lab1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Лабораторная №6\n",
    "\n",
    "##  Вариант №15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from numpy.linalg import inv, det\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "from copy import copy\n",
    "import random\n",
    "%matplotlib inline "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Аналитический метод"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def solve_analytically(matrix_c):\n",
    "    u = np.ones(matrix_c.shape[0])\n",
    "    v = 1/(u.dot(inv(matrix_c)).dot(u))\n",
    "    x_star = u.dot(inv(matrix_c))*v\n",
    "    y_star = inv(matrix_c).dot(u)*v\n",
    "    \n",
    "    return {\n",
    "        'x_strategies' : x_star,\n",
    "        'y_strategies' : y_star,\n",
    "        'v' : v\n",
    "    }"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Метод Брауна-Робинсон"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# выбор стратегий игроков\n",
    "def brown_robinson_step(a_strats_count, b_strats_count, matrix_c):\n",
    "    a_gains = matrix_c.dot(b_strats_count)\n",
    "    b_gains = a_strats_count.dot(matrix_c)\n",
    "    \n",
    "    indexes = np.linspace(0, matrix_c.shape[0] - 1, matrix_c.shape[0], dtype=int)\n",
    "    \n",
    "    a_max_ids = indexes[np.isin(a_gains, np.max(a_gains))]\n",
    "    b_min_ids = indexes[np.isin(b_gains, np.min(b_gains))]\n",
    "    \n",
    "    return random.choice(a_max_ids), random.choice(b_min_ids)\n",
    "\n",
    "def solve_brown_robinson(matrix_c, requred_epsilon=0, max_steps=100000):\n",
    "    a_strats_count = np.zeros(matrix_c.shape[0])\n",
    "    b_strats_count = np.zeros(matrix_c.shape[1])\n",
    "    \n",
    "    epsilon_history = []\n",
    "    epsilon = 0\n",
    "    \n",
    "    i = 0\n",
    "    j = 0\n",
    "    k = 0\n",
    "    # Задание числа, заведомо большего чем требуемая погрешность\n",
    "    epsilon = 9999999\n",
    "    \n",
    "    v_overline_min_k = 9999999\n",
    "    v_underline_max_k = 0\n",
    "    \n",
    "    table = pd.DataFrame(columns=['A', 'B', 'Выбор А', 'Выбор B', 'v_overline', 'v_underline', 'epsilon'])\n",
    "    \n",
    "    while k < max_steps and epsilon > requred_epsilon:\n",
    "        a_strats_count[i] += 1\n",
    "        b_strats_count[j] += 1\n",
    "        k += 1\n",
    "        \n",
    "        i, j = brown_robinson_step(a_strats_count, b_strats_count, matrix_c)\n",
    "        \n",
    "        v_overline = np.max(matrix_c.dot(b_strats_count))\n",
    "        v_underline = np.min(a_strats_count.dot(matrix_c))\n",
    "        \n",
    "        v_overline_min_k = min(v_overline/k, v_overline_min_k)\n",
    "        v_underline_max_k = max(v_underline/k, v_underline_max_k)\n",
    "        \n",
    "        epsilon = v_overline_min_k - v_underline_max_k\n",
    "        epsilon_history.append(epsilon)\n",
    "        \n",
    "        table.loc[k] = [i + 1, j + 1, copy(matrix_c.dot(b_strats_count)), copy(a_strats_count.dot(matrix_c)), round(v_overline / k, 2), round(v_underline / k, 2), round(epsilon, 2)]\n",
    "        \n",
    "    return {\n",
    "        'epsilon' : round(epsilon, 2),\n",
    "        'history' : epsilon_history,\n",
    "        'x_strategies' : np.round(a_strats_count / k, 2),\n",
    "        'y_strategies' : np.round(b_strats_count / k, 2),\n",
    "        'v_overline' : round(v_overline_min_k, 2),\n",
    "        'v_underline' : round(v_underline_max_k, 2),\n",
    "        'v' : round((v_overline_min_k + v_underline_max_k) / 2, 2),\n",
    "        'iterations' : k,\n",
    "        'table' : table,\n",
    "    }"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Решение"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Матрица по варианту"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[18 13 15]\n",
      " [ 0 13 16]\n",
      " [ 1 17  9]]\n"
     ]
    }
   ],
   "source": [
    "C = np.array([[18, 13, 15],\n",
    "              [ 0, 13, 16],\n",
    "              [ 1, 17, 9]])\n",
