Gil Kalai, a well known mathematician, has this to say on the topic of chess and luck:
http://gilkalai.wordpress.com/2009/07/05/chess-can-be-a-game-of-luck/
I didn't follow his argument at all, but it seems like something other LW posters may understand, so I decided to post it here. Do comment on his arguments if you agree or disagree with him.
I think the argument is that if the stakes are high enough people's betting patterns create a zero expectation on the bit itself. This seems wrong on the face of it. It assumes that the bettors on the chess match are perfectly evaluating their skills at making perfect bets with expectation of zero, that there is no skill in determining the bet. Thus with an expectation of zero, the winner of the bet is determined by luck.
This becomes more absurd in the poker game. The difference in skill of betting for action is a large part of the game. Most poker books try to teach it. Most people can't do it.
"Most people can't do it"
This is precisely my point and probably the basis for the judge's rationale in the old case. The situation of those" most people" who cannot do it but still take parts in betting on poker is similar to those playing the roulete. if this accounts for a large percent of participants than it is justified to regard the activity as primarily - gambling (or game of luck) I think there are additional ingredients that will push the situation towards a game of luck when the stakes are high.