mega_sena.ipynb

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    "# Mega-Sena\n",
    "\n",
    "- **Aluno**: Álvaro Ferreira Pires de Paiva\n",
    "- **Matrícula**: 2016039162\n",
    "\n",
    "**Sumário**\n",
    "- [Base de dados](#database)\n",
    "- [Preparando o ambiente](#env_treatment)\n",
    "  - Prêmio máximo\n",
    "  - Rótulo\n",
    "- [Análises](#analysis)\n",
    "  - Dicas"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "## <a id=\"database\">Base de dados</a>\n",
    "\n",
    "Nessa avaliação será utilizado a base de dados referente aos concursos da Mega-Sena. \n",
    "\n",
    "A **Mega-Sena** tem sido a maior modalidade lotérica do Brasil, sendo uma entre as dez modalidades atuais das loterias da Caixa (Caixa Econômica Federal), com sorteios ordinários duas vezes por semana, além da Mega-Sena da Virada.\n",
    "\n",
    "Para ganhar o **prêmio máximo da Mega-Sena** — **a sena** — , é necessário acertar a sena, o que significa obter coincidência entre **seis dos números** apostados e os seis números sorteados, de um total de sessenta dezenas (**de 01 a 60**), independentemente da ordem da aposta ou da ordem do sorteio. \n",
    "\n",
    "O concurso prevê também a chance de se ganhar parte do prêmio máximo, pelo acerto da **quina** (apenas cinco dos números sorteados), ou da **quadra** (apenas quatro dos números sorteados), com prêmios significativamente menores que aquele que seria pago na ocorrência do acerto da sena, o da quina maior que o da quadra. \n",
    "\n",
    "A base de dados está em formato de planilha em excel."
   ]
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    "## <a id=\"env_treatment\">Preparando o ambiente</a>\n",
    "Aqui iremos realizar as importações de bibliotecas necessárias e o armazenamento dos dados para podermos analisarmos logo em seguida.\n",
    "Dependencies\n",
    "```\n",
    "!conda install bokeh\n",
    "```"
   ]
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   "source": [
    "# Imports\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from bokeh.models import HoverTool\n",
    "from bokeh.plotting import figure, output_notebook, show"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
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   "source": [
    "# Leitura dos dados\n",
    "excel_file = 'mega_sena.xlsx'\n",
    "excel = pd.ExcelFile(excel_file)\n",
    "data = excel.parse(0)"
   ]
  },
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   "execution_count": 3,
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       "      <th></th>\n",
       "      <th>As Loterias - www.asloterias.com.br - Todos Resultados da Mega Sena</th>\n",
       "      <th>Unnamed: 1</th>\n",
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       "      <th>0</th>\n",
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       "  As Loterias - www.asloterias.com.br - Todos Resultados da Mega Sena  \\\n",
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   "source": [
    "data.head()"
   ]
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   "source": [
    "### Prêmio máximo\n",
    "Para cada concurso da Mega-Sena, a maior premiação está relacionada com o acerto das 6 dezenas, e o seu valor é dada pela seguinte relação:\n",
    "\n",
    "$$Prêmio = Ganhadores\\_Sena\t\\times Rateio\\_Sena$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "data['premio_maximo'] = data.Ganhadores_Sena * data.Rateio_Sena"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Rótulo\n",
    "Criaremos uma nova coluna chamada \"Rótulo\" baseada na faixa de valores da coluna \"prêmio_máximo\", como apresentado na seguinte tabela:\n",
    "\n",
    "| Intervalo [Milhões de Reais] | Rótulo |\n",
    "|------------------------------|--------|\n",
    "| 0 - 1                        | I      |\n",
    "| 1 - 5                        | II     |\n",
    "| 5 - 10                       | III    |\n",
    "| 10 - 20                      | IV     |\n",
    "| 20 - 40                      | V      |\n",
    "| 40 - 80                      | VI     |\n",
    "| 80 - 100                     | VII    |\n",
    "| 100 - 200                    | VIII   |\n",
