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c# - 计算序列在随机分布中出现的频率时出现意外结果

问题描述

给定一个硬币游戏：你从一美元开始，硬币被翻转。如果是正面，则美元翻倍，如果是反面，则游戏结束。但是，如果再次翻转正面，则收益现在是四倍，如果正面翻转 3 次 8 倍，依此类推。悖论是期望值是 1/2*1+1/4*2+1/8*4... = 无穷大。因此，如果您玩游戏的时间足够长，您应该会逐渐变得富有。蒙特卡罗模拟表明不是。这是著名的圣彼得堡悖论的模拟

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Sorrow
{
    class Program
    {
        static void Main(string[] args)
        {
            Random rnd = new Random(Environment.TickCount);
            double totalSum = 0;
            int bigWins = 0;
            double iterations = 1000;
            for (int z = 0; z < 10; z++)
            {
                iterations *= 10;
                for (double i = 1; i < iterations; i++)
                {
                    int sum = 1;
                    int a = 1;
                    while (a == 1)
                    {
                        //generate a random number between 1 and 2
                        a = rnd.Next(1, 3);

                        if (a == 1)
                        {
                            sum *= 2;
                        }
                        if (sum > 8000&&sum<12000)// given discrete probability landing 13 times
                        {
                            // if the sum is over 8000 that means that it scored 1 13 times in a row (2^13) - that should happen
                            //once every 8192 times. Given that we run the simulation 100 000 000 times it should hover around 
                            // 100 000 000/8192
                            //However is much , much bigger
                            bigWins++;
                        }
                    }

                    totalSum += sum;

                }

                Console.WriteLine("Average gain over : "+iterations+" iterations is:" + totalSum / iterations);
                Console.WriteLine("Expected big wins: " + iterations / 8192 + " Actual big wins: " + bigWins);
                Console.WriteLine();
            }


        }
    }
}

如您所见，我们应该期望这个数字小 7 倍。这让我觉得也许 c# random 很容易一遍又一遍地选择相同的数字？这是真的还是我的代码有问题？我该如何解决这个问题？

标签： c#random

解决方案

你有两个错误。您的循环在获胜后开始，因此大赢的机会是 1/2^12，并且您在 12 之后继续增加大赢以获得额外的胜利。

尝试

   static void Main(string[] args)
    {

        Random rnd = new Random(Environment.TickCount);


        double iterations = 1000;
        for (int z = 0; z < 10; z++)
        {
            double totalSum = 0;
            int bigWins = 0;
            iterations *= 10;
            for (double i = 1; i < iterations; i++)
            {
                int sum = 2;
                int a = 1;

                while (a == 1)
                {
                    //generate a random number between 1 and 2
                    a = rnd.Next(1, 3);


                    if (a == 1)
                    {
                        sum *= 2;
                    }
                    if (sum > 8000)
                    {
                        // if the sum is over 8000 that means that it scored 1 12 times in a row (2^12) - that should happen
                        //once every 4096 times. Given that we run the simulation 100 000 000 times it should hover around 
                        // 100 000 000/4096
                        bigWins++;
                        break;
                    }
                }

                totalSum += sum;

            }

            Console.WriteLine("Average gain over : " + iterations + " iterations is:" + totalSum / iterations);
            Console.WriteLine("Expected big wins: " + iterations / 4096 + " Actual big wins: " + bigWins);
            Console.WriteLine();
        }


        Console.ReadKey();
    }

输出类似：

Average gain over : 10000 iterations is:12.6774
Expected big wins: 2.44140625 Actual big wins: 1

Average gain over : 100000 iterations is:14.09468
Expected big wins: 24.4140625 Actual big wins: 21

Average gain over : 1000000 iterations is:14.022718
Expected big wins: 244.140625 Actual big wins: 249

Average gain over : 10000000 iterations is:14.0285748
Expected big wins: 2441.40625 Actual big wins: 2456

Average gain over : 100000000 iterations is:14.00012582
Expected big wins: 24414.0625 Actual big wins: 24574

Average gain over : 1000000000 iterations is:14.000105548
Expected big wins: 244140.625 Actual big wins: 244441

Average gain over : 10000000000 iterations is:13.9990068676
Expected big wins: 2441406.25 Actual big wins: 2440546

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