I love the Monty Hall problem because it's so unintuitive that even Paul Erdos struggled to believe it for a while.

> Vazsonyi ran the program 100,000 times. Erdos watched the results of the simulation. The simulation results indicated that by switching, the odds of winning are indeed two out of three. Finally, he was grudgingly convinced that switching was better. He did not like it but seeing was believing. He could not argue with the results.

Apparently he later called Ronald Graham and explained to him that he finally heard a proof of the problem that made perfect sense to him, which he explained to Graham. Graham said he didn't understand the proof at all, but was happy Erdos understood where he had been mistaken.