    "print(C)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "result_br = solve_brown_robinson(C, requred_epsilon=0.1)\n",
    "result_an = solve_analytically(C)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iterations: 71\n",
      "epsilon: 0.09\n",
      "(v_overline, v_underline): 13.89 13.8\n",
      "v_br:         13.84\n",
      "analytical v: 13.81592039800995\n",
      "analytical x_strategies: [0.75621891 0.039801   0.2039801 ] ; sum: 1.0\n",
      "analytical y_strategies: [0.0199005  0.62189055 0.35820896] ; sum: 1.0\n",
      "BR x_strategies:         [0.72 0.   0.28] ; sum: 1.0\n",
      "BR y_strategies:         [0.1 0.7 0.2] ; sum: 1.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f42f59ac208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print('Iterations:', result_br['iterations'])\n",
    "plt.plot(result_br['history'])\n",
    "print('epsilon:', result_br['epsilon'])\n",
    "print('(v_overline, v_underline):', result_br['v_overline'], result_br['v_underline'])\n",
    "print('v_br:        ', result_br['v'])\n",
    "print('analytical v:', result_an['v'])\n",
    "print('analytical x_strategies:', result_an['x_strategies'], '; sum:', np.sum(result_an['x_strategies']))\n",
    "print('analytical y_strategies:', result_an['y_strategies'], '; sum:', np.sum(result_an['y_strategies']))\n",
    "\n",
    "print('BR x_strategies:        ', result_br['x_strategies'], '; sum:', np.sum(result_br['x_strategies']))\n",
    "print('BR y_strategies:        ', result_br['y_strategies'], '; sum:', np.sum(result_br['y_strategies']))\n",
    "# print('delta x_strategies:', np.round(np.abs(result_an['x_strategies'] - result_br['x_strategies']), 2))\n",
    "# print('delta y_strategies:', np.round(np.abs(result_an['y_strategies'] - result_br['y_strategies']), 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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>Выбор А</th>\n",
       "      <th>Выбор B</th>\n",
       "      <th>v_overline</th>\n",
       "      <th>v_underline</th>\n",
       "      <th>epsilon</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>[18.0, 0.0, 1.0]</td>\n",
       "      <td>[18.0, 13.0, 15.0]</td>\n",
       "      <td>18.00</td>\n",
       "      <td>13.00</td>\n",
       "      <td>5.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>[31.0, 13.0, 18.0]</td>\n",
       "      <td>[36.0, 26.0, 30.0]</td>\n",
       "      <td>15.50</td>\n",
       "      <td>13.00</td>\n",
       "      <td>2.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>[44.0, 26.0, 35.0]</td>\n",
       "      <td>[54.0, 39.0, 45.0]</td>\n",
       "      <td>14.67</td>\n",
       "      <td>13.00</td>\n",
       "      <td>1.67</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>[57.0, 39.0, 52.0]</td>\n",
       "      <td>[72.0, 52.0, 60.0]</td>\n",
       "      <td>14.25</td>\n",
       "      <td>13.00</td>\n",
       "      <td>1.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>[70.0, 52.0, 69.0]</td>\n",
       "      <td>[90.0, 65.0, 75.0]</td>\n",
       "      <td>14.00</td>\n",
       "      <td>13.00</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>[83.0, 65.0, 86.0]</td>\n",
       "      <td>[108.0, 78.0, 90.0]</td>\n",
       "      <td>14.33</td>\n",
       "      <td>13.00</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>[96.0, 78.0, 103.0]</td>\n",
       "      <td>[109.0, 95.0, 99.0]</td>\n",
       "      <td>14.71</td>\n",
       "      <td>13.57</td>\n",
       "      <td>0.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>[109.0, 91.0, 120.0]</td>\n",
       "      <td>[110.0, 112.0, 108.0]</td>\n",
       "      <td>15.00</td>\n",
       "      <td>13.50</td>\n",
       "      <td>0.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>[124.0, 107.0, 129.0]</td>\n",
       "      <td>[111.0, 129.0, 117.0]</td>\n",
       "      <td>14.33</td>\n",
       "      <td>12.33</td>\n",
       "      <td>0.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>[142.0, 107.0, 130.0]</td>\n",
