MontyHall

using System;
using System.Security.Cryptography;

public class Program
{
    static int GetRandomNumber(byte max){
        //random generation
        byte[] buffer = new byte[1];
        RNGCryptoServiceProvider rng = new RNGCryptoServiceProvider();
        rng.GetBytes(buffer);

        return buffer[0]%max;
    }
    static bool[] InitGame(ref int boxIndex,  ref int toBeRemovedBox, ref int playerChoice){

        //init the random variables
        boxIndex = GetRandomNumber(3);
        toBeRemovedBox = GetRandomNumber(2);
        playerChoice = GetRandomNumber(3);

        //game init
        bool[] boxes = new bool[3];
        for(int i = 0; i < 3; i++)
        {
            boxes[i] = false;
        }
        boxes[boxIndex] = true;

        return boxes;
    }

    static bool NotChanging(){

        int boxIndex = -1,
            toBeRemovedBox = -1,
            playerChoice = -1;
        bool[] boxes = InitGame(ref boxIndex, ref toBeRemovedBox, ref playerChoice);

        return boxes[playerChoice];
    }

    static bool ChangingEveryTime(){

        int boxIndex = -1,
            toBeRemovedBox = -1,
            playerChoice = -1;
        bool[] boxes = InitGame(ref boxIndex, ref toBeRemovedBox, ref playerChoice);

        return !boxes[playerChoice];

    }
    static bool OnlyChoosingSecondTime(){
        int boxIndex = -1,
            toBeRemovedBox = -1,
            playerChoice = -1;
        bool[] boxes = InitGame(ref boxIndex, ref toBeRemovedBox, ref playerChoice);

        bool[] secondTurnBoxes = new bool[2];
        for(int i = 0, counter = 0; i < 3; i++){
            if(i == toBeRemovedBox) continue;
            secondTurnBoxes[counter++] = boxes[i];
        }

        int secondChoice = GetRandomNumber(2);
        return secondTurnBoxes[secondChoice];
    }
    public static void Main()
    {
        int noChange = 0,
            alwaysChange = 0,
            rechoose = 0;
        int numberOfGames= 10000;
        for(int i = 0; i < numberOfGames; i++){
            if(NotChanging()) noChange++;
            if(ChangingEveryTime()) alwaysChange++;
            if(OnlyChoosingSecondTime()) rechoose++;
        }
        Console.WriteLine("nc: " + noChange.ToString() + " /"+ numberOfGames.ToString() );
        Console.WriteLine("cet: "+ alwaysChange.ToString()+ " /"+ numberOfGames.ToString());
        Console.WriteLine("ocst: "+ rechoose.ToString()+ " /"+ numberOfGames.ToString());
    }
}