    "| 200 - 300                    | IX     |\n",
    "| 300 -                        | X      |"
   ]
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   "source": [
    "data['rotulo'] = pd.cut(data.premio_maximo,\n",
    "                        bins=[0,1e6,5e6,1e7,2e7,4e7,8e7,1e8,2e8,3e8,1e9],\n",
    "                        labels=[\"I\",\"II\",\"III\",\"IV\",\"V\",\"VI\",\"VII\",\"VIII\",\"IX\",\"X\"],\n",
    "                        include_lowest=True)"
   ]
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   "cell_type": "markdown",
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   "source": [
    "## <a id=\"analysis\">Análises</a>\n",
    "Nessa seção, iremos realizar algumas análises nos dados que temos em mãos.\n",
    "\n",
    "### Dicas\n",
    "Pela Mega-Sena possuir prêmios de valores bastantes elevados, é normal encontrar sites com dicas para o jogador ter mais chances de ganhar. Sendo assim, iremos análisar 8 dicas encontradas em alguns sites e verificar a sua veracidade. As dicas são:\n",
    "\n",
    "1. Os números com final 9 ou 0 saem pouco, por isso, é bom evitar escolher várias números com essa sequencia.\n",
    "2. As dezenas 01, 02, 03, 11, 22, 44, 55, 48 e 57 saem pouco.\n",
    "3. Não jogue números seguidos.\n",
    "4. Não jogue em números que estejam na mesma linha vertical.\n",
    "5. Divida a cartela em quatro quadrantes e distribua seu jogo entre eles.\n",
    "6. Jogue sempre a mesma quantidade de dezenas pares e ímpares. Na Mega-Sena, 81% dos sorteios têm o seguinte esquema: 3 números pares e 3 ímpares ou 4 pares e 2 ímpares, ou vice-versa.\n",
    "7. Prefira apenas um cartão com mais de seis dezenas do que vários cartões de seis dezenas. A regra é simples: quanto mais números você apostar, maiores são as chances de acertar um deles.\n",
    "8. Um jogo em que se preenche 12 dezenas utilizando essas regras teria mais chances de êxito. Logo, o bolão é a melhor chance que se tem de ganhar.\n",
    "\n",
    "Algumas variáveis iremos utilizar na validação de mais de uma dica, sendo elas:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Colunas que iremos trabalhar\n",
    "cols_dezenas = ['Dezena1', 'Dezena2', 'Dezena3', 'Dezena4', 'Dezena5', 'Dezena6']\n",
    "\n",
    "# Dataframe filtrado pelas colunas que queremos\n",
    "df_cols = data[cols_dezenas]\n",
    "\n",
    "# Dataframe com os últimos dígitos de cada número de cada jogo\n",
    "df_last_digit = df_cols.apply(lambda x: x%10)\n",
    "\n",
    "# Dezenas da mega-sena\n",
    "dezenas = [i for i in range(1, 61)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1. Os números com final 9 ou 0 saem pouco"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "scrolled": false
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 - 10.576131687242798%\n",
      "1 - 10.444444444444445%\n",
      "2 - 10.148148148148149%\n",
      "3 - 10.08230452674897%\n",
      "4 - 9.958847736625515%\n",
      "5 - 9.893004115226338%\n",
      "6 - 9.868312757201647%\n",
      "7 - 9.76954732510288%\n",
      "8 - 9.670781893004115%\n",
      "9 - 9.588477366255145%\n"
     ]
    }
   ],
   "source": [
    "# Series que usaremos para somar as ocorrências de cada último dígito\n",
    "last_digit_sum = pd.Series(0, index=[i for i in range(0, 10)])\n",
    "\n",
    "# Somatório das ocorrências\n",
    "for col in cols_dezenas:\n",
    "    last_digit_sum = last_digit_sum + df_last_digit[col].value_counts()\n",
    "\n",
    "for index, count in enumerate(last_digit_sum.sort_values(ascending=False)):\n",
    "    print(\"{} - {}%\".format(index, ((count*100)/last_digit_sum.sum())))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
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    {
     "data": {
      "text/plain": [
       "3    1285\n",
       "4    1269\n",
       "2    1233\n",
       "0    1225\n",
       "7    1210\n",
       "8    1202\n",
       "1    1199\n",
       "6    1187\n",
       "5    1175\n",
       "9    1165\n",
       "dtype: int64"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "last_digit_sum.sort_values(ascending=False)"
   ]
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       "    root._bokeh_onload_callbacks.push(callback);\n",
