toy trueskill simulation notebook

tiny_tester.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import trueskill\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy\n",
    "\n",
    "# make 10 \"agents\" with different mean skill, sigma 8.3333 \n",
    "SIGMA = 8.33333\n",
    "agent_mus = np.arange(0, 50, 5)    \n",
    "\n",
    "# true win prob is difference of normals\n",
    "def win_prob(a, b):\n",
    "    mu1, mu2 = agent_mus[a], agent_mus[b]\n",
    "    return scipy.stats.norm.cdf(0, mu2 - mu1, np.sqrt(2) * SIGMA)\n",
    "    \n",
    "exact_win_probs = np.array([[win_prob(i, j) for j in range(10)] for i in range(10)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "import itertools\n",
    "import math\n",
    "\n",
    "BETA = 4.166666666666667\n",
    "\n",
    "def win_probability(team1, team2):\n",
    "    delta_mu = sum(r.mu for r in team1) - sum(r.mu for r in team2)\n",
    "    sum_sigma = sum(r.sigma ** 2 for r in itertools.chain(team1, team2))\n",
    "    size = len(team1) + len(team2)\n",
    "    denom = math.sqrt(size * (BETA * BETA) + sum_sigma)\n",
    "    ts = trueskill.global_env()\n",
    "    return ts.cdf(delta_mu / denom)\n",
    "\n",
    "def empirical_win_probs(rating):\n",
    "    return np.array([[win_probability([rating[i]], [rating[j]]) for j in range(10)] for i in range(10)])\n",
    "\n",
    "def loss(rating):\n",
    "    return np.linalg.norm(exact_win_probs - empirical_win_probs(rating))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
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    {
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   ],
   "source": [
    "NUM_GAMES = 30000\n",
    "\n",
    "# simulate games while sampling from matchups in band, print loss\n",
    "\n",
    "# initialize trueskills for each agent\n",
    "draw_probability = 0.0\n",
    "tau = 0.0\n",
    "trueskill_env = trueskill.TrueSkill(draw_probability=draw_probability, tau=tau)\n",
    "rating = {i: trueskill_env.create_rating(mu=25.0, sigma=SIGMA) for i in range(10)}\n",
    "\n",
    "losses = []\n",
    "for i in range(NUM_GAMES):\n",
    "    if i % 200 == 0:\n",
    "        print(loss(rating))\n",
    "        losses.append((i, loss(rating)))\n",
    "    \n",
    "    agent_a, agent_b = -1, -1\n",
    "    while agent_a == agent_b:\n",
    "        agent_a = np.random.randint(10)\n",
    "        agent_b = np.random.randint(10)\n",
    "    \n",
    "    agent_a_win_prob = exact_win_probs[agent_a][agent_b]\n",
    "    if np.random.random() < agent_a_win_prob:\n",
    "        winner = agent_a\n",
    "        loser = agent_b\n",
    "    else:\n",
    "        winner = agent_b\n",
    "        loser = agent_a\n",
    "        \n",
    "    rating[winner], rating[loser] = trueskill.rate_1vs1(rating[winner], rating[loser], drawn=False, env=trueskill_env)\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
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   "source": [
    "# simulate games while sampling from matchups within +/- 1, print loss\n",
    "\n",
    "# initialize trueskills for each agent\n",
    "draw_probability = 0.0\n",
    "tau = 0.0\n",
    "trueskill_env = trueskill.TrueSkill(draw_probability=draw_probability, tau=tau)\n",
    "rating = {i: trueskill_env.create_rating(mu=25.0, sigma=SIGMA) for i in range(10)}\n",
    "\n",
    "losses_band = []\n",
    "for i in range(NUM_GAMES):\n",
    "    if i % 200 == 0:\n",
    "        print(loss(rating))\n",
    "        losses_band.append((i, loss(rating)))\n",
    "        \n",
