The Oxford press... Monty and his problem....

[Rick1234567S]

So ok it is not probability theory nor game theory it is a simple statement.

In the first game she has a 1/3 chance of getting the car and so he exposes a goat now she has a fifty fifty chance if she starts over and switches to that game.

Where the odds are better than they were at 1/3.

So in fact it is an if statement only. And always the odds would be better to go where the unknowns were reduced.