       "    if (root._bokeh_is_loading > 0) {\n",
       "      console.log(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
       "      return null;\n",
       "    }\n",
       "    if (js_urls == null || js_urls.length === 0) {\n",
       "      run_callbacks();\n",
       "      return null;\n",
       "    }\n",
       "    console.log(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
       "    root._bokeh_is_loading = js_urls.length;\n",
       "    for (var i = 0; i < js_urls.length; i++) {\n",
       "      var url = js_urls[i];\n",
       "      var s = document.createElement('script');\n",
       "      s.src = url;\n",
       "      s.async = false;\n",
       "      s.onreadystatechange = s.onload = function() {\n",
       "        root._bokeh_is_loading--;\n",
       "        if (root._bokeh_is_loading === 0) {\n",
       "          console.log(\"Bokeh: all BokehJS libraries loaded\");\n",
       "          run_callbacks()\n",
       "        }\n",
       "      };\n",
       "      s.onerror = function() {\n",
       "        console.warn(\"failed to load library \" + url);\n",
       "      };\n",
       "      console.log(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
       "      document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
       "    }\n",
       "  };var element = document.getElementById(\"9b68cfbb-faea-4b3c-ba1a-7426f94233f6\");\n",
       "  if (element == null) {\n",
       "    console.log(\"Bokeh: ERROR: autoload.js configured with elementid '9b68cfbb-faea-4b3c-ba1a-7426f94233f6' but no matching script tag was found. \")\n",
       "    return false;\n",
       "  }\n",
       "\n",
       "  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.15.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.15.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.15.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-0.12.15.min.js\"];\n",
       "\n",
       "  var inline_js = [\n",
       "    function(Bokeh) {\n",
       "      Bokeh.set_log_level(\"info\");\n",
       "    },\n",
       "    \n",
       "    function(Bokeh) {\n",
       "      \n",
       "    },\n",
       "    function(Bokeh) {\n",
       "      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-0.12.15.min.css\");\n",
       "      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.15.min.css\");\n",
       "      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.15.min.css\");\n",
       "      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.15.min.css\");\n",
       "      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.15.min.css\");\n",
       "      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.15.min.css\");\n",
       "    }\n",
       "  ];\n",
       "\n",
       "  function run_inline_js() {\n",
       "    \n",
       "    if ((root.Bokeh !== undefined) || (force === true)) {\n",
       "      for (var i = 0; i < inline_js.length; i++) {\n",
       "        inline_js[i].call(root, root.Bokeh);\n",
       "      }if (force === true) {\n",
       "        display_loaded();\n",
       "      }} else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(run_inline_js, 100);\n",
       "    } else if (!root._bokeh_failed_load) {\n",
       "      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
       "      root._bokeh_failed_load = true;\n",
       "    } else if (force !== true) {\n",
       "      var cell = $(document.getElementById(\"9b68cfbb-faea-4b3c-ba1a-7426f94233f6\")).parents('.cell').data().cell;\n",
       "      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
       "    }\n",
       "\n",
       "  }\n",
       "\n",
       "  if (root._bokeh_is_loading === 0) {\n",
       "    console.log(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
       "    run_inline_js();\n",
       "  } else {\n",
       "    load_libs(js_urls, function() {\n",
       "      console.log(\"Bokeh: BokehJS plotting callback run at\", now());\n",
       "      run_inline_js();\n",
       "    });\n",
       "  }\n",
       "}(window));"
      ],
