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.
My interpretation is that, before playing the actual game, they refuse to believe me. They don't trust me or the logic and so dismiss it. Once actual stakes are involved, even if it's their pride, only then do they start to be open to arguments as to why their intuition was wrong.