Poker News

Gini’s coefficient

Corrado Gini published his technique for finding a measure of variability in 1912. Brown and Adams, in their Bluff article, “Luck and Skill in Poker,” (2007 July p.104) used Gini’s coefficient to measure the degree of skill extant in tournament poker. Brown and Adams concluded that skill and luck existed in a 1-to-3 ratio for the 2006 WSOP $10,000 buy-in no-limit hold’em tournament, a Gini coefficient of 0.24. Gini’s coefficient ranges from 0 to 1.0: the lower, the luckier; the higher, the more skillful.

The Gini coefficient estimates luck and skill based just on the event’s odds. The posted odds reflect the combined opinion of the public: thus, you can use Gini’s coefficient to measure the betting public’s opinion of the balance between luck and skill for any sport.

Here’s how to do it. First, obtain the odds from someone who would take your action: do not use lines you might find in a newspaper or magazine. 2) Convert those odds to probabilities. 3) Their sum, expressed as fractions, will be more than 1 because of the vigorish, so divide each by their sum to normalize them. 4) Rank all those probabilities. 5) Compute the cumulative probability curve. 6) Find the area between the cumulative probability curve and the uniform cumulative probability. 7) Find the area of the uniform cumulative probability triangle. Compute the ratio of those areas to find the Gini coefficient. Using a modern spreadsheet application, all the computations are trivial. A century ago, I’m certain all those calculations were laborious for Dr. Gini.

The graph shows the cumulative probability curve for the 2008 Division I-A college football championship. The area shown in red, between the curved line and the uniform straight line, divided by the triangle’s area, is Gini’s coefficient, 0.48 in this case.The table shows Gini’s coefficients for the European Soccer Championship, the Div. I-A Championship, the NFL’s Superbowl, the Breeders’ Cup, the Nextel Cup champion, and Brown and Adams’ result for the 2006 WSOP main event.

Can one conclude from the table that there’s less luck in horse racing than in NASCAR auto racing? (Yes.) Note that skill and luck, as measured by Gini’s coefficients computed in the manner described, for European football, for NCAA Division I-A college football, and for the NFL, are about the same.

According to these results, even NASCAR has less luck than poker. So when you get rivered yet again, just remember that luck plays quite a large role in poker. If you didn’t get lucky once in a while, then poker would be an awful game. And, if your opponents didn’t get lucky once in a while, then they wouldn’t even play at your table.

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