      "application/vnd.bokehjs_load.v0+json": "\n(function(root) {\n  function now() {\n    return new Date();\n  }\n\n  var force = true;\n\n  if (typeof (root._bokeh_onload_callbacks) === \"undefined\" || force === true) {\n    root._bokeh_onload_callbacks = [];\n    root._bokeh_is_loading = undefined;\n  }\n\n  \n\n  \n  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n    root._bokeh_timeout = Date.now() + 5000;\n    root._bokeh_failed_load = false;\n  }\n\n  var NB_LOAD_WARNING = {'data': {'text/html':\n     \"<div style='background-color: #fdd'>\\n\"+\n     \"<p>\\n\"+\n     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n     \"</p>\\n\"+\n     \"<ul>\\n\"+\n     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n     \"</ul>\\n\"+\n     \"<code>\\n\"+\n     \"from bokeh.resources import INLINE\\n\"+\n     \"output_notebook(resources=INLINE)\\n\"+\n     \"</code>\\n\"+\n     \"</div>\"}};\n\n  function display_loaded() {\n    var el = document.getElementById(\"9b68cfbb-faea-4b3c-ba1a-7426f94233f6\");\n    if (el != null) {\n      el.textContent = \"BokehJS is loading...\";\n    }\n    if (root.Bokeh !== undefined) {\n      if (el != null) {\n        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n      }\n    } else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(display_loaded, 100)\n    }\n  }\n\n\n  function run_callbacks() {\n    try {\n      root._bokeh_onload_callbacks.forEach(function(callback) { callback() });\n    }\n    finally {\n      delete root._bokeh_onload_callbacks\n    }\n    console.info(\"Bokeh: all callbacks have finished\");\n  }\n\n  function load_libs(js_urls, callback) {\n    root._bokeh_onload_callbacks.push(callback);\n    if (root._bokeh_is_loading > 0) {\n      console.log(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n      return null;\n    }\n    if (js_urls == null || js_urls.length === 0) {\n      run_callbacks();\n      return null;\n    }\n    console.log(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n    root._bokeh_is_loading = js_urls.length;\n    for (var i = 0; i < js_urls.length; i++) {\n      var url = js_urls[i];\n      var s = document.createElement('script');\n      s.src = url;\n      s.async = false;\n      s.onreadystatechange = s.onload = function() {\n        root._bokeh_is_loading--;\n        if (root._bokeh_is_loading === 0) {\n          console.log(\"Bokeh: all BokehJS libraries loaded\");\n          run_callbacks()\n        }\n      };\n      s.onerror = function() {\n        console.warn(\"failed to load library \" + url);\n      };\n      console.log(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.getElementsByTagName(\"head\")[0].appendChild(s);\n    }\n  };var element = document.getElementById(\"9b68cfbb-faea-4b3c-ba1a-7426f94233f6\");\n  if (element == null) {\n    console.log(\"Bokeh: ERROR: autoload.js configured with elementid '9b68cfbb-faea-4b3c-ba1a-7426f94233f6' but no matching script tag was found. \")\n    return false;\n  }\n\n  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.15.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.15.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.15.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-0.12.15.min.js\"];\n\n  var inline_js = [\n    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\n    \n    function(Bokeh) {\n      \n    },\n    function(Bokeh) {\n      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-0.12.15.min.css\");\n      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.15.min.css\");\n      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.15.min.css\");\n      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.15.min.css\");\n      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.15.min.css\");\n      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.15.min.css\");\n    }\n  ];\n\n  function run_inline_js() {\n    \n    if ((root.Bokeh !== undefined) || (force === true)) {\n      for (var i = 0; i < inline_js.length; i++) {\n        inline_js[i].call(root, root.Bokeh);\n      }if (force === true) {\n        display_loaded();\n      }} else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(run_inline_js, 100);\n    } else if (!root._bokeh_failed_load) {\n      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n      root._bokeh_failed_load = true;\n    } else if (force !== true) {\n      var cell = $(document.getElementById(\"9b68cfbb-faea-4b3c-ba1a-7426f94233f6\")).parents('.cell').data().cell;\n      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n    }\n\n  }\n\n  if (root._bokeh_is_loading === 0) {\n    console.log(\"Bokeh: BokehJS loaded, going straight to plotting\");\n    run_inline_js();\n  } else {\n    load_libs(js_urls, function() {\n      console.log(\"Bokeh: BokehJS plotting callback run at\", now());\n      run_inline_js();\n    });\n  }\n}(window));"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "<div class=\"bk-root\">\n",
