> once you open the door, the situation resets That's the root cause error of your thinking. The prizes aren't reshuffled and the host's choice of doors depen

> once you open the door, the situation resets That's the root cause error of your thinking. The prizes aren't reshuffled and the host's choice of doors depends on both the player's choice and on information that is hidden to the player. No way you can treat that as a reset.