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reireias/rating.ipynb

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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]"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "dec55cda-3ccc-4f4e-9510-6ed17e195c1a",
"metadata": {},
"outputs": [],
"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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