https://zenn.dev/reireias/articles/77300e098be748

rating.ipynb

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    "# Elo Rating\n",
    "# 勝敗は実力に応じて確率的に\n",
    "# レート差マッチング禁止\n",
    "#   マッチング前にRateでGROUPS個のグループに分け、そのグループ内でマッチング\n",
    "\n",
    "import random\n",
    "import numpy\n",
    "import matplotlib.pyplot as plt\n",
    "import re\n",
    "\n",
    "USERS = 256\n",
    "TEAM_MEMBER = 4\n",
    "GAMES = 100 # 1人の試合数\n",
    "ELO_K = 32\n",
    "P = 0.8\n",
    "GROUPS = 4 # USERS / GROUP は TEAM_MEMBER の 2n倍である必要がる\n",
    "X = 16 # sim6でのマッチング範囲\n",
    "\n",
    "def elo(ra, rb, k=ELO_K):\n",
    "    ea = 1.0 / (1 + 10**((rb-ra)/400)) # Aが勝つ確率\n",
    "    # eb = 1.0 / (1 + 10**((ra-rb)/400))\n",
    "    nra = ra + k * (1-ea)\n",
    "    nrb = rb - k * (1-ea)\n",
    "    return [nra, nrb]\n",
    "\n",
    "def simulate_near(p=P):\n",
    "    users = [{ 'id': i, 'result': '', 'win': 0, 'lose': 0, 'rate': 1500, 'skill': random.random(), 'order': '' } for i in range(USERS)]\n",
    "    for _ in range(GAMES * USERS // TEAM_MEMBER // 2):\n",
    "        rate = random.choice(users)['rate']\n",
    "        near_users = []\n",
    "        x = 0\n",
    "        while len(near_users) < 2 * TEAM_MEMBER:\n",
    "            x += X\n",
    "            near_users = [user for user in users if rate-x <= user['rate'] <= rate+x]\n",
    "        target = [user['id'] for user in random.sample(near_users, 8)]\n",
    "        team_a = target[0 : TEAM_MEMBER]\n",
    "        team_b = target[TEAM_MEMBER :]\n",
    "        \n",
    "        # rateの降順にソート\n",
    "        team_a.sort(key = lambda x: users[x]['rate'], reverse=True)\n",
    "        team_b.sort(key = lambda x: users[x]['rate'], reverse=True)\n",
    "        # チーム内のrate順で何番目かを記録\n",
    "        for j in range(TEAM_MEMBER):\n",
    "            users[team_a[j]]['order'] += str(j)\n",
    "            users[team_b[j]]['order'] += str(j)\n",
    "        rate_a = numpy.average([users[id]['rate'] for id in team_a])\n",
    "        rate_b = numpy.average([users[id]['rate'] for id in team_b])\n",
    "\n",
    "        skill_a = sum([users[id]['skill'] for id in team_a])\n",
    "        skill_b = sum([users[id]['skill'] for id in team_b])\n",
    "\n",
    "        # Aが勝つ確率 win_a を算出\n",
    "        if isinstance(p, float) or isinstance(p, int):\n",
    "            # p が数値の場合\n",
    "            win_a = p if skill_a >= skill_b else 1 - p\n",
    "        else:\n",
    "            # p が関数の場合\n",
    "            win_a = p(skill_a - skill_b)\n",
    "\n",
    "        # ダイスを降って勝利判定\n",
    "        dice = random.random()\n",
    "        if (dice <= win_a):\n",
    "            winner, winner_rate, loser, loser_rate = team_a, rate_a, team_b, rate_b\n",
    "        else:\n",
    "            winner, winner_rate, loser, loser_rate = team_b, rate_b, team_a, rate_a\n",
    "\n",
    "        for id in winner:\n",
    "            users[id]['win'] += 1\n",
    "            users[id]['result'] += 'w'\n",
    "            nr = elo(users[id]['rate'], loser_rate)\n",
    "            users[id]['rate'] = nr[0]\n",
    "        for id in loser:\n",
    "            users[id]['lose'] += 1\n",
    "            users[id]['result'] += 'l'\n",
    "            nr = elo(winner_rate, users[id]['rate'])\n",
    "            users[id]['rate'] = nr[1]\n",
    "            \n",
    "    # 連勝->連敗 を懲罰マッチとみなした場合\n",
