During a train trip I cooked up a semi-autobiographical variation of The Monty Hall problem for people who already know the original. Perhaps it is more of a meta-puzzle than a puzzle, but I hope it is suitable for this site. (At least it got some people disagreeing who knew the correct answer to the original quite well.) So here goes.
John M. is a television mogul who at Friday night watches a new game show, produced by one of his production companies and aired on one of his networks. In it the host, Monty Hall, shows the candidate three doors to choose from. Behind one is a car and behind the others are goats.
'Good', murmurs John. 'Two doors with goats, so 2/3 chance for the candidate to make the wrong choice. This will only cost me one car per three episodes on average. Very good.' But then something annoying happens: after the candidate has chosen a door, the host announces that he will always open one of the doors the candidate did not choose, and even more annoyingly, always a door with a goat behind it, after which the candidate can choose again.
'Aaaaargh!' Shouts John at the monitor. 'Does Monty think cars grow on the tree in my garden?! This will cost me at least one car every two shows! But this will not stand! I will tell Monty to stop this nonsense tomorrow first thing in the morning!'
So the next morning John takes the train to Delft (where Monty lives) to give him a stern talking to. After said talking, on his way back home, John arrives again at Delft station (see picture) and finds himself in the situation of needing to choose between two blue stairways: the rightmost stairway leading to platform 1 or the leftmost stairway leading to platform 2 and 3. Too busy to check his phone he takes the left stairway so that he has 2/3 chance for his train to arrive at a railway that is adjacent to where he is standing.
But then something annoying happens. John suddenly remembers that he arrived, earlier that morning, on platform 2 and hence his train will not return form that platform (as apparently trains on rail 2 travel away from his house instead of towards it) leaving platforms 1 and 3 as the only viable options for his train to arrive.
Question: is (considering losing a car 'as bad as' missing a train) this situation on Saturday equivalent to the situation on Friday, i.e. to the Monty Hall problem? If yes, should he change platforms? If no what is the difference?