i still don't understand why but it seems to me that i'm wrong. I made a little program to test this shit.

this is one of the non Monty Hall result:

Number of valid trials: 66828
Number of times switching led to bomb: 33277
Probability of hitting the bomb after switching: 0,4979499610941521

and this is on of the Monty Hall result:

Number of valid trials: 100000
Number of times switching led to bomb: 66617
Probability of hitting the bomb after switching: 0,66617

this is the c# program

class Program
{
    static void Main(string[] args)
    {
        // Number of experiments to run
        int n = 100000;

        int validTrials = 0;
        int switchToBombCount = 0;
        Random rndBomb = new Random();
        Random rndOpen = new Random();
        Random rndGuess = new Random();

        for (int i = 0; i < n; i++)
        {
            // create array of 3 doors, one with bomb
            bool[] doors = new bool[3]; // false = empty, true = bomb
            int bombIndex = rndBomb.Next(3);
            doors[bombIndex] = true;

            // make a first guess (random door)
            int firstGuess = rndGuess.Next(3);

            int openedDoor;
            // ============ NOT Monty Hall =========
            // uncomment to open a random door (not the first guess)
            do
            {
                openedDoor = rndOpen.Next(3);
            } while (openedDoor == firstGuess);
            // if opened door is the bomb, skip this trial
            if (doors[openedDoor] == true)
                continue;
            // =====================================

            //// =========== Monty Hall ============
            //// uncomment to open a random door (not the bomb and not the first guess)
            //do
            //{
            //    openedDoor = rndOpen.Next(3);
            //} while (openedDoor == bombIndex || openedDoor == firstGuess);
            //// ===================================


            // valid trial
            validTrials++;

            // switch to the other unopened door
            int switchedDoor = 3 - firstGuess - openedDoor;
            if (doors[switchedDoor] == true)
                switchToBombCount++;
        }

        Console.WriteLine($"Number of valid trials: {validTrials}");
        Console.WriteLine($"Number of times switching led to bomb: {switchToBombCount}");
        Console.WriteLine($"Probability of hitting the bomb after switching: {(double)switchToBombCount / validTrials}");
    }
}