If you're already familiar with the problem, then you know the answer.

I recently became familiar with the problem and at first thought the answer was that the contestant had just as much chance of winning the car if he traded his pick away as kept it.

Then I had to convince myself that my intuition was wrong and that the math was right and that he has a better chance if he makes the trade.

I find this a fascinating problem because it's sort of like a mental illusion. People's intuition tells them one thing, but the math tells them another. You can then convince your intuition that the math is true by looking at the problem from a different prospective.

So, was I trying to start an argument? Of course not. I was just trying to introduce this problem to people who had not heard of it before so that they could also have the fun of changing their perspective.

But, it seems that probably most everyone in this group has already come across this problem and knows the answer already.