       "      <td>[112.0, 146.0, 126.0]</td>\n",
       "      <td>14.20</td>\n",
       "      <td>11.20</td>\n",
       "      <td>0.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>[160.0, 107.0, 131.0]</td>\n",
       "      <td>[130.0, 159.0, 141.0]</td>\n",
       "      <td>14.55</td>\n",
       "      <td>11.82</td>\n",
       "      <td>0.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>[178.0, 107.0, 132.0]</td>\n",
       "      <td>[148.0, 172.0, 156.0]</td>\n",
       "      <td>14.83</td>\n",
       "      <td>12.33</td>\n",
       "      <td>0.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>[196.0, 107.0, 133.0]</td>\n",
       "      <td>[166.0, 185.0, 171.0]</td>\n",
       "      <td>15.08</td>\n",
       "      <td>12.77</td>\n",
       "      <td>0.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>[214.0, 107.0, 134.0]</td>\n",
       "      <td>[184.0, 198.0, 186.0]</td>\n",
       "      <td>15.29</td>\n",
       "      <td>13.14</td>\n",
       "      <td>0.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>[232.0, 107.0, 135.0]</td>\n",
       "      <td>[202.0, 211.0, 201.0]</td>\n",
       "      <td>15.47</td>\n",
       "      <td>13.40</td>\n",
       "      <td>0.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>[247.0, 123.0, 144.0]</td>\n",
       "      <td>[220.0, 224.0, 216.0]</td>\n",
       "      <td>15.44</td>\n",
       "      <td>13.50</td>\n",
       "      <td>0.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>[262.0, 139.0, 153.0]</td>\n",
       "      <td>[238.0, 237.0, 231.0]</td>\n",
       "      <td>15.41</td>\n",
       "      <td>13.59</td>\n",
       "      <td>0.41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>[277.0, 155.0, 162.0]</td>\n",
       "      <td>[256.0, 250.0, 246.0]</td>\n",
       "      <td>15.39</td>\n",
       "      <td>13.67</td>\n",
       "      <td>0.33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>[292.0, 171.0, 171.0]</td>\n",
       "      <td>[274.0, 263.0, 261.0]</td>\n",
       "      <td>15.37</td>\n",
       "      <td>13.74</td>\n",
       "      <td>0.26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>[307.0, 187.0, 180.0]</td>\n",
       "      <td>[292.0, 276.0, 276.0]</td>\n",
       "      <td>15.35</td>\n",
       "      <td>13.80</td>\n",
       "      <td>0.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>[322.0, 203.0, 189.0]</td>\n",
       "      <td>[310.0, 289.0, 291.0]</td>\n",
       "      <td>15.33</td>\n",
       "      <td>13.76</td>\n",
       "      <td>0.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>[335.0, 216.0, 206.0]</td>\n",
       "      <td>[328.0, 302.0, 306.0]</td>\n",
       "      <td>15.23</td>\n",
       "      <td>13.73</td>\n",
       "      <td>0.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>[348.0, 229.0, 223.0]</td>\n",
       "      <td>[346.0, 315.0, 321.0]</td>\n",
       "      <td>15.13</td>\n",
       "      <td>13.70</td>\n",
       "      <td>0.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>[361.0, 242.0, 240.0]</td>\n",
       "      <td>[364.0, 328.0, 336.0]</td>\n",
       "      <td>15.04</td>\n",
       "      <td>13.67</td>\n",
       "      <td>0.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>[374.0, 255.0, 257.0]</td>\n",
       "      <td>[382.0, 341.0, 351.0]</td>\n",
       "      <td>14.96</td>\n",
       "      <td>13.64</td>\n",
       "      <td>0.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>[387.0, 268.0, 274.0]</td>\n",
       "      <td>[400.0, 354.0, 366.0]</td>\n",
       "      <td>14.88</td>\n",
       "      <td>13.62</td>\n",
       "      <td>0.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>[400.0, 281.0, 291.0]</td>\n",
       "      <td>[418.0, 367.0, 381.0]</td>\n",
       "      <td>14.81</td>\n",
       "      <td>13.59</td>\n",
       "      <td>0.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>[413.0, 294.0, 308.0]</td>\n",
       "      <td>[436.0, 380.0, 396.0]</td>\n",
       "      <td>14.75</td>\n",
