111.py

from collections import defaultdict
import numpy as np
import pandas as pd
from matplotlib import pyplot as plt


def calculate_exact_probabilities():
    """
    计算精确的概率分布
    """
    # 初始化概率字典
    probabilities = defaultdict(int)
    # 六面骰子的所有可能点数组合
    dice_values = np.arange(1, 7)

    # 枚举所有可能的四骰组合（考虑去除一个最小值后的和）
    for d1 in dice_values:
        for d2 in dice_values:
            for d3 in dice_values:
                for d4 in dice_values:
                    # 排序并去除最小值
                    rolls = sorted([d1, d2, d3, d4])[1:]
                    for _ in range(6):  # 重复六次
                        rolls_sum = sum(rolls)  # 当前组合的总和
                        probabilities[rolls_sum] += 1  # 累加次数

    probabilities_sum = defaultdict(int)
    for n in probabilities:
        print(n)
        for m in probabilities:
            for k in probabilities:
                for l in probabilities:
                    for o in probabilities:
                        for p in probabilities:
                            probabilities_sum[n+m+k+l+o+p] += probabilities[n]+probabilities[m]+probabilities[k]+probabilities[l]+probabilities[o]+probabilities[p]

    total_combinations = sum(probabilities_sum.values())  # 总的组合数
    for key in probabilities_sum:
        probabilities_sum[key] /= total_combinations
        print(f"{key}: {probabilities_sum[key]}")

    # 转换为DataFrame以便查看
    df = pd.DataFrame(list(probabilities_sum.items()), columns=['Total', 'Probability'])
    df['Total'] = df['Total'].astype(int)  # 确保“Total”列是整型
    df.sort_values(by='Total', inplace=True)  # 按照Total排序


    return df

# 计算并打印结果
exact_probability_table = calculate_exact_probabilities()


def visualize_probabilities(df):
    """
    可视化概率分布
    """
    plt.figure(figsize=(10, 5))
    plt.bar(df['Total'], df['Probability'], color='skyblue')
    plt.xlabel('Sum of Rolls (excluding the lowest roll)')
    plt.ylabel('Probability')
    plt.title('Probability Distribution of Sum of Rolls (excluding the lowest roll)')
    plt.grid(axis='y', linestyle='--', alpha=0.7)
    plt.show()


# 调用函数进行可视化
visualize_probabilities(exact_probability_table)