    "    agent_a, agent_b = -1, -1\n",
    "    while agent_a == agent_b:\n",
    "        agent_a = np.random.randint(10)\n",
    "        agent_b = min(9, max(0, agent_a + np.random.choice([-1, 1])))\n",
    "    \n",
    "    agent_a_win_prob = exact_win_probs[agent_a][agent_b]\n",
    "    if np.random.random() < agent_a_win_prob:\n",
    "        winner = agent_a\n",
    "        loser = agent_b\n",
    "    else:\n",
    "        winner = agent_b\n",
    "        loser = agent_a\n",
    "        \n",
    "    rating[winner], rating[loser] = trueskill.rate_1vs1(rating[winner], rating[loser], drawn=False, env=trueskill_env)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
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      "0.4799546586807792\n",
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      "0.47660753332326045\n"
     ]
    }
   ],
   "source": [
    "# simulate games while sampling from matchups within +/- 2, print loss\n",
    "LOSS_BAND = 2\n",
    "\n",
    "# initialize trueskills for each agent\n",
    "draw_probability = 0.0\n",
    "tau = 0.0\n",
    "trueskill_env = trueskill.TrueSkill(draw_probability=draw_probability, tau=tau)\n",
    "rating = {i: trueskill_env.create_rating(mu=25.0, sigma=SIGMA) for i in range(10)}\n",
    "\n",
    "losses_band2 = []\n",
    "for i in range(NUM_GAMES):\n",
    "    if i % 200 == 0:\n",
    "        print(loss(rating))\n",
    "        losses_band2.append((i, loss(rating)))\n",
    "        \n",
    "    agent_a, agent_b = -1, -1\n",
    "    while agent_a == agent_b:\n",
    "        agent_a = np.random.randint(10)\n",
    "        agent_b = min(9, max(0, agent_a + np.random.choice(np.arange(-LOSS_BAND, LOSS_BAND+1))))\n",
    "    \n",
    "    agent_a_win_prob = exact_win_probs[agent_a][agent_b]\n",
    "    if np.random.random() < agent_a_win_prob:\n",
    "        winner = agent_a\n",
    "        loser = agent_b\n",
    "    else:\n",
    "        winner = agent_b\n",
    "        loser = agent_a\n",
    "        \n",
    "    rating[winner], rating[loser] = trueskill.rate_1vs1(rating[winner], rating[loser], drawn=False, env=trueskill_env)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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     ]
    }
   ],
   "source": [
    "# simulate games while sampling from matchups within +/- 1, plus the endpoints are allowed. print loss\n",
    "LOSS_BAND = 1\n",
    "\n",
    "# initialize trueskills for each agent\n",
    "draw_probability = 0.0\n",
    "tau = 0.0\n",
    "trueskill_env = trueskill.TrueSkill(draw_probability=draw_probability, tau=tau)\n",
    "rating = {i: trueskill_env.create_rating(mu=25.0, sigma=SIGMA) for i in range(10)}\n",
    "\n",
    "losses_band1_ends = []\n",
    "for i in range(NUM_GAMES):\n",
    "    if i % 200 == 0:\n",
    "        print(loss(rating))\n",
    "        losses_band1_ends.append((i, loss(rating)))\n",
    "        \n",
    "    agent_a, agent_b = -1, -1\n",
    "    while agent_a == agent_b:\n",
    "        agent_a = np.random.randint(10)\n",
    "        agent_b = min(9, max(0, agent_a + np.random.choice(np.hstack([[-100, 100], np.arange(-LOSS_BAND, LOSS_BAND+1)]))))\n",
    "    \n",
    "    agent_a_win_prob = exact_win_probs[agent_a][agent_b]\n",
    "    if np.random.random() < agent_a_win_prob:\n",
    "        winner = agent_a\n",
    "        loser = agent_b\n",
    "    else:\n",
    "        winner = agent_b\n",
    "        loser = agent_a\n",
    "        \n",