       "      <td>13.57</td>\n",
       "      <td>0.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>[426.0, 307.0, 325.0]</td>\n",
       "      <td>[454.0, 393.0, 411.0]</td>\n",
       "      <td>14.69</td>\n",
       "      <td>13.55</td>\n",
       "      <td>0.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>[439.0, 320.0, 342.0]</td>\n",
       "      <td>[472.0, 406.0, 426.0]</td>\n",
       "      <td>14.63</td>\n",
       "      <td>13.53</td>\n",
       "      <td>0.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>[595.0, 476.0, 546.0]</td>\n",
       "      <td>[688.0, 562.0, 606.0]</td>\n",
       "      <td>14.17</td>\n",
       "      <td>13.38</td>\n",
       "      <td>0.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>[608.0, 489.0, 563.0]</td>\n",
       "      <td>[706.0, 575.0, 621.0]</td>\n",
       "      <td>14.14</td>\n",
       "      <td>13.37</td>\n",
       "      <td>0.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>[621.0, 502.0, 580.0]</td>\n",
       "      <td>[724.0, 588.0, 636.0]</td>\n",
       "      <td>14.11</td>\n",
       "      <td>13.36</td>\n",
       "      <td>0.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>[634.0, 515.0, 597.0]</td>\n",
       "      <td>[742.0, 601.0, 651.0]</td>\n",
       "      <td>14.09</td>\n",
       "      <td>13.36</td>\n",
       "      <td>0.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>[647.0, 528.0, 614.0]</td>\n",
       "      <td>[760.0, 614.0, 666.0]</td>\n",
       "      <td>14.07</td>\n",
       "      <td>13.35</td>\n",
       "      <td>0.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>[660.0, 541.0, 631.0]</td>\n",
       "      <td>[778.0, 627.0, 681.0]</td>\n",
       "      <td>14.04</td>\n",
       "      <td>13.34</td>\n",
       "      <td>0.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>[673.0, 554.0, 648.0]</td>\n",
       "      <td>[796.0, 640.0, 696.0]</td>\n",
       "      <td>14.02</td>\n",
       "      <td>13.33</td>\n",
       "      <td>0.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>[686.0, 567.0, 665.0]</td>\n",
       "      <td>[814.0, 653.0, 711.0]</td>\n",
       "      <td>14.00</td>\n",
       "      <td>13.33</td>\n",
       "      <td>0.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>[699.0, 580.0, 682.0]</td>\n",
       "      <td>[832.0, 666.0, 726.0]</td>\n",
       "      <td>13.98</td>\n",
       "      <td>13.32</td>\n",
       "      <td>0.18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>51</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>[712.0, 593.0, 699.0]</td>\n",
       "      <td>[850.0, 679.0, 741.0]</td>\n",
       "      <td>13.96</td>\n",
       "      <td>13.31</td>\n",
       "      <td>0.16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>52</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>[725.0, 606.0, 716.0]</td>\n",
       "      <td>[868.0, 692.0, 756.0]</td>\n",
       "      <td>13.94</td>\n",
       "      <td>13.31</td>\n",
       "      <td>0.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>53</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>[738.0, 619.0, 733.0]</td>\n",
       "      <td>[886.0, 705.0, 771.0]</td>\n",
       "      <td>13.92</td>\n",
       "      <td>13.30</td>\n",
       "      <td>0.12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>[751.0, 632.0, 750.0]</td>\n",
       "      <td>[904.0, 718.0, 786.0]</td>\n",
       "      <td>13.91</td>\n",
       "      <td>13.30</td>\n",
       "      <td>0.11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>55</th>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>[764.0, 645.0, 767.0]</td>\n",
       "      <td>[922.0, 731.0, 801.0]</td>\n",
       "      <td>13.95</td>\n",
       "      <td>13.29</td>\n",
       "      <td>0.11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>56</th>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>[777.0, 658.0, 784.0]</td>\n",
       "      <td>[923.0, 748.0, 810.0]</td>\n",
       "      <td>14.00</td>\n",