    "    count_a = [0, 0, 0] # 5連続, 6連続, 7連続\n",
    "    # 連勝->味方が低レート を懲罰マッチとみなした場合\n",
    "    count_b = [0, 0, 0] # 5連続, 6連続, 7連続\n",
    "    for user in users:\n",
    "        count_a[0] += user['result'].count('wwwwwlllll')\n",
    "        count_a[1] += user['result'].count('wwwwwwllllll')\n",
    "        count_a[2] += user['result'].count('wwwwwwwlllllll')\n",
    "        s = ''\n",
    "        for i in range(len(user['result'])):\n",
    "            s += user['result'][i] + user['order'][i]\n",
    "            \n",
    "        count_b[0] += len(re.findall('w.w.w.w.w..0.0.0.0.0', s))\n",
    "        count_b[1] += len(re.findall('w.w.w.w.w.w..0.0.0.0.0.0', s))\n",
    "        count_b[2] += len(re.findall('w.w.w.w.w.w.w..0.0.0.0.0.0.0', s))\n",
    "    return [count_a, count_b]\n",
    "\n",
    "def simulate(groups=GROUPS, p=P):\n",
    "    users = [{ 'id': i, 'result': '', 'win': 0, 'lose': 0, 'rate': 1500, 'skill': random.random(), 'order': '' } for i in range(USERS)]\n",
    "    \n",
    "    for _ in range(GAMES):\n",
    "        ids = list(range(USERS))\n",
    "        ids.sort(key = lambda x: users[x]['rate'])\n",
    "        group_list = []\n",
    "        users_in_group = USERS // groups\n",
    "        for g in range(groups):\n",
    "            group_list.append(ids[g * users_in_group : (g+1) * users_in_group])\n",
    "        for group in group_list:\n",
    "            ids = group\n",
    "            random.shuffle(ids)\n",
    "            for i in range(len(group) // (TEAM_MEMBER * 2)):\n",
    "                team_a = ids[TEAM_MEMBER * 2 * i : TEAM_MEMBER * (2*i + 1)]\n",
    "                team_b = ids[TEAM_MEMBER * (2*i+1) : TEAM_MEMBER * 2*(i+1)]\n",
    "                # rateの降順にソート\n",
    "                team_a.sort(key = lambda x: users[x]['rate'], reverse=True)\n",
    "                team_b.sort(key = lambda x: users[x]['rate'], reverse=True)\n",
    "                # チーム内のrate順で何番目かを記録\n",
    "                for j in range(TEAM_MEMBER):\n",
    "                    users[team_a[j]]['order'] += str(j)\n",
    "                    users[team_b[j]]['order'] += str(j)\n",
    "                rate_a = numpy.average([users[id]['rate'] for id in team_a])\n",
    "                rate_b = numpy.average([users[id]['rate'] for id in team_b])\n",
    "                \n",
    "                skill_a = sum([users[id]['skill'] for id in team_a])\n",
    "                skill_b = sum([users[id]['skill'] for id in team_b])\n",
    "                \n",
    "                # Aが勝つ確率 win_a を算出\n",
    "                if isinstance(p, float) or isinstance(p, int):\n",
    "                    # p が数値の場合\n",
    "                    win_a = p if skill_a >= skill_b else 1 - p\n",
    "                else:\n",
    "                    # p が関数の場合\n",
    "                    win_a = p(skill_a - skill_b)\n",
    "                \n",
    "                # ダイスを降って勝利判定\n",
    "                dice = random.random()\n",
    "                if (dice <= win_a):\n",
    "                    winner, winner_rate, loser, loser_rate = team_a, rate_a, team_b, rate_b\n",
    "                else:\n",
    "                    winner, winner_rate, loser, loser_rate = team_b, rate_b, team_a, rate_a\n",
    "\n",
    "                for id in winner:\n",
    "                    users[id]['win'] += 1\n",
    "                    users[id]['result'] += 'w'\n",
