I think the dichotomy you've established is a faulty one, as regards whether poker is a game of skill or chance. It certainly isn't a sport, I am sure. But the game itself can be played as primarily a game of chance by players who choose to do so (looking to push on any/all coin flip situations). But, if you haven't the necessary skill, then your chances are slim at best. It's a game of intuition, probabilities, and manipulation.