    "    rating[winner], rating[loser] = trueskill.rate_1vs1(rating[winner], rating[loser], drawn=False, env=trueskill_env)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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H63XPW+H5wyXL+PMPLhlqMxRFUZQO5K3wTHtuJ8kXnh9qMxRFGSKmTp1KTU0NAEVFnb05Xhkq8lZ4PAExPb4IT1EURRlk8ld4HJC0zrytKCOBs846i2OPPZYjjjiCm2++eajNUXogb8OpPQdEX/mgKIPKt+9by6vbG3Ja5+wJxVx5xhHdlrnlllsoKyujtbWV4447jnPOOSenNii5Jb+FRz0eRRkR3HDDDfz5z38GYMuWLaxfv36ILVK6I2+FxwiIp8KjKINJT57JQPDYY4/x8MMP88wzz1BQUMDSpUsPyt+2jCTydown7WpXm6KMBOrr6xk9ejQFBQW89tprrFixYqhNUnogb4XHE1GPR1FGAKeddhqpVIpZs2bxjW98g0WLFg21SUoP5G9XmwOORlMrSt4TDod54IEH9kvftGlT23ZTU9MgWqT0RP56PBrVpiiKMizJifCISEREnhORl0VkrYh8u5MyF4hItYis8peLctF2VxgRnPRAtqAoiqL0h1x1tcWBk4wxTSISBJ4UkQeMMR1H+f5ojPlcjtrsFs8BR8d4FEVRhh058XiMJdOJGvSXIX3qe47oGI+iKMowJGdjPCLiisgqYDfwkDHm2U6KnSMiq0Xk/0RkUjd1XSwiK0VkZXV1db/sMY4gKjyKoijDjpwJjzEmbYw5BqgCFojIkR2K3AdMNcYcDTwE3N5NXTcbY+YbY+ZXVlb2zx5HcLSnTVEUZdiR86g2Y0wd8ChwWof0WmNM3N/9FXBsrtvepz0NLlCUEcOFF17ImDFjOPLI9u+7S5cuZeXKlTlv67bbbuNznxuUoeq8JVdRbZUiUupvR4F3Aa91KDM+a/dMYF0u2u4KTz0eRRkxXHDBBfzjH/8YajOUXpIrj2c88KiIrAaex47x/E1EviMiZ/plLvVDrV8GLgUuyFHbneI5jo7xKMoIYcmSJZSVle2Xfscdd3DMMcdw5JFH8txzzwHw3HPPsXjxYubOncvxxx/P66+/DlhP5uyzz+a0007jsMMO42tf+1pbPbfeeiuHH344CxYs4Kmnnhqck8pjchJObYxZDcztJP1bWduXAZflor1e2aRRbYoy+DzwDdj5Sm7rHHcUnP69fh3a0tLCqlWrePzxx7nwwgtZs2YNM2fO5IknniAQCPDwww9z+eWXc8899wCwatUqXnrpJcLhMDNmzODzn/88gUCAK6+8khdeeIGSkhKWLVvG3Ln7Pe6UPpDHU+Y4Vng8D5y8naBBUZRuOO+88wDrETU0NFBXV0djYyPnn38+69evR0RIJpNt5U8++WRKSkoAmD17Nm+//TY1NTUsXbqUTKDThz70Id54443BP5k8Ir+FxwBeEpzwUJujKCODfnomA4WI7Ld/xRVXsGzZMv785z+zadMmli5d2pYfDrc/K1zXJZVKDZapI4q8dQWM4+CmgXSyx7KKouQnf/zjHwF48sknKSkpoaSkhPr6eiZOnAjYcZ2eWLhwIf/+97+pra0lmUxy9913D6TJI4L8FR7XwTVAOjHUpiiKMsCcd955LF68mNdff52qqip+/etfAxCJRJg7dy6XXHJJW9rXvvY1LrvsMubOndsrj2b8+PEsX76cxYsXc8IJJzBr1qwBPZeRgJhhPoPz/PnzTX9i8X//8SXMWlXN0U89gls8YQAsUxQFYN26dfowHkI6u/4i8oIxZv4QmdQj+evxOA6uB6mUvgJXURRlOJHHwuP6wtMy1KYoiqIoWeSt8OC6OAaSidahtkRRFEXJIm+Fx7g2UjwVU49HURRlOJG/wuP4whNvHmJLFEVRlGzyVngI+MKjXW2KoijDirwVnozHk06q8ChKvrNlyxaWLVvG7NmzOeKII7j++usBfTXCcCVvp8zBDQLq8SjKSCAQCPDjH/+YefPm0djYyLHHHsu73vWuoTZL6YL89Xh84UnGVXgUJd8ZP3488+bNA2DUqFHMmjWLbdu2AfpqhOFI3no8Esh4PPoDUkUZLL7/3Pd5bc9rPRfsAzPLZvL1BV/vdflNmzbx0ksvsXDhQkBfjTAcyVvh8Xzh0d/xKMrIoampiXPOOYfrrruO4uJiQF+NMBzJW+GRgJ3ePJXQSUIVZbDoi2eSa5LJJOeccw4f/ehHOfvss9vS9dUIw4+cjfGISEREnhORl/1XXH+7kzJhEfmjiLwpIs+KyNRctb8f/hhPOqldbYqS7xhj+MQnPsGsWbP48pe/vE+evhph+JFLjycOnGSMaRKRIPCkiDxgjFmRVeYTwF5jzKEi8mHg+8CHcmhDG+0eT3wgqlcUZRjx1FNPcccdd3DUUUdxzDHHAHD11VcD7a9GSCaT3HLLLYB9NcL555/Pd7/7Xd7znvf0WH/2qxFKS0vb2lD6x4C8FkFECoAngU8bY57NSv8nsNwY84yIBICdQKXpxoj+vhbh9h9dxYJf/ZadX3kHyz55c99PQlGUXqGvRRhaRvxrEUTEFZFVwG7goWzR8ZkIbAEwxqSAeqA8lza02RK0Ho9J6htIFUVRhhM5FR5jTNoYcwxQBSwQkSP7U4+IXCwiK0VkZXV1db9skWAUgFRKgwsURVGGEwPyA1JjTB3wKHBah6xtwCQAv6utBKjt5PibjTHzjTHzM+GLfSXj8aSTKjyKoijDiVxGtVWKSKm/HQXeBXT8Jdm9wPn+9geAf3U3vnMgOMEIAF5aQyEVRVGGE7mMahsP3C4iLlbQ7jLG/E1EvgOsNMbcC/wauENE3gT2AB/OYfv74AZCAHgag68oijKsyJnwGGNWA/vNIWGM+VbWdgw4N1dtdkcgqMKjKIoyHMnbSUKdNuHRqDZFUZThRN4KT8D/AamXTg+xJYqiDDQXXnghY8aM4cgj2wNpD9Z38Sxfvpwf/ehHA1b/cCB/hcf3eIwKj6LkPRdccAH/+Mc/htoMpZfk7SShgZCNajNpb4gtUZSRw86rrya+LrevRQjPmsm4yy/vtsySJUvYtGnTful33HEHF110EalUiltuuYUFCxbw3HPP8YUvfIFYLEY0GuXWW29lxowZ3Hbbbdx77720tLSwYcMG3v/+9/ODH/wAsO/iueaaaygtLWXOnDn7TCTakerqai655BI2b94MwHXXXccJJ5zA8uXL2bx5M2+99RabN2/mi1/8IpdeeikAV111Fbfffjtjxoxh0qRJHHvssQDccMMN3HTTTQQCAWbPns2dd97Zn0s47Mhf4QnaSUJNSj0eRRmpDMW7eL7whS/wpS99iRNPPJHNmzdz6qmnsm7dOgBee+01Hn30URobG5kxYwaf/vSnWb16NXfeeSerVq0ilUoxb968NuH53ve+x8aNGwmHw9TV1Q38BRsk8lZ4MuHUxlPhUZTBoifPZLAZinfxPPzww7z66qtt+w0NDTQ1NQHwnve8h3A4TDgcZsyYMezatYsnnniC97///RQUFABw5plnth179NFH89GPfpSzzjqLs846K0dXZejJ2zEeN+PxeNrVpigjle7exbNmzRruu+8+YrH2V6fk4l08nuexYsUKVq1axapVq9i2bRtFRUX9qv/+++/ns5/9LC+++CLHHXdc3rwbKG+FxwlaZ07HeBRl5DIU7+I55ZRT+OlPf9q2v2rVqm7LL1myhL/85S+0trbS2NjIfffdB1gB27JlC8uWLeP73/8+9fX1bZ7TwU7edrU5Af/U1ONRlLznvPPO47HHHqOmpoaqqiq+/W37HsqheBfPDTfcwGc/+1mOPvpoUqkUS5Ys4aabbuqy/Lx58/jQhz7EnDlzGDNmDMcddxwA6XSaj33sY9TX12OM4dJLL6W0tLS3l2RYMyDv48kl/X0fzwtv7KDgzJN46R1BPvLL1QNgmaIooO/jGWpG/Pt4hhPtHs/wFlZFUZSRRt52tblBFR5FUQaOq666ar/xnnPPPZdvfvObQ2TRwUPeCo/jOKQFFR5FGQSMMftFkOU73/zmN4dcZIb7UElX5G1XW8AVPAcVHkUZYCKRCLW1tQftQ/BgxRhDbW0tkUhkqE3pM3nr8biiwqMog0FVVRVbt26lv6+pV/pPJBKhqqpqqM3oM3krPI4jpB1Ao6kVZUAJBoMccsghQ22GchCRv11tjuAJiHo8iqIow4q8FR5HBM8R9XgURVGGGTkRHhGZJCKPisirIrJWRL7QSZmlIlIvIqv85Vud1ZUrXL+rTXTAU1EUZViRqzGeFPAVY8yLIjIKeEFEHjLGvNqh3BPGmPfmqM1ucZ0sj8cYGGGhnoqiKMOVnHg8xpgdxpgX/e1GYB0wMRd19xe3bYwHSCd7LK8oiqIMDjkf4xGRqcBc4NlOsheLyMsi8oCIHNFNHReLyEoRWdnfEE3XH+MRT8BT4VEURRku5FR4RKQIuAf4ojGmoUP2i8AUY8wc4KfAX7qqxxhzszFmvjFmfublS33FcYS0CGKAdKJfdSiKoii5J2fCIyJBrOj8zhjzp475xpgGY0yTv/13ICgiFblqvyMBJ+PxoF1tiqIow4hcRbUJ8GtgnTHm2i7KjPPLISIL/LZrc9F+Z9ioNr+rTYVHURRl2JCrqLYTgI8Dr4hI5nV7lwOTAYwxNwEfAD4tIimgFfiwGcDJnRwRPO1qUxRFGXbkRHiMMU8C3cYrG2NuBG7MRXu9od3jQT0eRVGUYUQez1wAngiOh0a1KYqiDCPyVnhEBM9xrPBoV5uiKMqwIW+FByDtOP4Yj3o8iqIow4W8Fh5PMh6PCo+iKMpwIa+FJ+13tZlUfKhNURRFUXzyWng8x8H1IJ1W4VEURRku5LXwpMUKT0qFR1EUZdiQ18LjOa4VnlTrUJuiKIqi+OS18KQdF8eDdErDqRVFUYYLeS88rgdJDS5QFEUZNuS58AT8MZ7YUJuiKIqi+OS18LSP8ajHoyiKMlzIa+HJeDxpT8d4FEVRhgt5LTyeE8DRcGpFUZRhRV4LT9oJ+mM86vEoiqIMF/JaeIwbwDWQ0nBqRVGUYUNeC4/n2PfcJZMa1aYoijJcyGvhMY4LQDqpHo+iKMpwISfCIyKTRORREXlVRNaKyBc6KSMicoOIvCkiq0VkXi7a7hbXejyplL4WQVEUZbgQyFE9KeArxpgXRWQU8IKIPGSMeTWrzOnAYf6yEPiFvx4wjN/Vlk5qVJuiKMpwIScejzFmhzHmRX+7EVgHTOxQ7H3Ab4xlBVAqIuNz0X6XdmU8noSO8SiKogwXcj7GIyJTgbnAsx2yJgJbsva3sr84Zeq4WERWisjK6urq/hvjBgFINx5AHYqiKEpOyanwiEgRcA/wRWNMQ3/rMcbcbIyZb4yZX1lZ2X+DMl1tDbv6X4eiKIqSU3ImPCISxIrO74wxf+qkyDZgUtZ+lZ82YEjG40m0QnPtQDalKIqi9JJcRbUJ8GtgnTHm2i6K3Qv8px/dtgioN8bsyEX7XZEZ40kjULt+IJtSFEVRekmuotpOAD4OvCIiq/y0y4HJAMaYm4C/A+8G3gRagP/KUdtdkvF4PA+oWQ+TFw10k4qiKEoP5ER4jDFPAtJDGQN8Nhft9ZY24REXat8czKYVRVGULsjrmQsyUW2p8GgVHkVRlGFCXguPEwgB4IVKbFeboiiKMuTktfBkPB4TKoY9b0E6NcQGKYqiKHktPE5mjCdYBF4S6t4eYosURVGUvBYeyXS1BQptgo7zKIqiDDn5LTxBG7TnBQpsgo7zKIqiDDn5LTz+D0g9HIiWQfVrQ2yRoiiKkufCY18EZ5JJmLYU1vwJmnYPqU2KoigjnbwWHifgezzpFCz7JqTj8O/vD7FViqIoI5u8Fh4CvseTSkHFoXDsf8HKW6FGgwwURVGGirwWHvE9HpNO24R3fh2CUfjbFyGlbyVVFEUZCkaE8KQSvsgUVcK7fwSbnoB7LgIvPYTWKYqijEzyWngyYzzxeHN74jHnwanXwLp74b4vgDFDZJ2iKMrIJFevRRiWOH5UWyLZum/G4s9A6154/AcQKYFTvgvS7eTaiqIoSo7Ia+GhzeOJ7Z+37HKI1cMzN0J4lB3/UfFRFEUZcPJaeJygnast2dHjASsyp30PEk3w2DXQtAtO/yG4eX1JFEVRhpy8fsq6fjh1KhnHGIN09GgcB868EQor4anroHEXnHsb+HO8KYqiKLknr4MLMlFtpD03GcadAAAgAElEQVRaU514PWDF513fhtN/AK/fD3+6SF+foCiKMoDkTHhE5BYR2S0ia7rIXyoi9SKyyl++lau2uyIT1eZ60JBo6L7wwk/BKVfBq3+Fey6Elj0DbZ6iKMqIJJcez23AaT2UecIYc4y/fCeHbXeKG3DxANczNCYaez7g+M/Bu74D6/4GN86H1XcNtImKoigjjpwJjzHmcWBYuQmuI6Qdp3ceT4YTvgCfehzKpsOfPgmPfEd/66MoipJDBnuMZ7GIvCwiD4jIEV0VEpGLRWSliKysrq7ud2OuCGlxcDxoiPdSeADGHQn/9QDMOx+e+DH84Tx49mbY9mK/bVEURVEsgxnV9iIwxRjTJCLvBv4CHNZZQWPMzcDNAPPnz++3u+E4QlpcXC9NY7IXXW3ZuAE443oonQxP3wBvPGDTDz/ddsdVHt5fsxRFUUY0g+bxGGMajDFN/vbfgaCIVAxkm4Hsrra+eDwZRGDJV+Hrb8OXX4P/WA6bnoSfL4L7vwrNNbk2WVEUJe8ZNI9HRMYBu4wxRkQWYEWvdiDbbPd4+jDG0xkiUDweTvwSHPMx+4PTlbfAi7+BcUfBxHlw+GlwyBJwg7k7AUVRlDwkZ8IjIn8AlgIVIrIVuBIIAhhjbgI+AHxaRFJAK/BhYwZ21D4zxhMmQH1votp6Q1ElvPdaWHAxvHQHbF8FL/0WnrvZvl574afsEh2dm/YURVHyjJwJjzHmvB7ybwRuzFV7vcF1hIQbpDCZZMuBeDydMWYmnHqV3U62woZ/WQF67Bp4+kZY8ElY/FkoHNDeREVRlIOOvJ65wHWETaPGMXlnun9jPL0lGIWZ74Hz/gCXPAWHvQue/AlcdxQ8eZ3OhKAoipJFngsPrB89iTE1CWINewen0XFHwrm3wueeh+knwcNXwi+XwvO/gj0bB8cGRVGUYUxeTxLqiLC+tAqAURt3D27jFYfBh38Hr95rxef+r9j0sulw6MlQORNKqiBUCE7QBiUEwlB+mE5SqihKXpPXwhNwHNaXTgKg4u36oTFi9pkw6wyo3QAbHoE3H4YX74CuJi0tGgcLL7ZRcqVTIFw0uPYqiqIMMHktPI4DDeFCGssLGb+lZegMEYGKQ+2y8FPgpe37fxq2Q7IF0glIJyHeCKt+b6fpecSfyq5wDIyeCqECSMVt5NzY2faHreFRUFAOxROheIIda1IURRnm5LXwuP77d/ZMGcPUtzaS9JIEnWHwOxvHtUJRPGH/vKM/CDXrYedq2LvJjgvt3WQj59wQ1K63sygYb/9jo2VQMtEKUWGlFaaiMVC1ACbMteKlKIoyxOS18ARcKzz1UyZy9Isbqdu9lcpxhwyxVb2g4jC7dEUyBs3VEG+wsyc0bIeGrf56O9Rvs78vSjRD5vdLTgDGz4Gq42zd5Yfa8aTiCfrKb0VRBpW8Fh7Hf6A2T5sKPEnD6pcODuHpiWAE/LGrHmnZA1uetcvmZ+1sC8msbsdgAZRPbxeicr9LsPxQiJQMjP2Kooxo8lp4XMcKT2zadABa17wCp5w9lCYNPgVlMON0uwB4HjTugNo3bbdd7Qbbtbd9lX0JXnYXXuGYdiEqm26776KlECm16+houx2MqtekKEqvyWvhyXg8blElO0ZD2bo3htiiYYDj2HGgkokw7Z375qXidjypZr0vTP7y+gO2a68r3FC7CLUJ0+j9t6NlUFgOBRV2RodQ4YCeqqIow5O8Fp7MGE9YithcKVRs3DrEFg1zAmGonGGXjsQaoHUPtNZB616I1e2/HfP3G3dA9Tqb1t2MEYGoFaDwKDsGFSqCUWOhyF8KK2xXYKhw33UwmrVdYMVUUZSDhrwWnkxUW8gtYEMlLHimGi8exwmHh9iyg5BIsV36OvdpOmXFp3WvHW9qqbEBES010FILzbU230vZcPKdr0Djw+1BEb0hELURe8FCf50tVgXtAhUqhFHjbEBFQYXthoyW2bXOKq4og0ZeC4/jj/GEpIgtFYJ4HomNG4nMnDnElo0g3IB9sBeU2SCG3pJotkKVbLHbyRZItECy2V9np3eR37jDrpOtfoRfkxW4zggVQbjYBlRESuwPd0OFvpgV2v198n0hzl6HitT7UpRekNfCE/CFxyHIrnFhoJX4+jdVeA4GQoW5HwMyxopZ43brdbXu8b2wPRCrt0vcX7fuhfqt7YIVb+xatNoQ2224T3dgFNywnQbJ9ZdAuD0tEPHPtcgXu1HtopfZDkZtnYGI3Xbc3F4XRRlk8lp4MsEFac/QPLYYz40RX79+iK1ShgwRG9xQWN73Y42xnlO8wY53xRt8ocreb7AClWxp98BSrZBK2PRU3M5Skb1Oxay40YdXUwUi7V2H2eNf2d2LoaJOtv0ygXC7CLrBrO1Qu1gGouq9KQNGXgtPJpzaM4aK4nHsLK8l9NoaxgyxXcpBiIj/EC+w40S5xPPauwwz3lWiCeJNdp1stUuqtb3bsK181nZmCqZEc3u3Y49eWjdkPLfM2Fkg0i5aGa8tM7ltT2mBsF9fxIpa9joY9euO+MdEbBetkrfk9aebEZ60B1csvoKVFecRWvMcpS3VVBZUDrF1iuLjOP4YUhEwNnf1GmM9q+wxsERTu8eVToKXbN/OCFyyeV+Ba9tu9csmoKV5X++t43Y6cWC2i5MldL5wBSJZXZaZ7stw52kZ8ct0T2a8uEy3Zds60t6NuY9YhvS3aQPICBEejyPKj8BbfBbOr+/m6n9fyU9O//kQW6coA4yI//ANA2WD23ZG9DJilGy13YrZ6zYvLmbT0gm7TsXbuyH3SYvZbsuMsCVaIL1337RUHNJxK6SpOJh0/88hI3hOwAqZE7SeWOY1JvukZ/ZDneR1cUwgtK/3l2krswTCMH1Z7j6TYUTOhEdEbgHeC+w2xhzZSb4A1wPvBlqAC4wxL+aq/c5ws8Z4AKbMOZFt3M22V1YQPyVO2NWwakUZEPYRvSEknWrvoky2WJHLeHHZ3ZfJFl/A4h3G4OK+V5i03ZZtXmIn+8lWfzvVRZns9GTPtoeL4bItA3+NhoBcejy3ATcCv+ki/3TgMH9ZCPzCXw8YmXDqtD9uGz7MTrw5Zlecl3a/xKLxiwayeUVRhho3AO4oG204nMh4hNkeYDphX5ni+YLVh3iTg42cCY8x5nERmdpNkfcBvzHGGGCFiJSKyHhjzI5c2dCRtuAC3+MJTZ4MoRBTatM8ve1pFR5FUYaG4eIRDhGDGS85Ecj2G7f6afshIheLyEoRWVld3c0cYT2Q+R1PyhcecV0iM2eybI2w4/GH+l2voiiK0n+GZaC+MeZmY8x8Y8z8ysr+R59lfsfjmXafdcLVVyElxVzwy01suf2XB2yroiiK0jcGU3i2Adkvkany0waM9qi2duEJH3oo0dtuYPVUoeHan5Lau3cgTVAURVE6MJjCcy/wn2JZBNQP5PgOgK87bV1tGWZWzeUv7xmNJJLsue32gTRBURRF6UDOhEdE/gA8A8wQka0i8gkRuURELvGL/B14C3gT+CXwmVy13Y1NuI60BRdkcMRhyYkfYcUMYedvbiFVXz/QpiiKoig+ORMeY8x5xpjxxpigMabKGPNrY8xNxpib/HxjjPmsMWa6MeYoY8zKXLXdHa4IabN/XOJn5nyG5EfPJNia5A9X/ydbGvMzXl5RFGW4MSyDC3KJ47CfxwPWG7r4A9dQe8wUDn34Dc76v/dy1YqrSPbmh12KoihKv8l74Qk4zn5jPBlEhGM+fRmlzfC5xgXc+fqdfP6Rz9OcbB5kKxVFUUYOeS88juwb1daRwhNPJDhhAie9mGL54uWs2LGCc+87l1+98ivW1q5l1e5VbG7YPIgWK4qi5Dd5LzyuI/v8jqcj4rqUfvCDtKxYwXuD8/j5yT+nIlrB9S9ez4f/9mE+/sDHOeMvZ3DtC9cST8cH0XJFUZT8JK9npwZwu+lqy1B6ztlU33gjdXfdzfFf/xrHTzyezQ2bWb93PZFAhIc3P8yta27lwU0PsmzSMo4ZcwxhN0xpuJQ5lXMQnT5dURSl14wA4ek8uCCbQGUlxae8i71//COjP/oRQlVVTC6ezOTiyQCcMPEETp58MrevvZ27Xr+L3677bduxi8cv5hsLvsG00mkDeh6Koij5Qt4LT3fBBdmM+epXafr34+y44gom33LLfl7MiRNP5MSJJxJLxdjUsIm0l+al3S/x81U/531/fR+TR03miIojGF84nvJIOUE3SEGggFOnnkokEBmo01MURTnoyHvhKS8Ksash1mO54IQJjPnv/2bn8uXU3X03oz/4wU7LRQIRZpbNBOCIiiM4/ZDT+euGv7K6ejWrq1fz0NsPkcp63fAdr97BtUuvbfOeFEVRRjp5LzyTygpYu613MxOUfvBcGh54gF3/