       "    <div class=\"bk-plotdiv\" id=\"b9ba6192-bcb9-4459-889b-57a47519791b\"></div>\n",
       "</div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
       "  var docs_json = {\"3ddf8e3b-6ab8-48dd-b7b9-a3c931ce462d\":{\"roots\":{\"references\":[{\"attributes\":{},\"id\":\"680dadde-09ed-4134-ac29-698fd967ca24\",\"type\":\"SaveTool\"},{\"attributes\":{\"callback\":null},\"id\":\"204e01f3-4fdd-4191-9b1e-82193fc7806e\",\"type\":\"DataRange1d\"},{\"attributes\":{},\"id\":\"f25898dd-d21d-4fda-825f-af041a6abd91\",\"type\":\"ResetTool\"},{\"attributes\":{},\"id\":\"ac537e3a-9a66-416a-b61a-2899f2758379\",\"type\":\"BasicTicker\"},{\"attributes\":{},\"id\":\"f2121920-dc13-4bd0-a49b-d93200ab34ee\",\"type\":\"HelpTool\"},{\"attributes\":{\"callback\":null},\"id\":\"ea271ad4-2543-483e-af57-945fba85d3c0\",\"type\":\"DataRange1d\"},{\"attributes\":{},\"id\":\"64f928f4-4350-4cc0-80d1-23904665f934\",\"type\":\"LinearScale\"},{\"attributes\":{\"data_source\":{\"id\":\"99738b11-42cd-4023-a0c8-943e5e084bf6\",\"type\":\"ColumnDataSource\"},\"glyph\":{\"id\":\"49342673-f0f5-4a54-b9bb-df9ce9fc0b02\",\"type\":\"VBar\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"ab03378e-78b6-4622-8629-3d78d9f89811\",\"type\":\"VBar\"},\"selection_glyph\":null,\"view\":{\"id\":\"8fbfb1c0-de17-4ff7-bb37-c7ca95182e2c\",\"type\":\"CDSView\"}},\"id\":\"4ca77656-cebe-444b-a8ce-3aae9e082931\",\"type\":\"GlyphRenderer\"},{\"attributes\":{},\"id\":\"1ee722d8-72b1-4236-8c65-fa7a840580b5\",\"type\":\"LinearScale\"},{\"attributes\":{\"source\":{\"id\":\"99738b11-42cd-4023-a0c8-943e5e084bf6\",\"type\":\"ColumnDataSource\"}},\"id\":\"8fbfb1c0-de17-4ff7-bb37-c7ca95182e2c\",\"type\":\"CDSView\"},{\"attributes\":{\"plot\":{\"id\":\"79d3ab37-41a9-4852-a9fa-57f509b38674\",\"subtype\":\"Figure\",\"type\":\"Plot\"},\"ticker\":{\"id\":\"ac537e3a-9a66-416a-b61a-2899f2758379\",\"type\":\"BasicTicker\"}},\"id\":\"dfa2863d-bd38-412c-9689-c6bac1442d45\",\"type\":\"Grid\"},{\"attributes\":{},\"id\":\"f90c2c1a-4e9e-47b4-9c48-f2524e0678f0\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"formatter\":{\"id\":\"27e0d637-387b-48e8-a856-c47e4e8742e6\",\"type\":\"BasicTickFormatter\"},\"plot\":{\"id\":\"79d3ab37-41a9-4852-a9fa-57f509b38674\",\"subtype\":\"Figure\",\"type\":\"Plot\"},\"ticker\":{\"id\":\"ae8d2161-9c3f-4417-be19-9cfb5cbd42f5\",\"type\":\"BasicTicker\"}},\"id\":\"078c3806-2dec-42c7-8f34-0a1333d09c77\",\"type\":\"LinearAxis\"},{\"attributes\":{},\"id\":\"27e0d637-387b-48e8-a856-c47e4e8742e6\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"formatter\":{\"id\":\"f90c2c1a-4e9e-47b4-9c48-f2524e0678f0\",\"type\":\"BasicTickFormatter\"},\"plot\":{\"id\":\"79d3ab37-41a9-4852-a9fa-57f509b38674\",\"subtype\":\"Figure\",\"type\":\"Plot\"},\"ticker\":{\"id\":\"ac537e3a-9a66-416a-b61a-2899f2758379\",\"type\":\"BasicTicker\"}},\"id\":\"da590a8a-caad-4ce3-86c1-3722b03f83ad\",\"type\":\"LinearAxis\"},{\"attributes\":{},\"id\":\"ae8d2161-9c3f-4417-be19-9cfb5cbd42f5\",\"type\":\"BasicTicker\"},{\"attributes\":{\"dimension\":1,\"plot\":{\"id\":\"79d3ab37-41a9-4852-a9fa-57f509b38674\",\"subtype\":\"Figure\",\"type\":\"Plot\"},\"ticker\":{\"id\":\"ae8d2161-9c3f-4417-be19-9cfb5cbd42f5\",\"type\":\"BasicTicker\"}},\"id\":\"126f744c-3f78-4290-911a-6cd5a48fbd01\",\"type\":\"Grid\"},{\"attributes\":{},\"id\":\"9bf2a9b6-09c9-455c-bbf0-7e1f3bada996\",\"type\":\"PanTool\"},{\"attributes\":{\"callback\":null,\"tooltips\":[[\"D\\u00edgito\",\"@x\"],[\"Ocorr\\u00eancias\",\"@top\"]]},\"id\":\"da2dce80-4910-4177-89ba-0d26042f9b93\",\"type\":\"HoverTool\"},{\"attributes\":{\"fill_color\":{\"value\":\"#1f77b4\"},\"line_color\":{\"value\":