])\n",
    "plt.xticks(rotation='vertical');\n",
    "plt.title(\"Unfair Game Plot\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "55d101f2-feaf-4a15-a0d7-8dcf4fbc04e0",
   "metadata": {},
   "source": [
    "## Scenario 3: A 6-sided die"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d74c2c7-e075-44b5-be47-99647ad1db92",
   "metadata": {},
   "source": [
    "---\n",
    "Create a \"die\" of letters from a to z with weights based on their frequency of usage."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "fde78535-b1d8-4c1a-a081-c230c75195a2",
   "metadata": {},
   "outputs": [],
   "source": [
    "letters = ['a','b','c','d','e','f','g','h','i','j','k','l','m','n','o','p',\n",
    "           'q','r','s','t','u','v','w','x','y','z']\n",
    "values = [8.4966, 2.0720, 4.5388, 3.3844, 11.1607, 1.8121, 2.4705, 3.0034, 7.5448, \n",
    "          0.1965, 1.1016, 5.4893, 3.0129, 6.6544, 7.1635, 3.1671, 0.1962, 7.5809, 5.7351,\n",
    "          6.9509, 3.6308, 1.0074, 1.2899, 0.2902, 1.7779, 0.2722]\n",
    "\n",
    "alphabet = Die(letters)\n",
    "for i in range(0,len(letters)):\n",
    "    alphabet.change_weight(letters[i], values[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "3b3839e7-8d44-4b90-afa5-e27ee63b0c92",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>a</th>\n",
       "      <th>b</th>\n",
       "      <th>c</th>\n",
       "      <th>d</th>\n",
       "      <th>e</th>\n",
       "      <th>f</th>\n",
       "      <th>g</th>\n",
       "      <th>h</th>\n",
       "      <th>i</th>\n",
       "      <th>j</th>\n",
       "      <th>...</th>\n",
       "      <th>q</th>\n",
       "      <th>r</th>\n",
       "      <th>s</th>\n",
       "      <th>t</th>\n",
       "      <th>u</th>\n",
       "      <th>v</th>\n",
       "      <th>w</th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>z</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Weight</th>\n",
       "      <td>8.4966</td>\n",
       "      <td>2.072</td>\n",
       "      <td>4.5388</td>\n",
       "      <td>3.3844</td>\n",
       "      <td>11.1607</td>\n",
       "      <td>1.8121</td>\n",
       "      <td>2.4705</td>\n",
       "      <td>3.0034</td>\n",
       "      <td>7.5448</td>\n",
       "      <td>0.1965</td>\n",
       "      <td>...</td>\n",
       "      <td>0.1962</td>\n",
       "      <td>7.5809</td>\n",
       "      <td>5.7351</td>\n",
       "      <td>6.9509</td>\n",
       "      <td>3.6308</td>\n",
       "      <td>1.0074</td>\n",
       "      <td>1.2899</td>\n",
       "      <td>0.2902</td>\n",
       "      <td>1.7779</td>\n",
       "      <td>0.2722</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1 rows × 26 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             a      b       c       d        e       f       g       h  \\\n",
       "Weight  8.4966  2.072  4.5388  3.3844  11.1607  1.8121  2.4705  3.0034   \n",
       "\n",
       "             i       j  ...       q       r       s       t       u       v  \\\n",
       "Weight  7.5448  0.1965  ...  0.1962  7.5809  5.7351  6.9509  3.6308  1.0074   \n",
       "\n",
       "             w       x       y       z  \n",
       "Weight  1.2899  0.2902  1.7779  0.2722  \n",
       "\n",
       "[1 rows x 26 columns]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alphabet.show().T"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1a32ddf-1b52-47b6-a71c-66bb19290ec3",
   "metadata": {},
   "source": [
    "---\n",
    "Play a game involving 5 of these dice with 1000 rolls."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "c8508176-5e66-48c4-9182-580ba7b74e02",
   "metadata": {},
   "outputs": [],
   "source": [
    "alphabet_game = Game([alphabet, alphabet, alphabet, alphabet, alphabet])\n",
    "alphabet_game.play(1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "7fa77dd9-1ff8-43fe-9612-e478289fa439",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "pd.set_option('display.max_rows', 1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5d1df0e4-2ccd-4de7-bdeb-c1e1b9ac66c5",
   "metadata": {},
   "source": [
    "---\n",
    "How many combos can you see that look like actual English words?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc9f70e0-5c3f-4458-bda7-8e552cc4e3e7",
   "metadata": {},
   "source": [
    "I found the following words: teeny, saint, coder,  peeks, peel, terf, night. \\\n",
    "It appears that words with consecutive vowels, such as e's, are more common. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "2e3f6608-fef3-43fb-b796-c01d808b0484",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Roll</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>...</th>\n",
       "      <th>990</th>\n",
       "      <th>991</th>\n",
       "      <th>992</th>\n",