812caAElZ7y3x2PKo+VceOSFbfvGGBqTjaS8FKt2r+KKp67gQ3/7EKdMPYXFExazaNwiSiOl/T4fRVGUg528F54pZQX8c81O0p5pmzS0K8RxqLr+OrZ+/lK2//d/E9/wJpWf+QwSCvW6PRGhOFQMwEmTT2JG2QyuXXktD216iD+t/xOCMKt8FnPHzOWoiqM4uuJoqkZVaYCCoigjBjHdhBoPB+bPn29Wruz/7Dp3PreZb/zpFZ742jImlRX06hiTSLBj+bep/9OfCE2bxrgrr6Rw4YJ+2wCQ8lKsrV3LM9ufYcWOFbxa+yqtqVYARodHs2D8ApZULeHYsccyoXCCCpGiKP1GRF4wxswfaju6Iu+F5+k3a/jIr57l9xct5PhDK/p0bONjj7HrqqtJbtnC6I99jDFf+TJONNpvW7JJeSnerHuT1dWrebn6ZZ7e/jQ1rTUAFIeKmVYyjapRVRw2+jDmVM7h0NJDKQ4VqyApitIjw1148r6rbXK59XLe3tPC8X08dtTSpRQuWkT1T37Cntt/Q9Ojj1J67rkUn3YqgQkTkGCQdE0NJpkkOGFCn+oOOAFmls1kZtlMPjjjg3jG47U9r7GmZg3r9qzj7Ya3WblrJX97629txxQGC4kGoqS8FAWBAsYWjmVMwRjGFoy1S6FdjyscR3GomKSXJOyGNapOUZRhRd57PGnPMPOKB7joHdP4+mkz+11P84pnqfnZz2h5/vn2xGAQknZS0fJLPkXl5z+PuG6/2+iMPbE9vFL9CpsaNrGjeQexVIyAE6Al2cKull12ad5FLN155J4gTCmewsyymcwom8GhpYdSHilndGQ0ZZEyooGoelGKkmeoxzPEuI5QNbqAzXtaDqiewkULKVy0kMSWLTSvWEG6pgavpYXAuHHE1qyl9qb/pfXllylcuJBAZSWFixf32QvqjLJIGe+c9E7eyTu7LGOMoSHRwM7mnW1i1JRoIuAEaEo08fre13ml5hX+sekf+x0bdIIUBAsoDBRSUVDB2ALrRWWWsQVjKQmXUBoupSJagSN5P8uSoigDTN4LD9iQ6s21ByY8GUKTJhGaNGmfNGMM0aOPovq662l5ZkVbevjww3GKihDHoWjpOyl5//sJlJfnxI5sRISScAkl4RJmlM3oslxDooG3699mb3wvta217I3vpS5WR0uqheZkM9Ut1azfu56ntj1FS2r/61UQKGBayTQqCyoZHRlNabiU0eHRFAQLiAailEfKGVMwhqJQESE3RMgJEXbDBJyAelWKorSR911tAP/vL69w38s7ePnKU3JkVdd48TjJrVtp/Ne/aFnxLCadxmtsJLZ2LbguwaqJhCZOxCkpwSksJHrkURSeeCLiCMnt20k3NmLiCSQcwi0qInz44bglJQNud0eaEk3sbtnN7tbd1Mfr2RPbw6b6TWys30htrJa6WB174nv2+bFsVwhihShLjDL7YTdMNBClOFRMcbjYrkPFlIRL2raLQkVEA1EigYhduxEigQgBZ0R8b1KUPqNdbcOAKWWF1LcmqW9JUlIQHNC2nHCY8PTphKdPh09+si09vmEDDfffT3zjRpLbtpPcuYt0XR31/3dPt/VJMEjRsmVEjjoSJxQiMGECBfPmgQitq1djWlsJVk0iUFEOrotbUoITDh/weRSFiigKFXU7B50xps1bakm2sCe2h90tu2lJtRBPx0mkEyTSifZtL9FpekuqhY31G2lINNCQaOj1LOBBJ2jFyLWilFky+xmxirhZ2x32Oy3jC1s0ECXoBNVbU5QckzPhEZHTgOsBF/iVMeZ7HfIvAH4IbPOTbjTG/CpX7XdH5vc7m/e0cFTB4HsPAOHp06m89NJ90owxJN56i+ann0HCIYITJuKWFCOhMCaRIF1XR9MTj9Nw/99pfPDB3jUUDBKdPZvoMXMIHXIIoSlTCE2dSmDsWMTJ7fiMiFAYLKQwWAjA1JKpOak3no7TEG+gPl5PQ6KBpmQTralWYqmYXdKx9v20TWtNte6T1tDSYPf9/Ex6X3HFJRqIti2ZbsV90gJ+WrA9LeJG2ry6oBMk5IQIukG77Xt+QXf/9KATVE9OyXtycoeLiAv8DHgXsBV4XkTuNca82qHoH40xn8tFm31hclkmpLqZo6qGRng6Q0TavaMuKHrHiYz9xjcw8TgmHif+1kZaX3oJMESPPhqnuJjkli2k6+owqRTJrVtpeeFF9v7xLkwslt0YEghAIIAEAjhFRURmzyYyexaBikrcstEERo/GLSsnOHFCTrym/hJ2w1QWVFJZUJnTej3jEU/H24SoNdVKazpL0FKxffYzYpZZWlItdjvZ2tYV2bFMLnDEsYLkBK04ZYlXZjtbtDqKV0ACBJwAQSeI67j7iFpXoge2S9QRB0FAaNt2xCHgBAhIANdx7ba/n9l2xW1rM5OmgShKV+Tqq9UC4E1jzFsAInIn8D6go/AMCZnf8hxoZNtQIY6DRKMQjVIwby4F8+bukx+ZsX9AgfE8Urt3k9i0icSmt0nt3oVJpjApu6T37iW2Zg1NjzzSSYNCYMwYnKIinEgEiUbseNQRRxCdOw8wpPfuxYvFMKkUgcpKwlOn4paWIpGIDagYht1TjjhtHslA4BmPWCpGS6qFWCpG0kuSSCdIeSkSnu1ezKRlr5PpZKf5me2O+5l1c6qZZHz/9JRJkfbSpLyUXUzP43ADgSNOmyC1iVK2WGVETPYVrGwh2+fYTtKzj3Udd5/6s+vsrL6MfY44bQKdvWSLfKa8khtyJTwTgS1Z+1uBhZ2UO0dElgBvAF8yxmzppAwicjFwMcDkyQc+q3NROEB5YYg3dzUdcF0HC+I4BMeNIzhuHIWLFnVZzovHSdfVkd6zh9SePaRrakhs2Upy2za8lha8WCumNUZq5y5qnngSPK/ntoNBAmPHWgEKBDDpNKa1FRwHp7AQp6DALv62O3q0DbqoqiJYVUWgogJcF9JpvNZWTCqFW1iIFBQMS0HL4IhDQbCAgmDvpmYaLIwx7SKWEbgssUt5KUzmz7SvPeNhsOu0lyZlUm1iljbtwpb0kvvsZwteX9LSXpqklySWju2Tn6k76SU7TU+b9KBcR1fcfYQos7iOFS8HB8exYiaIFTXHTxdnH6HL3heRfdaZvGggyrcWf2tQzm2wGczO5PuAPxhj4iLyKeB24KTOChpjbgZuBhvVlovGT5o5hnte3Mo5x1ZxQh+nzslnnHAYZ+xYgmPH9lg23dREbM1aJBTCHV1qpw9yHFK7dpN4+228xga81hjpPbUkd+7Ca2nBpJKIG0AiYTDgNTfjtbSQ3LkTr6UZr7mFdF0dpHoRHRcMEpwwgeCkSQSrJlqbxQEMGPuwJBOlabDbxgDteSaewMRjeDHbdSnRCO6oYtziUTijipFgEATbNSkCIiBWMAPlZUg0asfKHMeWyazDYdxRo6zY5vhHxAeKSHtUYT6SEcauBDBpkvt5gBnB8jyv3UM0qTZBzniiGU9zv31/O+El8DyPtEljMKS9NB6etcmkMcbYdoxNS3iJtu3O8rPzBsozHw7kJJxaRBYDy40xp/r7lwEYY67