So would it be better to show the formal solution for the standard MHP at the beginning of the article without door numbers I suggest this variant  Formal solution for the standard Monty Hall problem  When selecting one of three doors the chances on the car are  each The possibilities to open one door showing a goat are The Car being behind the hosts second door that he offers as an alternative to switch on he must open the door with his only Goat behind x   The Car being behind the guests selected door then the host though disposing of two Goats opens just one of his two doors x   These are the only possibilities for the host to open a door showing a Goat Altogether the host opens that door with probability    After the host opened one door showing a Goat the Car is behind his second door offered as an alternative to switch on exactly    of the time Result In the standard Monty Hall problem the odds for switching versus staying are exactlly  irrespective of any particular actual door numbers Would that be easier to access