Skall has been so preoccupied lately with following how "skill v. chance" IS making a difference to take notice of this thread, sorry. But over the last 3 weeks we have prevailed on this argument in front of 2 judges and one jury. I love it when a plan comes together ;).
The short answer is not much more than what TE said. In 33 to 38 states (there are plenty of open questions throughout this area of law, some state laws can be read 2 ways) whether playing a game for money is "gambling" or not is decided by whether the "outcome" of the game (winning at the game) is more often the result of chance or more often the result of skill. More often chance and the game is gambling and is either illegal or limited (to one degree or another) in all states. If wining the game is more often the result of skill, then the game is not gambling legally, even if you are wagering money against the other players when you play it. If its not gambling, playing it for money fits into the same legal category as playing chess for money - the same laws (if any) apply.
When's the last time you heard of a SWAT team busting a chess tournament?
In the "Ask Skallagrim" Forum you will find threads on this subject giving further details.
Skallagrim