porwL7DHG9DjgkotwaoDmeIqzfvYUNU1x7vv8iVSNHl7fSkcyJpUitWuX72ltJbVnD3gGHMEpKEBcF6+5mdSePTYicMsWklu3kq7v3esuAF9ArEA44TASiSDhEKY1ZkPYW3MzPgNYT6642ApR8SjcolFINOKLq+CWluIUFmISCUwqhRONIqGQ9TBbW5FQECcStV2ckShONGK7MKNRu45EcSLhtvE6HAcJBKzgOS4SCiLBIBIKIUFfbFJJCARxCqI5DzJRhh8jJZz6eeAwETkEG7X2YeAj2QVEZLwxZoe/eyawLkdt94rCcID//fixvO/Gp/ifv73K/3582H4mIw4JBAhOnEhw4kQ676HtHC+RsMdDm7C0LX5ab7vmTDJpBSiZIuNBZRbjGbzmJlI1NTZgwxiM51lxNB7G8zCxOF5TI+nGJrzGBtINjaQbG/AaGknu2oVpbUWCQYzxSNfX4zU144RCEAxiWlvxEgncggIkGsUkEnb8rLW13YPLIVJQgFNYgBOOWIEKBKyn5ziYdBpSSUzKdl9JOIyEQzihdrF2QuH29HAYCYWRSLh928+TQNB6tS0tSCCIE/HzQmEk4FrBzIil69i1I+C6VhzdgE3P3g+49phA0G4HAuAGcEJBCGro+8FCToTHGJMSkc8B/8SGU99ijFkrIt8BVhpj7gUuFZEzgRSwB7ggF233hWmVRZxxzATuW7WdVNoj4Oo3v4MZpw/vSeoJCQYJlJV1X6iTII6BxBhjvaJYrE2IvFjMjnv5gR0mnYZ0un2dStv0RKJtsRGNLiaZauvq9Jqb8eIxSKUwyaQNPPHSSCCIuC4SDPjtJ21EZSxGur6+LbrSS8Rtt2UsZr8A+HMWDimO43uEEb/LtBMRErFi2+YRZrb9dTDUvh3wRTkQQIKZiNBMmi+YAdcKoy+KdrtDWseghI52dTTTzxc3wKiTluXu+gwjcjbGY4z5O/D3Dmnfytq+DLgsV+31l0XTyvn9s5tZu72BOZP0TaDK8EX8rkHC4SGZvaIvmHTaCl08jhdPYBJxTDLZFkhiUimbF4tZ8UqnbaBKOm29x3Qa4xnw0pi0568zourvp9L+OuULbNIKZyqNSfpeYixuA2K6EkLPtAtzMtm+jifwGpt8EU62dYOaVAqSybZtk0pBenCCGZzCQma8cODDDMOREfdLtUXT7LfaFW/VMmdSKQ2xJOm0YXRhfg68KspgIK7bFvI/vEIrco8xZl8vM51uEyTbVZmy3a+plN3O7i7dr+e0Q0J22TwO3x5xwjNmVITplYWseKuWi5dM4+O/fo4dda08+KUllBao+CiK0j0i0h7YofSL/JXUblg0rZznN+3lX6/t5uUtdexujHPFX9cOtVmKoigjghEpPIunl9MUT3H5n19hQkmES08+jPte3s4dK96mvnUYDJIqiqLkMSNSeBYeYt+Js6shzsVLpnHpSYcyb3IpV/xlDXO+/SAX3b6SXPy+SVEURdmfEdlJWTkqzGFjitjbkuDDCyYTcB1+d9EiVrxVy4Ov7uIPz23mmbdqOX565zMcxJJpIsF8H0JVFEUZGEakxwPww3PncPN/zm8TkGjIZdnMMVx5xmzKCkPc8uTGTo/7+WNvcvTyB7nhkfUkUl3PW7atrpUf/vM13tjVOCD2K4qiHKyMSI8H4JgufsMTCbp8bNEUfvqv9bxV3cS0yqK2vM21LVz/8HpGFwa59qE3uO/l7XzllMM5ZfY43tjdyEub66goClPTFOfq+9fRGE/xi8c2cOacCdQ2J1i3o4GzjpnIl951OIXhEXvpFUUZ4YyIV1/3lerGOCd871+ceuQ4Ljh+CmOLI0wsjfLJ36zk6Q21/OsrS1m7vZ7v3r+OjTXNjIoEaIztO8nl/CmjueK9s/nzS9v4/bObmVJewJTyAh5et5uJpVG+eurhnHH0BJ09QVGUnDPc52pT4emCb9yzmjufb39rQ3lhiNrmBJe/eyYXL7EvbkulPe5bvZ3HXq9mwSFlnDC9gvrWJE3xFIumleM6duoLzzM4/vZzG/fwrb+u4bWdjUwuK+DUI8ZydFUpjbEU63c3srshTl1rgtOOHM/HFk7WuacURekzKjwHyFAJTzyV5rUdjextSbBlTwsvba4jbQw/OncOwQP0UjzP8PC6Xdzy1EZe3FzXNlZUEHIZVxLBEeHN3U2875gJLD/jiE5nVXjh7b18+761bKxuZmpFIYf4y6Jp5SyeXt4rOxpjSf79RjWFoQDlRSHKi8KUFYSIBJ19BM8YQ0NriqJIANcRmuMp3tjVyJTyQsp0xgdFGXao8BwgQyU8g0U8lWb9riZKokEmlkZxHMHzDL/49wZ+9ODrGANjRoU5fno5HzxuEomUx90rt3L/KzsYVxzh5Flj2LynhY01zWyra8UYOHveRK587xGUFAS7bHdDdRMX/2YlG6qb98tzBApCAaIhl5DrUN0UJ5HyCLpCZVGYnQ0xPGPnMjxyQgknHlbBOw6t4NAxRZQVhmiOp9lW10pJQZAJJRH12hRlkFHhOUDyXXi6Y/XWOp7eUMtrOxp45LXdbeNIJdEgH1k4mc8tO3SfIIXWRJqfP/YmP39sA47AIRWFzBpfzHFTyygtCPLQq7tYu72BwpDLW9XNBAMOPzjnaMqKQtQ2JdjTHGdPc5KWRIqWRJqWRIp4yqOyKEzlqDA1TQl21rcyubyQ2eNH8cauJp5YX81Lm+tIeZ3fR6PCASaOjlJeFGLS6AJmTyhmemURE0ujFIRcGuMpgo7D+NLIAXuSiqJYVHgOkJEsPNm0JtI8vG4XQddh2cxKwoGuf0e0dns99728g/W7Glm9rZ7qxjgAowuCzJ9aRjzlURhy+eZ7ZuXkhXhN8RTPb9zD1r0t1DQlKAoHmFAaZW9Lgjd2NbKjPkZNU5yNNc3UtXQ+M4QjMK44QtXoAqpGR6kaHWXi6ChVowuYVlnI+JLO38aY9gzxVJqCkEYJKkoGFZ4DRIXnwDDGsMQNbcYAAAqCSURBVKm2hT3NceZUlQ5pFJ0xhp0NMTbVtLBlbwvxlEdxJEA86bG1rpVte1vZureFrXtb2VHfSrYTNaksylETSwg4Dsm0x86GGLvqY+xqjJP2DDPGjmLu5FIiQZdk2mN3Y5z6liRzp5Ry8syxzJ5QTFEvQthjyTRrt9eTTBuKI0EmlUUZFem6y1JRhiMqPAeICs/IJJn22FkfY+veVl7b2cCKt2pZv6sJzxgCrsO44ghjiyOMKwkTcl1e2LyXNdvqSXsG1xHGjAoTDbm8srW+rRuwoijMIRUFTCkvpLwwREEowPa6VjZUN9GcSJNMe2yqad6v23BKeQGTywqoLArb4IpEioJQgEMqCgkHHHbWx9jbkiSWTOMZQzTkUhByKQgFiARdwgGHoCuEXAfHEZriKZIpQ1EkQHEkQHE0SEk0SOWoMBVFYYKu4EhmAdfp/ZtUM7QkUtQ2JahpiuMZQyToEg26RENuW7RlTyRSHnUtSZrjKdKeIW0Mac9ggIAjuI4QdB27dvy1K0SCLhNKo71uR8k9KjwHiAqPciA0xJKs2FDLhupmNtU0s7G