From my experience, the issue is that the 50% intuition is hard to overcome (and it takes an overwhelming amount of evidence for the 33%/66% reality in order to

From my experience, the issue is that the 50% intuition is hard to overcome (and it takes an overwhelming amount of evidence for the 33%/66% reality in order to overcome that intuition). Here's an alternate version of the game which aims to dismantle the 50% intuition directly, instead of trying to argue for 33%/66%. You pick a box, and another empty box is revealed. Then, the two remaining boxes are shuffled so that you no longer can tell which is which (but the game host still knows). You then choose one of four options: - take box A, - take box B, - ask the host to give you the box you picked initially, or - ask the host to give you the box you didn't pick initially.