    "                    nr = elo(users[id]['rate'], loser_rate)\n",
    "                    users[id]['rate'] = nr[0]\n",
    "                for id in loser:\n",
    "                    users[id]['lose'] += 1\n",
    "                    users[id]['result'] += 'l'\n",
    "                    nr = elo(winner_rate, users[id]['rate'])\n",
    "                    users[id]['rate'] = nr[1]\n",
    "\n",
    "    # high_skill = [user['rate'] for user in users if user['skill'] < 0.5]\n",
    "    # low_skill = [user['rate'] for user in users if user['skill'] >= 0.5]\n",
    "    # plt.hist([high_skill, low_skill], stacked=True)\n",
    "\n",
    "    # 連勝->連敗 を懲罰マッチとみなした場合\n",
    "    count_a = [0, 0, 0] # 5連続, 6連続, 7連続\n",
    "    # 連勝->味方が低レート を懲罰マッチとみなした場合\n",
    "    count_b = [0, 0, 0] # 5連続, 6連続, 7連続\n",
    "    for user in users:\n",
    "        count_a[0] += user['result'].count('wwwwwlllll')\n",
    "        count_a[1] += user['result'].count('wwwwwwllllll')\n",
    "        count_a[2] += user['result'].count('wwwwwwwlllllll')\n",
    "        s = ''\n",
    "        for i in range(GAMES):\n",
    "            s += user['result'][i] + user['order'][i]\n",
    "            \n",
    "        count_b[0] += len(re.findall('w.w.w.w.w..0.0.0.0.0', s))\n",
    "        count_b[1] += len(re.findall('w.w.w.w.w.w..0.0.0.0.0.0', s))\n",
    "        count_b[2] += len(re.findall('w.w.w.w.w.w.w..0.0.0.0.0.0.0', s))\n",
    "    return [count_a, count_b]"
   ]
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   "cell_type": "code",
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   "source": [
    "NAME = ['定義A', '定義B']\n",
    "\n",
    "def sim_average_near(times=100, p=P):\n",
    "    print('| | 5連続 | 6連続 | 7連続 |')\n",
    "    print('|--|--:|--:|--:|')\n",
    "    results = []\n",
    "    for i in range(times):\n",
    "        results.append(simulate_near(p=p))\n",
    "    for i in range(2):\n",
    "        row = []\n",
    "        for j in range(3):\n",
    "            row.append(numpy.average([result[i][j] for result in results]))\n",
    "        print(f'| {NAME[i]} |', ' | '.join(map(str, row)), '|')\n",
    "\n",
    "def sim_average(times=100, groups=GROUPS, p=P):\n",
    "    print('| | 5連続 | 6連続 | 7連続 |')\n",
    "    print('|--|--:|--:|--:|')\n",
    "    results = []\n",
    "    for i in range(times):\n",
    "        results.append(simulate(groups=groups, p=p))\n",
    "    for i in range(2):\n",
    "        row = []\n",
    "        for j in range(3):\n",
    "            row.append(numpy.average([result[i][j] for result in results]))\n",
    "        print(f'| {NAME[i]} |', ' | '.join(map(str, row)), '|')\n",
    "\n",
    "# 1\n",
    "sim_average(groups=1, p=0.5)\n",
    "\n",
    "# 2\n",
    "# sim_average(groups=1, p=1.0)\n",
    "\n",
    "# 3\n",
    "# sim_average(groups=1, p=0.6)\n",
    "# sim_average(groups=1, p=0.7)\n",
    "# sim_average(groups=1, p=0.8)\n",
    "\n",
    "# 4\n",
    "# sim_average(groups=1, p=lambda x: 0.5 + 0.1 * x)\n",
    "\n",
    "# 5\n",
    "# sim_average(groups=4, p=lambda x: 0.5 + 0.1 * x)\n",
    "# sim_average(groups=8, p=lambda x: 0.5 + 0.1 * x)\n",
    "# sim_average(groups=16, p=lambda x: 0.5 + 0.1 * x)\n",
    "# sim_average(groups=32, p=lambda x: 0.5 + 0.1 * x)\n",
    "\n",
    "# 6\n",
    "# sim_average_near(p=lambda x: 0.5 + 0.1 * x)"
   ]
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