原神抽卡模拟.py

import random

import click
import numpy as np
import seaborn as sns
from matplotlib import pyplot as plt


角色概率 = np.array(
    [0.006] * 73 +  # 1 ~ 73
    [
        0.066, 0.126, 0.186, 0.246, 0.306, 0.366, 0.426,  # 74 ~ 80
        0.486, 0.546, 0.606, 0.666, 0.726, 0.786, 0.846, 0.906, 0.966, 1.0  # 81 ~ 90
    ]
)
武器概率 = np.array(
    [0.007] * 62 +  # 1 ~ 62
    [
        0.077, 0.147, 0.217, 0.287, 0.357, 0.427, 0.497, 0.567, # 63 ~ 70
        0.637, 0.707, 0.777, 0.847, 0.917, 0.987, 0.998, 0.999, 1.0  # 71 ~ 80
    ]
)


def 出金次数(probs, N=1):
    K = len(probs)
    dice = np.random.random(size=[N, len(probs)])
    counts = [K] * N
    for i in range(N):
        for k, p in enumerate(probs):
            if dice[i, k] <= p:
                counts[i] = k + 1
                break

    if len(counts) == 1:
        return counts[0]
    return np.array(counts)


def 限定角色次数(N=1):
    counts = [None] * N
    for i in range(N):
        c = 0
        for _ in range(2):
            c += 出金次数(角色概率)
            if random.random() < 0.5:
                break
        counts[i] = c

    if len(counts) == 1:
        return counts[0]
    return np.array(counts)


def 限定武器次数(N=1):
    counts = [None] * N
    for i in range(N):
        c = 0
        last_is_up = True
        for _ in range(3):
            c += 出金次数(武器概率)
            if last_is_up:
                a = random.random()
                if a < 0.75:
                    # 75% 概率是 up 武器
                    last_is_up = True
                    if a < 0.75 * 0.5:
                        # 1/2 概率抽中定轨
                        break
                else:
                    last_is_up = False
            else:
                # 一定是 UP 武器
                last_is_up = True
                if random.random() < 0.5:
                    # 1/2 概率抽中定轨
                    break

        counts[i] = c

    if len(counts) == 1:
        return counts[0]
    return np.array(counts)


def 角色命座抽数(k=0, N=1):
    if k < 0:
        return np.zeros([N])
    counts = 限定角色次数(N * (k + 1)).reshape([-1, (k + 1)]).sum(-1)
    return counts


def 武器精炼抽数(k=0, N=1):
    if k < 1:
        return np.zeros([N])
    counts = 限定武器次数(N * k).reshape([-1, k]).sum(-1)
    return counts


def plot_counts(counts):
    sns.ecdfplot(
        counts,
        stat='proportion'
    )
    plt.grid()
    ax2 = plt.twinx()
    sns.histplot(
        counts,
        stat='density',
        discrete=True,
        alpha=.4,
        ax=ax2
    )
    # sns.ecdfplot(counts, stat='count')
    print('平均次数: ', np.mean(counts))
    plt.show()


@click.command()
@click.option('-c', 'character', type=int, default=0, help='角色命座。')
@click.option('-w', 'weapon', type=int, default=0, help='武器精炼。')
@click.option('-N', 'repeat', type=int, default=10000, help='模拟次数。')
def main(character, weapon, repeat):
    counts = 角色命座抽数(k=character, N=repeat) + 武器精炼抽数(k=weapon, N=repeat)
    print(f'{character}命{weapon}精抽卡次数概率')
    plot_counts(counts)


if __name__ == '__main__':
    main()