       "      <td>13.36</td>\n",
       "      <td>0.11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>57</th>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>[790.0, 671.0, 801.0]</td>\n",
       "      <td>[924.0, 765.0, 819.0]</td>\n",
       "      <td>14.05</td>\n",
       "      <td>13.42</td>\n",
       "      <td>0.11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58</th>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>[803.0, 684.0, 818.0]</td>\n",
       "      <td>[925.0, 782.0, 828.0]</td>\n",
       "      <td>14.10</td>\n",
       "      <td>13.48</td>\n",
       "      <td>0.11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>59</th>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>[816.0, 697.0, 835.0]</td>\n",
       "      <td>[926.0, 799.0, 837.0]</td>\n",
       "      <td>14.15</td>\n",
       "      <td>13.54</td>\n",
       "      <td>0.11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>60</th>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>[829.0, 710.0, 852.0]</td>\n",
       "      <td>[927.0, 816.0, 846.0]</td>\n",
       "      <td>14.20</td>\n",
       "      <td>13.60</td>\n",
       "      <td>0.11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>61</th>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>[842.0, 723.0, 869.0]</td>\n",
       "      <td>[928.0, 833.0, 855.0]</td>\n",
       "      <td>14.25</td>\n",
       "      <td>13.66</td>\n",
       "      <td>0.11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>62</th>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>[855.0, 736.0, 886.0]</td>\n",
       "      <td>[929.0, 850.0, 864.0]</td>\n",
       "      <td>14.29</td>\n",
       "      <td>13.71</td>\n",
       "      <td>0.11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>63</th>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>[868.0, 749.0, 903.0]</td>\n",
       "      <td>[930.0, 867.0, 873.0]</td>\n",
       "      <td>14.33</td>\n",
       "      <td>13.76</td>\n",
       "      <td>0.11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>64</th>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>[881.0, 762.0, 920.0]</td>\n",
       "      <td>[931.0, 884.0, 882.0]</td>\n",
       "      <td>14.38</td>\n",
       "      <td>13.78</td>\n",
       "      <td>0.11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>65</th>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>[896.0, 778.0, 929.0]</td>\n",
       "      <td>[932.0, 901.0, 891.0]</td>\n",
       "      <td>14.29</td>\n",
       "      <td>13.71</td>\n",
       "      <td>0.11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>66</th>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>[911.0, 794.0, 938.0]</td>\n",
       "      <td>[933.0, 918.0, 900.0]</td>\n",
       "      <td>14.21</td>\n",
       "      <td>13.64</td>\n",
       "      <td>0.11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>67</th>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>[926.0, 810.0, 947.0]</td>\n",
       "      <td>[934.0, 935.0, 909.0]</td>\n",
       "      <td>14.13</td>\n",
       "      <td>13.57</td>\n",
       "      <td>0.11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>68</th>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>[941.0, 826.0, 956.0]</td>\n",
       "      <td>[935.0, 952.0, 918.0]</td>\n",
       "      <td>14.06</td>\n",
       "      <td>13.50</td>\n",
       "      <td>0.11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69</th>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>[956.0, 842.0, 965.0]</td>\n",
       "      <td>[936.0, 969.0, 927.0]</td>\n",
       "      <td>13.99</td>\n",
       "      <td>13.43</td>\n",
       "      <td>0.11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>70</th>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>[971.0, 858.0, 974.0]</td>\n",
       "      <td>[937.0, 986.0, 936.0]</td>\n",
       "      <td>13.91</td>\n",
       "      <td>13.37</td>\n",
