No idea why this problem came into my head, but it did so I was having a little browse.
But anyway, what I'm thinking is that ultimately, you're not making a decision until there's two boxes; one winner, one loser. Is it not irrelevant which box you pick first?
The diagram that you posted Kyle, should there not be 4 choices? Option 1 could be split into two as there's two possibilities for which un-chosen, empty cup to remove. That would make it a 1/2.
I've always leant towards it being a 1/3, but for some reason I can't decide now, which annoys me.