### Success in Poker: How much of it is luck? How much of it is skill?

Since the Main Event of the 2007 World Series of Poker is coming up in a matter of days, I found an article I came across in the July 2007 issue of Bluff magazine written by Aaron Brown and Brandon Adams that combined quantitative social science with poker to be extremely interesting. Aaron Brown, a financial trader and poker aficionado, has written a book about the intersection between poker and finance: The Poker Face of Wall Street. Brandon Adams has written a couple of books dealing with similar themes: Broke: A Poker Novel and The Story of Behavioral Finance.

What was interesting to me about their article, Luck and Skill in Poker, is that they came up with a way to quantify the extent to which luck (and skill) contribute to success in poker. They took the pre-tournament betting odds posted on Betfair.com of various professional poker players for the Main Event of the World Series of Poker. The authors used these odds to come up with implied probabilities of success (at least for the players whose odds were quoted on Betfair.com); in effect, they use Betfair.com and the odds it quotes as a predictive market. Using this probability function, they applied the Gini coefficient -- which is a concept usually used by economists to measure the inequality of income -- to the problem of how to measure the relative contributions of luck and skill to success in poker.

A Gini coefficient, as applied to poker rather than income, of zero would imply that poker is all luck. A Gini coefficient of one would imply that poker is all skill. The authors of the article found that the Gini coefficient applied to their method of assigning the probability of success to poker players is 24%. In other words, poker (at least by the authors' measure) is 24% skill and 76% luck.

From my personal experiences with poker, I think this split between three-quarters luck and one-quarter skill is about right (at least for no limit hold'em in large tournaments; other types of poker may have a larger skill component). As the article concludes about the Gini coefficient of poker, "It's far enough from zero to make skill obvious, but far enough from one to keep you humble ..."

What was interesting to me about their article, Luck and Skill in Poker, is that they came up with a way to quantify the extent to which luck (and skill) contribute to success in poker. They took the pre-tournament betting odds posted on Betfair.com of various professional poker players for the Main Event of the World Series of Poker. The authors used these odds to come up with implied probabilities of success (at least for the players whose odds were quoted on Betfair.com); in effect, they use Betfair.com and the odds it quotes as a predictive market. Using this probability function, they applied the Gini coefficient -- which is a concept usually used by economists to measure the inequality of income -- to the problem of how to measure the relative contributions of luck and skill to success in poker.

A Gini coefficient, as applied to poker rather than income, of zero would imply that poker is all luck. A Gini coefficient of one would imply that poker is all skill. The authors of the article found that the Gini coefficient applied to their method of assigning the probability of success to poker players is 24%. In other words, poker (at least by the authors' measure) is 24% skill and 76% luck.

From my personal experiences with poker, I think this split between three-quarters luck and one-quarter skill is about right (at least for no limit hold'em in large tournaments; other types of poker may have a larger skill component). As the article concludes about the Gini coefficient of poker, "It's far enough from zero to make skill obvious, but far enough from one to keep you humble ..."

Labels: betting, economics, Gini coefficient, luck, poker, predictive markets, probability, skill

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