The only explanation that 'felt' acceptable to me is to imagine that you're really playing two games instead of one. In the first game, you're right 1/3rd of th

The only explanation that 'felt' acceptable to me is to imagine that you're really playing two games instead of one. In the first game, you're right 1/3rd of the time. Then you get to play a new game where you're right half the time, but you can also choose to not play that game and stick with the results of the first game. Playing the second game (picking another door) is more obviously the right thing to do in this case.