       "      <td>0.11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>71</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>[986.0, 874.0, 983.0]</td>\n",
       "      <td>[938.0, 1003.0, 945.0]</td>\n",
       "      <td>13.89</td>\n",
       "      <td>13.21</td>\n",
       "      <td>0.09</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>71 rows × 7 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    A  B                Выбор А                 Выбор B  v_overline  \\\n",
       "1   1  2       [18.0, 0.0, 1.0]      [18.0, 13.0, 15.0]       18.00   \n",
       "2   1  2     [31.0, 13.0, 18.0]      [36.0, 26.0, 30.0]       15.50   \n",
       "3   1  2     [44.0, 26.0, 35.0]      [54.0, 39.0, 45.0]       14.67   \n",
       "4   1  2     [57.0, 39.0, 52.0]      [72.0, 52.0, 60.0]       14.25   \n",
       "5   1  2     [70.0, 52.0, 69.0]      [90.0, 65.0, 75.0]       14.00   \n",
       "6   3  2     [83.0, 65.0, 86.0]     [108.0, 78.0, 90.0]       14.33   \n",
       "7   3  2    [96.0, 78.0, 103.0]     [109.0, 95.0, 99.0]       14.71   \n",
       "8   3  3   [109.0, 91.0, 120.0]   [110.0, 112.0, 108.0]       15.00   \n",
       "9   3  1  [124.0, 107.0, 129.0]   [111.0, 129.0, 117.0]       14.33   \n",
       "10  1  1  [142.0, 107.0, 130.0]   [112.0, 146.0, 126.0]       14.20   \n",
       "11  1  1  [160.0, 107.0, 131.0]   [130.0, 159.0, 141.0]       14.55   \n",
       "12  1  1  [178.0, 107.0, 132.0]   [148.0, 172.0, 156.0]       14.83   \n",
       "13  1  1  [196.0, 107.0, 133.0]   [166.0, 185.0, 171.0]       15.08   \n",
       "14  1  1  [214.0, 107.0, 134.0]   [184.0, 198.0, 186.0]       15.29   \n",
       "15  1  3  [232.0, 107.0, 135.0]   [202.0, 211.0, 201.0]       15.47   \n",
       "16  1  3  [247.0, 123.0, 144.0]   [220.0, 224.0, 216.0]       15.44   \n",
       "17  1  3  [262.0, 139.0, 153.0]   [238.0, 237.0, 231.0]       15.41   \n",
       "18  1  3  [277.0, 155.0, 162.0]   [256.0, 250.0, 246.0]       15.39   \n",
       "19  1  3  [292.0, 171.0, 171.0]   [274.0, 263.0, 261.0]       15.37   \n",
       "20  1  3  [307.0, 187.0, 180.0]   [292.0, 276.0, 276.0]       15.35   \n",
       "21  1  2  [322.0, 203.0, 189.0]   [310.0, 289.0, 291.0]       15.33   \n",
       "22  1  2  [335.0, 216.0, 206.0]   [328.0, 302.0, 306.0]       15.23   \n",
       "23  1  2  [348.0, 229.0, 223.0]   [346.0, 315.0, 321.0]       15.13   \n",
       "24  1  2  [361.0, 242.0, 240.0]   [364.0, 328.0, 336.0]       15.04   \n",
       "25  1  2  [374.0, 255.0, 257.0]   [382.0, 341.0, 351.0]       14.96   \n",
       "26  1  2  [387.0, 268.0, 274.0]   [400.0, 354.0, 366.0]       14.88   \n",
       "27  1  2  [400.0, 281.0, 291.0]   [418.0, 367.0, 381.0]       14.81   \n",
       "28  1  2  [413.0, 294.0, 308.0]   [436.0, 380.0, 396.0]       14.75   \n",
       "29  1  2  [426.0, 307.0, 325.0]   [454.0, 393.0, 411.0]       14.69   \n",
       "30  1  2  [439.0, 320.0, 342.0]   [472.0, 406.0, 426.0]       14.63   \n",
       ".. .. ..                    ...                     ...         ...   \n",
       "42  1  2  [595.0, 476.0, 546.0]   [688.0, 562.0, 606.0]       14.17   \n",
       "43  1  2  [608.0, 489.0, 563.0]   [706.0, 575.0, 621.0]       14.14   \n",
       "44  1  2  [621.0, 502.0, 580.0]   [724.0, 588.0, 636.0]       14.11   \n",
       "45  1  2  [634.0, 515.0, 597.0]   [742.0, 601.0, 651.0]       14.09   \n",
       "46  1  2  [647.0, 528.0, 614.0]   [760.0, 614.0, 666.0]       14.07   \n",
       "47  1  2  [660.0, 541.0, 631.0]   [778.0, 627.0, 681.0]       14.04   \n",
       "48  1  2  [673.0, 554.0, 648.0]   [796.0, 640.0, 696.0]       14.02   \n",
       "49  1  2  [686.0, 567.0, 665.0]   [814.0, 653.0, 711.0]       14.00   \n",
       "50  1  2  [699.0, 580.0, 682.0]   [832.0, 666.0, 726.0]       13.98   \n",
       "51  1  2  [712.0, 593.0, 699.0]   [850.0, 679.0, 741.0]       13.96   \n",
       "52  1  2  [725.0, 606.0, 716.0]   [868.0, 692.0, 756.0]       13.94   \n",
       "53  1  2  [738.0, 619.0, 733.0]   [886.0, 705.0, 771.0]       13.92   \n",
       "54  1  2  [751.0, 632.0, 750.0]   [904.0, 718.0, 786.0]       13.91   \n",
       "55  3  2  [764.0, 645.0, 767.0]   [922.0, 731.0, 801.0]       13.95   \n",
       "56  3  2  [777.0, 658.0, 784.0]   [923.0, 748.0, 810.0]       14.00   \n",
       "57  3  2  [790.0, 671.0, 801.0]   [924.0, 765.0, 819.0]       14.05   \n",
       "58  3  2  [803.0, 684.0, 818.0]   [925.0, 782.0, 828.0]       14.10   \n",
       "59  3  2  [816.0, 697.0, 835.0]   [926.0, 799.0, 837.0]       14.15   \n",
       "60  3  2  [829.0, 710.0, 852.0]   [927.0, 816.0, 846.0]       14.20   \n",
       "61  3  2  [842.0, 723.0, 869.0]   [928.0, 833.0, 855.0]       14.25   \n",
       "62  3  2  [855.0, 736.0, 886.0]   [929.0, 850.0, 864.0]       14.29   \n",
       "63  3  2  [868.0, 749.0, 903.0]   [930.0, 867.0, 873.0]       14.33   \n",
       "64  3  3  [881.0, 762.0, 920.0]   [931.0, 884.0, 882.0]       14.38   \n",
       "65  3  3  [896.0, 778.0, 929.0]   [932.0, 901.0, 891.0]       14.29   \n",
       "66  3  3  [911.0, 794.0, 938.0]   [933.0, 918.0, 900.0]       14.21   \n",
       "67  3  3  [926.0, 810.0, 947.0]   [934.0, 935.0, 909.0]       14.13   \n",
       "68  3  3  [941.0, 826.0, 956.0]   [935.0, 952.0, 918.0]       14.06   \n",
       "69  3  3  [956.0, 842.0, 965.0]   [936.0, 969.0, 927.0]       13.99   \n",
       "70  3  3  [971.0, 858.0, 974.0]   [937.0, 986.0, 936.0]       13.91   \n",
       "71  1  1  [986.0, 874.0, 983.0]  [938.0, 1003.0, 945.0]       13.89   \n",
       "\n",
       "    v_underline  epsilon  \n",
       "1         13.00     5.00  \n",
       "2         13.00     2.50  \n",
       "3         13.00     1.67  \n",
       "4         13.00     1.25  \n",
       "5         13.00     1.00  \n",
       "6         13.00     1.00  \n",
       "7         13.57     0.43  \n",
       "8         13.50     0.43  \n",
       "9         12.33     0.43  \n",
       "10        11.20     0.43  \n",
       "11        11.82     0.43  \n",
       "12        12.33     0.43  \n",
       "13        12.77     0.43  \n",
       "14        13.14     0.43  \n",
       "15        13.40     0.43  \n",
       "16        13.50     0.43  \n",
       "17        13.59     0.41  \n",
       "18        13.67     0.33  \n",
       "19        13.74     0.26  \n",
       "20        13.80     0.20  \n",
       "21        13.76     0.20  \n",
       "22        13.73     0.20  \n",
       "23        13.70     0.20  \n",
       "24        13.67     0.20  \n",
       "25        13.64     0.20  \n",
       "26        13.62     0.20  \n",
       "27        13.59     0.20  \n",
       "28        13.57     0.20  \n",
       "29        13.55     0.20  \n",
       "30        13.53     0.20  \n",
       "..          ...      ...  \n",
       "42        13.38     0.20  \n",
       "43        13.37     0.20  \n",
       "44        13.36     0.20  \n",
       "45        13.36     0.20  \n",
       "46        13.35     0.20  \n",
       "47        13.34     0.20  \n",
       "48        13.33     0.20  \n",
       "49        13.33     0.20  \n",
       "50        13.32     0.18  \n",
       "51        13.31     0.16  \n",
       "52        13.31     0.14  \n",
       "53        13.30     0.12  \n",
       "54        13.30     0.11  \n",
       "55        13.29     0.11  \n",
       "56        13.36     0.11  \n",
       "57        13.42     0.11  \n",
       "58        13.48     0.11  \n",
       "59        13.54     0.11  \n",
       "60        13.60     0.11  \n",
       "61        13.66     0.11  \n",
       "62        13.71     0.11  \n",
       "63        13.76     0.11  \n",
       "64        13.78     0.11  \n",
       "65        13.71     0.11  \n",
       "66        13.64     0.11  \n",
       "67        13.57     0.11  \n",
       "68        13.50     0.11  \n",
       "69        13.43     0.11  \n",
       "70        13.37     0.11  \n",
       "71        13.21     0.09  \n",
       "\n",
       "[71 rows x 7 columns]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result_br['table']"
   ]
  }
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