I have a much easier explanation than this: By offering you the switch, the host has given you two doors to open - it's irrelevant that he opened one for you -

I have a much easier explanation than this: By offering you the switch, the host has given you two doors to open - it's irrelevant that he opened one for you - so, it comes down to picking one door (the one you're on) or two doors (of which he has opened one for you, again, irrelevant - the effect is the same) ergo, it's 1/3 or 2/3.