This animated simulation allows you to explore the Monty Hall problem in depth.

The underlying methodology is called a "discrete event simulation", in which random numbers are used to create probabilistic outcomes. This means for instance, that the simulation places the prize you are seeking behind a random door each time, with equal probability for each of the 3 or 6 doors. And each play of the game is 100% independent of previous plays. You can play the same game you saw on the video, with 3 doors and one bad prize shown. Or you can switch to 6 doors and specify how many doors you want opened (1, 2, 3 or 4) revealing bad prizes before you make a decision to stay or switch doors.

We recommend playing the game a few times in manual mode, both with 3 doors and then with 6 doors. Then, once you are comfortable and familiar with the setup, you can play many times quickly in succession (10, 100 or even 1,000 times), specifying ahead of time whether you are a "Switcher" or a "Stayer". This multi-game option allows you to see how the winning probabilities translate with large numbers of games into stable fractions of times winning, the fractions corresponding to the theoretical probabilities that you have derived. And allowing 6 doors with a specified number of doors to be opened (each revealing a bad prize), provides an opportunity for you to show that you understand fully the decision tree construct as applied in these types of situations.