An interesting article on this topic was recently published by Steven D. Levitt, well known economist and author of the following book:

Emphasis is mine:

Abstract:

In determining the legality of online poker – a multibillion dollar industry – courts have relied heavily on the issue of whether or not poker is a game of skill. Using newly available data, we analyze that question by examining the performance in the 2010 World Series of Poker of a group of poker players identified as being highly skilled prior to the start of the events. Those players identified a priori as being highly skilled achieved an average return on investment of over 30 percent, compared to a -15 percent for all other players. This large gap in returns is strong evidence in support of the idea that poker is a game of skill.

Conclusion:

This paper attempts to shed light on the extent to which pre-existing metrics of poker skill are useful in predicting tournament outcomes. Our results suggest that players who are a priori identified as “high skill” do indeed substantially outperform other competitors. This predictability in returns is evidence for a substantial role of skill in poker.

It is not immediately obvious how one measures the importance of skill versus luck in poker relative to other activities. One approach that problem is to estimate the probability that a randomly drawn high skill poker player will outperform a randomly drawn low-skilled poker player over the course of a tournament. An important limitation of our data in this regard is that we do not observe the complete order of finish, but rather, only the order of finish for those who make the money. Because of this limitation, we can make pairwise comparisons between two players in a tournament only when at least one makes the money. Subject to that constraint, an exhaustive pairwise comparison of high skilled and low skilled players entered in each tournament in the WSOP finds that the high skilled player wins 54.9 percent of the match ups. For purposes of comparison, we calculated the regular season win rates for professional sports teams that made the playoffs in the previous season – making the playoffs last year is akin to being a highly skilled player entering the WSOP. Since the year 2007, teams that made the playoffs the previous season win 55.7 percent of their games in Major League Baseball against teams that failed to make the playoffs in the previous year. Thus, in some crude sense, the predictability of outcomes for pairs of players in a poker tournament is similar to that between teams in Major League Baseball. To the extent that baseball would unquestionably be judged a game of skill, the same conclusion might reasonably be applied to poker in light of the data.

Asset management is another domain where skill is generally believed to be important, as evidenced by consumers paying billions of dollars annually in fees to money managers. Academic analysis, however, has generally found little evidence for skill in this domain as demonstrated by low rates of persistence in mutual fund returns (Carhart 1997, Bollen and Busse 2004) and evidence of inferior or superior performance only in the extreme tails of the mutual fund distribution (Fama and French 2010).

Link to full text.