\"#1f77b4\"},\"top\":{\"field\":\"top\"},\"width\":{\"value\":0.5},\"x\":{\"field\":\"x\"}},\"id\":\"49342673-f0f5-4a54-b9bb-df9ce9fc0b02\",\"type\":\"VBar\"},{\"attributes\":{\"plot\":null,\"text\":\"\"},\"id\":\"7950b67f-48d0-4441-b014-b72deded7e01\",\"type\":\"Title\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.1},\"fill_color\":{\"value\":\"#1f77b4\"},\"line_alpha\":{\"value\":0.1},\"line_color\":{\"value\":\"#1f77b4\"},\"top\":{\"field\":\"top\"},\"width\":{\"value\":0.5},\"x\":{\"field\":\"x\"}},\"id\":\"ab03378e-78b6-4622-8629-3d78d9f89811\",\"type\":\"VBar\"},{\"attributes\":{\"bottom_units\":\"screen\",\"fill_alpha\":{\"value\":0.5},\"fill_color\":{\"value\":\"lightgrey\"},\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":{\"value\":1.0},\"line_color\":{\"value\":\"black\"},\"line_dash\":[4,4],\"line_width\":{\"value\":2},\"plot\":null,\"render_mode\":\"css\",\"right_units\":\"screen\",\"top_units\":\"screen\"},\"id\":\"20d2384f-0de4-4a10-960a-737204ce36fc\",\"type\":\"BoxAnnotation\"},{\"attributes\":{\"below\":[{\"id\":\"da590a8a-caad-4ce3-86c1-3722b03f83ad\",\"type\":\"LinearAxis\"}],\"left\":[{\"id\":\"078c3806-2dec-42c7-8f34-0a1333d09c77\",\"type\":\"LinearAxis\"}],\"plot_height\":500,\"plot_width\":500,\"renderers\":[{\"id\":\"da590a8a-caad-4ce3-86c1-3722b03f83ad\",\"type\":\"LinearAxis\"},{\"id\":\"dfa2863d-bd38-412c-9689-c6bac1442d45\",\"type\":\"Grid\"},{\"id\":\"078c3806-2dec-42c7-8f34-0a1333d09c77\",\"type\":\"LinearAxis\"},{\"id\":\"126f744c-3f78-4290-911a-6cd5a48fbd01\",\"type\":\"Grid\"},{\"id\":\"20d2384f-0de4-4a10-960a-737204ce36fc\",\"type\":\"BoxAnnotation\"},{\"id\":\"4ca77656-cebe-444b-a8ce-3aae9e082931\",\"type\":\"GlyphRenderer\"}],\"title\":{\"id\":\"7950b67f-48d0-4441-b014-b72deded7e01\",\"type\":\"Title\"},\"toolbar\":{\"id\":\"5aa60bfe-ef88-4d4a-b5bf-f80307a0645f\",\"type\":\"Toolbar\"},\"x_range\":{\"id\":\"204e01f3-4fdd-4191-9b1e-82193fc7806e\",\"type\":\"DataRange1d\"},\"x_scale\":{\"id\":\"64f928f4-4350-4cc0-80d1-23904665f934\",\"type\":\"LinearScale\"},\"y_range\":{\"id\":\"ea271ad4-2543-483e-af57-945fba85d3c0\",\"type\":\"DataRange1d\"},\"y_scale\":{\"id\":\"1ee722d8-72b1-4236-8c65-fa7a840580b5\",\"type\":\"LinearScale\"}},\"id\":\"79d3ab37-41a9-4852-a9fa-57f509b38674\",\"subtype\":\"Figure\",\"type\":\"Plot\"},{\"attributes\":{\"callback\":null,\"column_names\":[\"x\",\"top\"],\"data\":{\"top\":[1285,1269,1233,1225,1210,1202,1199,1187,1175,1165],\"x\":[3,4,2,0,7,8,1,6,5,9]},\"selected\":null,\"selection_policy\":null},\"id\":\"99738b11-42cd-4023-a0c8-943e5e084bf6\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"e1be119b-8d63-4ea1-8f4e-3914595514d8\",\"type\":\"WheelZoomTool\"},{\"attributes\":{\"overlay\":{\"id\":\"20d2384f-0de4-4a10-960a-737204ce36fc\",\"type\":\"BoxAnnotation\"}},\"id\":\"0a11af1c-4e61-47be-b409-c62bcf6d85c2\",\"type\":\"BoxZoomTool\"},{\"attributes\":{\"active_drag\":\"auto\",\"active_inspect\":\"auto\",\"active_scroll\":\"auto\",\"active_tap\":\"auto\",\"tools\":[{\"id\":\"9bf2a9b6-09c9-455c-bbf0-7e1f3bada996\",\"type\":\"PanTool\"},{\"id\":\"e1be119b-8d63-4ea1-8f4e-3914595514d8\",\"type\":\"WheelZoomTool\"},{\"id\":\"0a11af1c-4e61-47be-b409-c62bcf6d85c2\",\"type\":\"BoxZoomTool\"},{\"id\":\"680dadde-09ed-4134-ac29-698fd967ca24\",\"type\":\"SaveTool\"},{\"id\":\"f25898dd-d21d-4fda-825f-af041a6abd91\",\"type\":\"ResetTool\"},{\"id\":\"f2121920-dc13-4bd0-a49b-d93200ab34ee\",\"type\":\"HelpTool\"},{\"id\":\"da2dce80-4910-4177-89ba-0d26042f9b93\",\"type\":\"HoverTool\"}]},\"id\":\"5aa60bfe-ef88-4d4a-b5bf-f80307a0645f\",\"type\":\"Toolbar\"}],\"root_ids\":[\"79d3ab37-41a9-4852-a9fa-57f509b38674\"]},\"title\":\"Bokeh Application\",\"version\":\"0.12.15\"}};\n",
       "  var render_items = [{\"docid\":\"3ddf8e3b-6ab8-48dd-b7b9-a3c931ce462d\",\"elementid\":\"b9ba6192-bcb9-4459-889b-57a47519791b\",\"modelid\":\"79d3ab37-41a9-4852-a9fa-57f509b38674\"}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\")\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "79d3ab37-41a9-4852-a9fa-57f509b38674"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "last_digit_sum\n",
    "\n",
    "# Gráfico para melhor visualização\n",
    "dica1 = figure(plot_width=500, plot_height=500)\n",
