Monty Hall Simulation https://en.wikipedia.org/wiki/Monty_Hall_problem

Game.cs

using System;
using System.Linq;

namespace MontyHall
{
    public class Game
    {
        private static Random Random = new Random();

        public static void Main(string[] args)
        {
            const int TRIES = 1000000;

            var stayWins = PlayGame(TRIES, false);
            PrintResult("Stay strategy", TRIES, stayWins);

            var switchWins = PlayGame(TRIES, true);
            PrintResult("Switch strategy", TRIES, switchWins);

            Console.ReadLine();
        }

        private static void PrintResult(string game, int numberOfTries, int wins)
        {
            Console.WriteLine(game + ": " + ((float) wins / numberOfTries * 100) + "% wins");
        }

        private static int PlayGame(int numberOfTries, bool switchDoor)
        {
            var doors = new[] { "Car", "Goat", "Goat" };
            var indexes = new[] { 0, 1, 2 };
            int wins = 0;

            for (var i = 0; i < numberOfTries; i++)
            {
                Random.Shuffle(doors);

                var choice = Random.Next(0, 3);

                var car = Array.IndexOf(doors, "Car");

                if (switchDoor)
                {
                    int reveal;
                    while (true)
                    {
                        reveal = Random.Next(0, 3);
                        if (reveal != choice && doors[reveal] != "Car")
                            break;
                    }

                    choice = indexes.SingleOrDefault(index => index != reveal && index != choice);
                }

                if (choice == car)
                    wins++;
            }

            return wins;
        }
    }

    static class RandomExtensions
    {
        public static void Shuffle<T>(this Random rng, T[] array)
        {
            int n = array.Length;
            while (n > 1)
            {
                int k = rng.Next(n--);
                T temp = array[n];
                array[n] = array[k];
                array[k] = temp;
            }
        }
    }
}

Monty Hall Problem

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
https://en.wikipedia.org/wiki/Monty_Hall_problem

Looks like you're always better to switch: