When I was a child, my grandfather blew my mind with a bit of basic probability and statistics. If you play the lottery, he explained, you might as well just play the numbers 1, 2, 3, 4, 5, 6. Your chance of winning will be exactly the same as with any other particular combination of numbers. I was astonished and incredulous at first, but then I thought it through, and had to admit, of course, that he was right.
Now, years later, I am not so sure anymore.