    "dica1.vbar(x=[i for i,v in last_digit_sort],\n",
    "       width=0.5,\n",
    "       bottom=0,\n",
    "       top=[v for i,v in last_digit_sort])\n",
    "\n",
    "dica1.add_tools(HoverTool(tooltips = [\n",
    "    (\"Dígito\", \"@x\"),\n",
    "    (\"Ocorrências\", \"@top\"),\n",
    "]))\n",
    "\n",
    "output_notebook()\n",
    "show(dica1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Através das informações apresentadas logo acima, podemos constatar que:\n",
    "- Números com último dígito sendo **0** possuem a quarta maior ocorrência nos sorteios até agora;\n",
    "- Realmente os números com último dígito sendo **9** são os que menos saem nos sorteios. \n",
    "\n",
    "Sendo assim, a dica é verdade quando se trata apenas do dígito 9.\n",
    "\n",
    "#### 2. As dezenas 01, 02, 03, 11, 22, 44, 55, 48 e 57 saem pouco"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Vetor com dígitos de 1 a 60\n",
    "count_digit = [0 for i in range(0, 60)]\n",
    "\n",
    "# Iremos percorrer cada celula do dataframe\n",
    "for np_array in data_cols.values:\n",
    "    for number in np_array:\n",
    "        count_digit[ number-1 ] += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Ordenamos a lista pela quantidade de ocorrências de cada dígito (do menor para o maior)\n",
    "digit_sort = sorted(enumerate(count_digit), key=lambda x:x[1])\n",
    "# Invertemos a ordem para facilitar a visualização\n",
    "digit_sort.reverse()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dezena: 22 | Lugar no ranking de ocorrências: 3\n",
      "Dezena: 3 | Lugar no ranking de ocorrências: 4\n",
      "Dezena: 1 | Lugar no ranking de ocorrências: 21\n",
      "Dezena: 55 | Lugar no ranking de ocorrências: 23\n",
      "Dezena: 44 | Lugar no ranking de ocorrências: 32\n",
      "Dezena: 48 | Lugar no ranking de ocorrências: 34\n",
      "Dezena: 11 | Lugar no ranking de ocorrências: 37\n",
      "Dezena: 57 | Lugar no ranking de ocorrências: 39\n",
      "Dezena: 2 | Lugar no ranking de ocorrências: 46\n"
     ]
    }
   ],
   "source": [
    "# Dezenas informadas na dica\n",
    "find_digits = [1, 2, 3, 11, 22, 44, 55, 48, 57]\n",
    "\n",
    "# Mostramos o lugar no ranking de ocorrências \n",
    "for digit, value in digit_sort:\n",
    "    if digit in find_digits:\n",
    "        print(\"Dezena: {} | Lugar no ranking de ocorrências: {}\".format(digit, digit_sort.index((digit, value))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Através das informações apresentadas acima, podemos ver que a dica 2 é falsa.\n",
    "\n",
    "#### 3. Não jogue números seguidos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ocorrências de números seguidos: 994\n",
      "Ocorrências de números que não formam uma sequência: 9131\n"
     ]
    }
   ],
   "source": [
    "ocor_seguidos = 0\n",
    "ocor_not_seguidos = 0\n",
    "\n",
    "# Percorremos cada jogo da mega\n",
    "for np_array in data_cols.values:\n",
    "    # Ordenamos o array\n",
    "    np_array = np.sort(np_array)\n",
    "    \n",
    "    # Contamos a quantidade de ocorrências de números seguidos\n",
    "    for index, number in enumerate(np_array[1:]):\n",
    "        # Verificamos se os números formam uma sequência\n",
    "        if np_array[index] == (np_array[index+1]-1):\n",
    "            ocor_seguidos += 1\n",
    "        else:\n",
    "            ocor_not_seguidos += 1\n",
    "            \n",
    "print(\"Ocorrências de números seguidos: {}\".format(ocor_seguidos))\n",
    "print(\"Ocorrências de números que não formam uma sequência: {}\".format(ocor_not_seguidos))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podemos ver que a quantidade de vezes que dois números formaram uma sequência foi ínfima se comparado a quantidade de números jogados até agora. Portanto, a dica é verdadeira.\n",
    "\n",
    "#### 4. Não jogue em números que estejam na mesma linha vertical"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Porcentagem de números que pertencem a mesma linha vertical: 19.613168724279834%\n"
     ]
    }
   ],
   "source": [
    "# Contador de ocorrências de dezenas de mesma linha vertical e de diferentes linhas verticais, respectivamente\n",
