{}
// Online C# Editor for free
// Write, Edit and Run your C# code using C# Online Compiler
using System;
using System.Collections.Generic;
using System.Linq;
public class HelloWorld
{
static void Main(string[] args)
{
// Range of numbers (as in your example: from 1 to 100)
int minNumber = 1;
int maxNumber = 100;
int rangeCount = maxNumber - minNumber + 1;
// Batch sizes to demonstrate the Law of Large Numbers
// Added more steps to make the convergence visually clear
int[] batches = { 10, 50, 100, 500, 1000, 5000, 10000, 50000, 100000, 500000, 1000000, 6000000 };
Random random = new Random();
Console.WriteLine("Random Distribution Convergence Demo");
Console.WriteLine("Demonstrating the Law of Large Numbers\n");
Console.WriteLine($"Number Range: {minNumber}-{maxNumber}");
Console.WriteLine($"Expected Probability per Number: {100.0 / rangeCount:F4}%");
Console.WriteLine(new string('-', 70));
foreach (int batchSize in batches)
{
// Dictionary to count frequency of each number
Dictionary<int, int> counts = new Dictionary<int, int>();
for (int i = minNumber; i <= maxNumber; i++)
{
counts[i] = 0;
}
// Generate random numbers
for (int i = 0; i < batchSize; i++)
{
int num = random.Next(minNumber, maxNumber + 1);
counts[num]++;
}
// Calculate percentages and find min/max deviations
double expectedPercent = 100.0 / rangeCount;
double minPercent = double.MaxValue;
double maxPercent = double.MinValue;
// Track which numbers had min/max percentages for display
int minNum = 0;
int maxNum = 0;
foreach (var kvp in counts)
{
double percent = (double)kvp.Value / batchSize * 100.0;
if (percent < minPercent)
{
minPercent = percent;
minNum = kvp.Key;
}
if (percent > maxPercent)
{
maxPercent = percent;
maxNum = kvp.Key;
}
}
double spread = maxPercent - minPercent;
// Output results
Console.WriteLine($"Batch: {batchSize,7} rolls");
Console.WriteLine($" Min %: {minPercent,7:F4}% (Number {minNum,3})");
Console.WriteLine($" Max %: {maxPercent,7:F4}% (Number {maxNum,3})");
Console.WriteLine($" Spread (Max - Min): {spread,7:F4}%");
Console.WriteLine(new string('-', 70));
}
Console.WriteLine("\nAs the number of rolls increases, the spread decreases.");
Console.WriteLine("Press any key to exit...");
Console.ReadKey();
}
}