dice.py

import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import norm

def normal_distribution(n, m):
    # 单个骰子的均值和方差
    mean = (m + 1) / 2
    variance = (m ** 2 - 1) / 12

    # 总和的均值和方差
    sum_mean = n * mean
    sum_variance = n * variance

    # 正态分布对象
    distribution = norm(loc=sum_mean, scale=np.sqrt(sum_variance))

    # 返回正态分布对象
    return distribution

# 设置不同的参数组合
parameters = [
    {'n': 6, 'm': 4},
    {'n': 4, 'm': 6},
    {'n': 2, 'm': 12},
]

# 创建一个图表
plt.figure(figsize=(12, 8))

# 遍历参数组合
for param in parameters:
    n = param['n']
    m = param['m']

    # 计算正态分布
    distribution = normal_distribution(n, m)

    # 绘制概率分布
    x = np.linspace(distribution.ppf(0.01), distribution.ppf(0.99), 100)
    plt.plot(x, distribution.pdf(x), label=f'{n}D{m}', marker=',')

# 图表配置
plt.xlabel('Sum of Dice')
plt.ylabel('Probability Density')
plt.title('Normal Distribution Approximation for Dice Sum')
plt.legend()
plt.grid(axis='y', linestyle='--', alpha=0.7)
plt.show()