    "dv_ocor = 0\n",
    "not_dv_ocor = 0\n",
    "\n",
    "# Percorremos as linhas\n",
    "for np_array in data_cols.values:\n",
    "    # Usaremos essa variável para pegar as linhas verticais presentes no jogo sorteado\n",
    "    dv_digit = []\n",
    "\n",
    "    # Percorremos os números\n",
    "    for number in np_array:\n",
    "        # Último dígito da dezena\n",
    "        last_digit = number%10\n",
    "        # Se o dígito não foi salvo anteriormente, ele salva\n",
    "        if not (last_digit in dv_digit):\n",
    "            dv_digit.append(last_digit)\n",
    "    \n",
    "    # Salvamos a quantidade de linhas verticais do jogo sorteado \n",
    "    dv_ocor += (6 - len(dv_digit))\n",
    "    not_dv_ocor += len(dv_digit)\n",
    "    \n",
    "por_dv_ocor = (dv_ocor*100)/(dv_ocor+not_dv_ocor)\n",
    "    \n",
    "print(\"Porcentagem de números que pertencem a mesma linha vertical: {}%\".format(por_dv_ocor))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Como podemos ver, pouco mais de 19.5% dos números sorteados na mega-sena pertenciam a mesma linha vertical de outra dezena no mesmo jogo. Sendo assim, é correto afirmar que devemos evitar dezenas que pertençam a mesma linha vertical.\n",
    "\n",
    "#### 5. Divida a cartela em quatro quadrantes e distribua seu jogo entre eles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1, 2, 3, 4, 5, 11, 12, 13, 14, 15, 21, 22, 23, 24, 25],\n",
       " [6, 7, 8, 9, 10, 16, 17, 18, 19, 20, 26, 27, 28, 29, 30],\n",
       " [31, 32, 33, 34, 35, 41, 42, 43, 44, 45, 51, 52, 53, 54, 55],\n",
       " [36, 37, 38, 39, 40, 46, 47, 48, 49, 50, 56, 57, 58, 59, 60]]"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Separamos as dezenas em grupos de 5 dezenas\n",
    "dezenas_q = [dezenas[i:(i+5)] for i in range(0, 61, 5)]\n",
    "del(dezenas_q[-1])\n",
    "\n",
    "# Variável que usaremos para acoplar as dezenas de cada quadrante\n",
    "dezenas_quadrantes = [[] for i in range(0, 4)]\n",
    "\n",
    "# Organizar os quadrantes\n",
    "for i in range(0, 12, 2):\n",
    "    if i < 6:\n",
    "        dezenas_quadrantes[0] = dezenas_quadrantes[0] + dezenas_q[i]\n",
    "        dezenas_quadrantes[1] = dezenas_quadrantes[1] + dezenas_q[i+1]\n",
    "    else:\n",
    "        dezenas_quadrantes[2] = dezenas_quadrantes[2] + dezenas_q[i]\n",
    "        dezenas_quadrantes[3] = dezenas_quadrantes[3] + dezenas_q[i+1]\n",
    "        \n",
    "dezenas_quadrantes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Quadrantes**:\n",
    "<table>\n",
    "    <tbody>\n",
    "        <tr>\n",
    "            <td>dezenas_quadrantes[0]</td>\n",
    "            <td>dezenas_quadrantes[1]</td>\n",
    "        </tr>\n",
    "        <tr>\n",
    "            <td>dezenas_quadrantes[2]</td>\n",
    "            <td>dezenas_quadrantes[3]</td>\n",
    "        </tr>\n",
    "    </tbody>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1140, 885]"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "quadrantes_count = [0, 0, 0, 0]\n",
    "quad_count_yn = [0, 0]\n",
    "\n",
    "# Percorremos as linhas\n",
    "for np_array in data_cols.values:\n",
    "    # Usaremos essa variável para pegar os quadrantes envolvidos\n",
    "    quad_envolvidos = []\n",
    "\n",
    "    # Percorremos os números\n",
    "    for number in np_array:\n",
    "        \n",
    "        # Percorremos os quadrantes\n",
    "        for index, quadrante in enumerate(dezenas_quadrantes):\n",
    "            # Verificamos em qual quadrante o número se encontra\n",
    "            if number in quadrante:\n",
    "                quadrantes_count[index] += 1\n",
    "                # Verifica se o quadrante já havia saído antes no mesmo jogo\n",
    "                if not (index in quad_envolvidos):\n",
    "                    quad_envolvidos.append(index)\n",
    "                break\n",
    "                \n",
    "    \n",
    "    if len(quad_envolvidos) < 4:\n",
    "        quad_count_yn[0] += 1\n",
    "    else:\n",
    "        quad_count_yn[1] += 1\n",
    "        \n",
    "quad_count_yn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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