Likewise, for some reason the Monty Hall problem is hard to understand in three door form. But if you change the problem to 100 doors, and explain that Monty's assistant closes 98 bad doors, it's easier (at least for me) to see that the original guess had a 1/100 chance of being right, while the other door is 99/100 likely to be the right one.
This is by far the most insightful thing I have ever read about this problem. Furthermore, this being a site about startups, I would say that you will be more successful if you understanding people and math than if you just understand math.
I've tried explaining the problem to both people who've seen the show and those who haven't. My experience is that if you've seen the show you'll never accept the question, let alone the answer. Meanwhile, those who never watched the show can be convinced.
If you phrase the question like that, everyone will get the right answer. The reason people get it wrong is that people don't normally talk like that. Imagine you're at a party, and someone tells you they have two kids, and "one of them is a girl." Clearly, they mean that the other is a boy, which means the answer is 100%.
But the most intuitive way of interpreting the question is that you know that a specific child is a girl, say because the person brought one kid to the party, who turns out to be a girl. With this interpretation, the obvious answer of 50% is in fact correct.
You often hear the complaint that people don't understand math. In this instance, however, an equally valid way of explaining what's going on is that mathematicians don't understand people.
This criticism applies partially to the normal game-show version of the Monty Hall problem, but I think there the wording is genuinely ambiguous regarding the host's behavior, and my answer would be "not enough information."