       "      <th>993</th>\n",
       "      <th>994</th>\n",
       "      <th>995</th>\n",
       "      <th>996</th>\n",
       "      <th>997</th>\n",
       "      <th>998</th>\n",
       "      <th>999</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Die</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>a</td>\n",
       "      <td>u</td>\n",
       "      <td>k</td>\n",
       "      <td>n</td>\n",
       "      <td>r</td>\n",
       "      <td>e</td>\n",
       "      <td>t</td>\n",
       "      <td>y</td>\n",
       "      <td>y</td>\n",
       "      <td>u</td>\n",
       "      <td>...</td>\n",
       "      <td>h</td>\n",
       "      <td>g</td>\n",
       "      <td>s</td>\n",
       "      <td>a</td>\n",
       "      <td>g</td>\n",
       "      <td>a</td>\n",
       "      <td>r</td>\n",
       "      <td>h</td>\n",
       "      <td>n</td>\n",
       "      <td>n</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>d</td>\n",
       "      <td>i</td>\n",
       "      <td>t</td>\n",
       "      <td>y</td>\n",
       "      <td>a</td>\n",
       "      <td>d</td>\n",
       "      <td>c</td>\n",
       "      <td>i</td>\n",
       "      <td>h</td>\n",
       "      <td>o</td>\n",
       "      <td>...</td>\n",
       "      <td>i</td>\n",
       "      <td>l</td>\n",
       "      <td>l</td>\n",
       "      <td>o</td>\n",
       "      <td>s</td>\n",
       "      <td>a</td>\n",
       "      <td>i</td>\n",
       "      <td>e</td>\n",
       "      <td>o</td>\n",
       "      <td>d</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>y</td>\n",
       "      <td>n</td>\n",
       "      <td>a</td>\n",
       "      <td>p</td>\n",
       "      <td>n</td>\n",
       "      <td>d</td>\n",
       "      <td>n</td>\n",
       "      <td>k</td>\n",
       "      <td>a</td>\n",
       "      <td>n</td>\n",
       "      <td>...</td>\n",
       "      <td>l</td>\n",
       "      <td>y</td>\n",
       "      <td>l</td>\n",
       "      <td>r</td>\n",
       "      <td>r</td>\n",
       "      <td>e</td>\n",
       "      <td>r</td>\n",
       "      <td>t</td>\n",
       "      <td>s</td>\n",
       "      <td>a</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>n</td>\n",
       "      <td>o</td>\n",
       "      <td>t</td>\n",
       "      <td>t</td>\n",
       "      <td>t</td>\n",
       "      <td>i</td>\n",
       "      <td>o</td>\n",
       "      <td>s</td>\n",
       "      <td>s</td>\n",
       "      <td>b</td>\n",
       "      <td>...</td>\n",
       "      <td>y</td>\n",
       "      <td>o</td>\n",
       "      <td>h</td>\n",
       "      <td>c</td>\n",
       "      <td>r</td>\n",
       "      <td>b</td>\n",
       "      <td>r</td>\n",
       "      <td>m</td>\n",
       "      <td>d</td>\n",
       "      <td>a</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>n</td>\n",
       "      <td>a</td>\n",
       "      <td>e</td>\n",
       "      <td>i</td>\n",
       "      <td>y</td>\n",
       "      <td>c</td>\n",
       "      <td>s</td>\n",
       "      <td>o</td>\n",
       "      <td>h</td>\n",
       "      <td>v</td>\n",
       "      <td>...</td>\n",
       "      <td>t</td>\n",
       "      <td>t</td>\n",
       "      <td>e</td>\n",
       "      <td>f</td>\n",
       "      <td>d</td>\n",
       "      <td>c</td>\n",
       "      <td>r</td>\n",
       "      <td>o</td>\n",
       "      <td>o</td>\n",
       "      <td>a</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 1000 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "Roll 0   1   2   3   4   5   6   7   8   9    ... 990 991 992 993 994 995 996  \\\n",
       "Die                                           ...                               \n",
       "0      a   u   k   n   r   e   t   y   y   u  ...   h   g   s   a   g   a   r   \n",
       "1      d   i   t   y   a   d   c   i   h   o  ...   i   l   l   o   s   a   i   \n",
       "2      y   n   a   p   n   d   n   k   a   n  ...   l   y   l   r   r   e   r   \n",
       "3      n   o   t   t   t   i   o   s   s   b  ...   y   o   h   c   r   b   r   \n",
       "4      n   a   e   i   y   c   s   o   h   v  ...   t   t   e   f   d   c   r   \n",
       "\n",
       "Roll 997 998 999  \n",
       "Die               \n",
       "0      h   n   n  \n",
       "1      e   o   d  \n",
       "2      t   s   a  \n",
       "3      m   d   a  \n",
       "4      o   o   a  \n",
       "\n",
       "[5 rows x 1000 columns]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alphabet_game.show().T # transposed to save space!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e40a8654-b385-43a6-bd7a-d662270707b3",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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