蒙蒂霍尔程序仿真(c#)

我正在尝试用c#(我最熟悉的编程语言)模拟Monty Hall问题(因为我从Think Statistics这本书中读到，有一个人只有在看到计算机模拟后才被说服)。我的场景是这样的，奖品的位置是随机的(在每次运行中)，我的选择是随机的，游戏主持人打开门的选择是随机的(如果我选择了非奖品，它就不可能是随机的)。

令人惊讶的是，我的程序达到了50:50的获胜机会，无论我是否切换。下面是它的代码(请原谅我的冗长):

class Program
{
    static void Main(string[] args)
    {
        Random rand = new Random();
        int noSwitchWins = RunGames(rand, false, 10000);
        int switchWins = RunGames(rand, true, 10000);
        Console.WriteLine(string.Format("If you don't switch, you will win {0} out of 1000 games.", noSwitchWins));
        Console.WriteLine(string.Format("If you switch, you will win {0} out of 1000 games.", switchWins));
        Console.ReadLine();
    }
    static int RunGames(Random rand, bool doSwitch, int numberOfRuns)
    {
        int counter = 0;
        for (int i = 0; i < numberOfRuns; i++)
        {
            bool isWin = RunGame(rand, doSwitch);
            if (isWin)
                counter++;
        }
        return counter;
    }
    static bool RunGame(Random rand, bool doSwitch)
    {
        int prize = rand.Next(0, 2);
        int selection = rand.Next(0, 2);
        // available choices
        List<Choice> choices = new List<Choice> { new Choice(), new Choice(), new Choice() };
        choices[prize].IsPrize = true;
        choices[selection].IsSelected = true;
        Choice selectedChoice = choices[selection];
        int randomlyDisplayedDoor = rand.Next(0, 1);
        // one of the choices are displayed
        var choicesToDisplay = choices.Where(x => !x.IsSelected && !x.IsPrize);
        var displayedChoice = choicesToDisplay.ElementAt(choicesToDisplay.Count() == 1 ? 0 : randomlyDisplayedDoor);
        choices.Remove(displayedChoice);
        // would you like to switch?
        if (doSwitch)
        {
            Choice initialChoice = choices.Where(x => x.IsSelected).FirstOrDefault();
            selectedChoice = choices.Where(x => !x.IsSelected).FirstOrDefault();
            selectedChoice.IsSelected = true;
        }
        return selectedChoice.IsPrize;
    }
}
class Choice
{
    public bool IsPrize = false;
    public bool IsSelected = false;
}

这完全是为了我自己的兴趣，我用我最熟悉和最舒服的方式来写它。请随时提出自己的意见和批评，非常感谢!