Prove Poker is a Skill Game?

[Sciolist]

I haven't read up on any of this, so stop me if it's been suggested before...

Look at every (say) PokerStars $215 tournament run. Only include players who have played ten times or more. If the game was random and you have a 15% chance at cashing, then we should know how many players will cash how many times, i.e, x% have cashed 10%, y% 20%, etc.

If poker is a skill game, then we should see that there's a higher percentage of people who cash more often than if it were random. Correspondingly, we should see a higher percentage of people who cash less frequently than if it were random.

Does this work? My knowledge of stats is not great. What sample size of players with > 10 tournaments entered do you need? Do you have to control for the size of the tournaments?