星塔旅人抽卡模拟

StellaSoraGacha.py

import random
import numpy as np
import matplotlib.pyplot as plt
from tqdm import trange

P = 0.01           # 抽中概率
GIFT_LIMIT = 120   # 领取阈值
GLOBAL_LIMIT = 160 # 全局保底
N_PERIODS = 500    # 模拟期数
TRIALS = 1000      # 重复次数

def simulate_period(strategy, g):
    pulls = 0
    obtained = [False, False]
    pool_counts = [0, 0]

    while not all(obtained):
        for pid in range(2):  # 每期两池
            if obtained[pid]:
                continue

            if strategy == "single": # 顺序抽池, 一池出货后切换抽另一池
                if pid == 1 and not obtained[0]:
                    continue
            elif strategy == "alt": # 交替抽池, 轮流抽两池
                pass
            elif strategy == "switch": # 切换抽池, 一池80抽不出货切换抽另一池，出货后再回来继续抽
                if pool_counts[0] >= 80 and not obtained[1]:
                    if pid == 0:
                        continue
                elif pid == 1 and not obtained[0]:
                        continue
            else:
                raise ValueError("Unknown strategy")

            pulls += 1
            pool_counts[pid] += 1
            g += 1

            if random.random() < P or g >= GLOBAL_LIMIT:
                obtained[pid] = True
                g = 0  # 出货重置保底
            elif pool_counts[pid] == GIFT_LIMIT:
                obtained[pid] = True  # 领取不重置保底

    # print(f"抽数: {pulls}, 保底计数: {g}, 池抽数: {pool_counts[0]} {pool_counts[1]}, 策略: {strategy}")
    return pulls, g

def simulate(strategy, periods=N_PERIODS, trials=TRIALS):
    results = []
    for _ in trange(trials, desc=f"{strategy}"):
        g = 0
        total_pulls = 0
        for _ in range(periods):
            pulls, g = simulate_period(strategy, g)
            total_pulls += pulls
        results.append(total_pulls/periods)
    return np.array(results)


alt_results = simulate("alt")
single_results = simulate("single")
switch_results = simulate("switch")

print(f"交替抽池 平均每期抽数: {alt_results.mean():.2f}")
print(f"顺序抽池 平均每期抽数: {single_results.mean():.2f}")
print(f"切换抽池 平均每期抽数: {switch_results.mean():.2f}")

plt.rc('font',family='SimHei')
plt.figure(figsize=(8,5))
plt.hist(alt_results, bins=50, alpha=0.6, label="交替抽池")
plt.hist(single_results, bins=50, alpha=0.6, label="顺序抽池")
# plt.hist(switch_results, bins=50, alpha=0.6, label="切换抽池")
plt.xlabel("平均每期抽数")
plt.ylabel("出现次数")
plt.title(f"{N_PERIODS} 期模拟 ({TRIALS} 次重复)")
plt.legend()
plt.show()

交替抽池 平均每期抽数: 125.10
顺序抽池 平均每期抽数: 123.15
切换抽池 平均每期抽数: 125.25

结论：在每期两池的情况下，应该在一池出货后再切换抽另一池，平均每个概率提升5星角色需要62抽