Are people lucky or unlucky?
I'm going to cover a very sensitive topic here and that's whether or not people are lucky or unlucky. Most professionals live by the credo that there is no such thing as luck and that over the course of a lifetime the great
hands and the horrid hands will even themselves out so the only thing that matters is the skill used to play all the average and mediocre hands. And the rules of a Gaussian distribution (i.e. the bell curve) would seem to support this hypothesis. When given an infinite number of random hands the hands received should have a large proportion in the average range with an equal number of great and horrid hands drifting off to either side. And if you're talking about dealing an infinite number of random hands to a single individual, then Gaussian distribution should come into play and the professionals should be proven correct.
However, poker is not about dealing an infinite number of random hands to a single person. it is about randomly dealing an infinite number of random hands to an infinite number of players. To accurately portray the entire poker world, you have to consider that the random hands are spread across all players randomly. This Gaussian distribution (bell curve) would also have a majority of people in the middle, but also edge cases tapering off to the left and right. The meaning of this bell curve is that the majority of players will be dealt an even number of great and horrid hands and will end up in the middle of the bell curve. But as you move away from the middle there will be players who will randomly receive more great hands than horrid hands, and an equal number of players who will randomly receive more horrid hands than great hands. It's the nature of bell curves, Gaussian distribution. Since hands are randomly distributed there will be people who receive better hands and people who receive worse hands over the course of their careers. And on the extreme ends there will be people who are very lucky and people who are very unlucky with the random distribution of the infinite number of hands.
So, although the sum total of the infinite hands would result in a bell curve which "evens itself out", the same is true of a bell curve of players receiving random hands. And in order for a bell curve of players receiving random hands to "even itself out" some players have to be very lucky and others have to be very unlucky.