The situation is the same as the standard Monty Hall Problem. However, this time Monty has forgotten which door hides the million dollars. He lets you know that he has no memory of which door is which, but since the game calls for him to reveal one door, he holds his breath and opens one of the doors you did not pick. To his relief, there is nothing behind that door. Now, as in the original game, he gives you the offer to swap from the door you picked to the other door remaining closed.

Do you swap doors? Are the odds now the same or different than they were in the original puzzle?