I am surprised that you have never seen the technique used before in mathematics where two different problems are shown to be equivalent That is to say it is shown that the answer to both problems must be the same In that case a solution to one problem becomes a solution to the other Vos Savant justifies her answer by saying that she took the host to be acting as the agent of chance This means that the host chooses evenly between goat doors and thus the problem is equivalent to the unconditional one Falk describes the symmetry argument as impeccable Rosenthal says about the simple solution It is actually correct but I consider it shaky because it fails for slight variants of the problem By slight variants he obviously means that the host does not choose a goat door uniformly Please demonstrate that you are not pushing a personal POV by providing either A mathematical argument which shows that in the standard K W case the answer to the conditional problem is not certain to be equal to the answer to the unconditional problem A source which says that a simple solution to the standard case is incorrect