> I sometimes give people the Monty Hall problem. When they get it wrong, it often falls into the category of staying with the initial pick increases chances or switching has equal odds. I then proceed to give them the example of N=100 doors, opening 98 others, leaving their pick and another closed and then asking them whether that makes a difference.

> If they insist that it makes no difference, I then start to play the actual game with them, writing down the prize door before the game starts and then proceeding with the game as normal. Only after a few rounds of them losing do they accept the proofs of what the optimal strategy is.

That is all way too much work. I draw a decision tree and let them fill in the fractions for each edge leaving a node (2/3 edges result in this outcome 3 nodes later while 1/3 edges result in that outcome 2 nodes later).

If that doesn't work, I'll just give up.