2mc21LextSRBPeZQXhpg+pojiSBDXsW+pnTuplKJwgLrWJBtrmlm7vZ5te1upaUrgGUNhOEBTLMXOhhgAkaBDeaEVOgFak+m2MbJYsuvZLfpKtgi5vig5jhUo9/+3d3ahcl1VHP/958zHvcnNd0IMtdRGA1JBahpqhNIHpWmalygoDQgNWiioBX3wIVIo1ScrKCgWS9VAU8TWT8xDpVYt+NSkqSZp0pLmpkbakDZp0nzc5M6dr+XD3vdm7mXm9t6bMzNnJusHh9mz9jmz1zprz1mz99lzVi68l8RYucZ4tTvJytoxXEjYsHaEYpKjYTY1eh0uJIwM5VlSyjMylGeklGdxKc/iYjI1Wr1SqZNITQE81C0qhqyoVyt1jOnBdDiWh2J5rvcLzYxKvUGlFra6hZHupC5j5RpjE+GeZ05QSHIU8jkKOV3LHNoi3Y5Z6HvvX57gUrnGRK3OeKVOOfqlVEgYKuQYyidIoc+Uqw3GK3VqjQZJLsdQIcdXP3vLgs5/1gOPT4w7A83SoQJbPvWRlnWVWoNifuFTj1cmatTqxtLhfNsRiZlRrV+7uDXMWFzMU0jElYk6l8pVLo5XuXC1ytmxMufGKlOjC7NwD6thRqMRLt4Na18X5MZIKc+qkRKrFhdZHUdp4cIWAmK9zUKQmRQSsXxRkZFSWEafxCAnhb8EVOthBFRtNKjXjVqjQbVuXK3UOPbuGMfPXKZhRq7p3JSrdd4+f5WxiXBBHyvX2i5MuR6SnEIgKiQMF3MUcrkpH1QnA0096Nvu+Lmep06xpJRfcODJOqkFHklbgZ8CCfArM/vhjPoSsAe4AzgH3G9mJ9Nq33Hmy/UEHWBOjz2SRDGv0FZpet2yRTmWLSpw83Vp0d+YGRO18Et/vFqnkORYVExomDFeCYFycgQ5XqkjMTWyLFcblKuhfvL48rRyY0pWqTcoJTkKSY5i/tpWSHKU8jmKUZ4TXI4BcXJ0FkZkeRoWg2st/JBopvl3h+JQaMlQntUjJZYO56eC4FAh6l6rT+lvxrRRW5KEoNfoceDrJKkEHkkJ8ARwD/AO8IqkvWb2etNuDwIfmNknJO0AHgfuT6N9x3H6E0lTF+QVM+p8UcfgktYSpzuBUTN7y8wqwLPA9hn7bAeejuU/AF+Q/7PQcRznhiOtwHMT8HbT+3eirOU+ZlYDLgItn+0i6SFJByQdOHv2bEoqOo7jOFkgk38VN7OnzGyTmW1as2ZNr9VxHMdxUiStwHMKpt0j/WiUtdxHUh5YRlhk4DiO49xApBV4XgE2SLpVUhHYAeydsc9eYGcsfxn4p2X9T0SO4zhO6qSyqs3MapIeBl4gLKfebWZHJf0AOGBme4FfA89IGgXOE4KT4ziOc4OR2v94zOx54PkZskebymXgK2m15ziO4/QnmVxc4DiO4wwumX9Wm6SzwP8WePhq4P0U1eklbks2cVuyyY1uyy1mltklwZkPPNeDpANZflDefHBbsonbkk3clmzjU22O4zhOV/HA4ziO43SVQQ88T/VagRRxW7KJ25JN3JYMM9D3eBzHcZzsMegjHsdxHCdjeOBxHMdxuspABh5JWyUdkzQqaVev9WmHpJOSXpN0UNKBKFsp6UVJx+PriiiXpJ9Fmw5L2tj0OTvj/scl7WzXXsq675Z0RtKRJllquku6I56b0Xhsx3I3tbHlMUmnom8OStrWVPe9qNcxSfc2yVv2u/gMw31R/lx8nmGnbLlZ0kuSXpd0VNK3o7zvfDOLLX3nG0lDkvZLOhRt+f5s7Usqxfejsf5jC7Uxk1jM0z4oG+FZcSeA9UAROATc1mu92uh6Elg9Q/YjYFcs7wIej+VtwF8BAZuBfVG+Engrvq6I5RVd0P1uYCNwpBO6A/vjvorH3tdlWx4Dvtti39tinyoBt8a+lszW74DfATti+UngGx20ZR2wMZaXAG9GnfvON7PY0ne+iedqJJYLwL54Dlu2D3wTeDKWdwDPLdTGLG6DOOKZSzbULNOcqfVp4ItN8j0WeBlYLmkdcC/wopmdN7MPgBeBrZ1W0sz+RXjYa+q6x7qlZvayhW/bnqbP6pYt7dgOPGtmE2b2X2CU0Oda9rs4Gvg8IesuTD8vqWNmp83s37F8GXiDkISx73wziy3tyKxv4vkdi28LcbNZ2m+XsXleNnbCljQYxMAzl2yoWcGAv0l6VdJDUbbWzE7H8rvA2lhuZ1eW7E1L95tieaa82zwcp592T05NMX9bVgEXLGTdbZZ3nDg98xnCr+u+9s0MW6APfSMpkXQQOEMI5Cdmab9dxuZ+uA58KIMYePqJu8xsI3Af8C1JdzdXxl+UfbnevZ91j/wC+DhwO3Aa+HFv1ZkfkkaAPwLfMbNLzXX95psWtvSlb8ysbma3ExJl3gl8sscq9YxBDDxzyYaaCczsVHw9A/yZ0Bnfi9MZxNczcfd2dmXJ3rR0PxXLM+Vdw8zeixeKBvBLgm9g/racI0xf5WfIO4akAuFC/Rsz+1MU96VvWtnSz74BMLMLwEvA52Zpv13G5n64Dnwogxh45pINtedIWixpyWQZ2AIcYXqm1p3AX2J5L/BAXIW0GbgYp05eALZIWhGnHLZEWS9IRfdYd0nS5jiv/UDTZ3WFyYt05EsE30CwZUdcdXQrsIFws71lv4uji5cIWXdh+nnphN4iJF18w8x+0lTVd75pZ0s/+kbSGknLY3kYuIdwz6pd++0yNs/Lxk7Ykgq9Xt3QiY2wUudNwhzqI73Wp42O6wkrTw4BRyf1JMzj/gM4DvwdWBnlAp6INr0GbGr6rK8TbjKOAl/rkv6/JUxzVAnzyQ+mqTuwiXBBOQH8nPiUjS7a8kzU9TDhC7yuaf9Hol7HaFrR1a7fRV/vjzb+Hih10Ja7CNNoh4GDcdvWj76ZxZa+8w3waeA/UecjwKOztQ8MxfejsX79Qm3M4uaPzHEcx3G6yiBOtTmO4zgZxgOP4ziO01U88DiO4zhdxQOP4ziO01U88DiO4zhdxQOP4ziO01U88DiO4zhd5f83UbUiv5/qRwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "plt.figure()\n",
    "for label, loss_plot in [(\"all\", losses), (\"1band\", losses_band), (\"2band\", losses_band2), (\"1band_ends\", losses_band1_ends)]:\n",
    "    xs, ys = zip(*loss_plot)\n",
    "    plt.plot(xs, ys, label=label)\n",
    "plt.legend()\n",
    "plt.title(\"l2 error between exact probabilities and empirical TS probabilities\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "exact_win_probs"
   ]
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