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Poker is a Game of Skill — The Proof!

by Brendan Murray |  Published: Nov 01, 2012


Lawrence DiCristina was arrested last year in New York, charged and convicted of running an illegal gambling business and faced up to 10 years in prison for spreading a poker game in a warehouse while taking a five percent rake.

New York courts have long considered that poker contains a sufficient element of chance to constitute gambling under that state’s laws, however, DiCristina was convicted of violating the Illegal Gambling Business Act (IGBA) of 1955, a federal law.

The jury’s verdict, however, didn’t sit well with Federal Judge Jack B. Weinstein, who overturned the conviction and ruled that poker is more of a game of skill than a game of chance.

Weinstein pointed out that the goal of the IGBA was “to give the Federal Government a new substantive weapon which will strike at organized crime’s principal source of revenue: illegal gambling. The statute’s scope did not encompass all state gambling crimes, but only betting, lottery or numbers activity.”

This historic decision marks the first time that a federal court in the U.S. has ever ruled on whether or not poker constitutes a game of skill.

During the trial, DiCristina’s lawyer Kannan Sundaram called an expert witness, Dr. Randal D. Heeb. The statistician, economist, and poker player testified that in the long run, the game favored those with the most skill.

In his testimony, Heeb said, “Over how long does it take for skill to essentially show itself and predominate over the element of chance? And the answer is that it’s sufficiently few number of hands, that a player could reach that number of hands in a few playing sessions. And, again, depending on how skillful that player is, an extremely skillful player, that player’s skill would manifest itself in that player’s results relatively quickly.”

Weinstein agreed, stating in his ruling that “the most skillful [poker] professionals earn the same celestial salaries as professional ballplayers.”

He added in his conclusion, “Neither the text of the IGBA nor its legislative history demonstrate that Congress designed the statute to cover all state gambling offenses. Nor does the definition of gambling include games, such as poker, which are predominated by skill.”


Heeb also commented on the strategy involved in poker and how it differs from other gambling options.

“The player in a poker game is making all of the decisions, making all the plays, which include whether or not to wager on a particular hand and how much. And, in fact, the act of wagering itself is the essence of the decision. So in one sense in a gamble over any other mechanism, whether it was a bet on a baseball game or a bet on the roll of the dice, the wager itself is completely independent of the event being wagered on. Whereas, in poker, the wager is not in the same sense a wager on the outcome. It is the strategic choice that you are making. You are trying to influence the outcome of the game, either by the amount that you are wagering, trying to build up and win more money.”

Heeb discovered that, “many people make a living playing poker and win consistently over time” whereas “it is impossible to make a living and to win consistently playing casino games such as roulette” where chance predominates.

Furthermore, Weinstein addressed the Unlawful Internet Gambling Enforcement Act (UIGEA) of 2006 by allowing data sets from online poker in Heeb’s testimony. Heeb testimony hinged on his analysis of 415 million hands of no-limit hold’em that were played on PokerStars from April of 2010 to March of 2011.

Heeb stated, “The game is a game of skill in exactly the same way, whether it’s played live or played over the internet. So my conclusions carry over exactly to when the exact same game is played, whether it is played in person, played with cards, or played electronically over the internet. The only difference between playing live and playing [online] is that the live game brings in some additional elements of skill which are not available to the internet player.”

The Poker Players Alliance (PPA) filed an amicus curiae brief on the case, presenting arguments and providing expert witnesses for the defense. In a statement, PPA Executive Director John Pappas said, “As we worked for years defending players against vague gambling laws, we have patiently waited for the right opportunity to raise the issue in federal court. Today’s federal court ruling is a major victory for the game of poker and the millions of Americans who enjoy playing it.”

The U.S. attorney’s office has not confirmed whether or not it would appeal.

Online Study

At almost exactly the same time of the U.S. court ruling three academics from the Erasmus School of Economics, Erasmus University Rotterdam, Holland published the first draft of a paper entitled Beyond Chance? The Persistence of Performance in Online Poker.

PhD candidates Rogier J.D. Potter van Loon and Dennie van Dolder and Associate Professor of Finance Martijn J. van den Assem have analysed 415.9 million player hands, purchased from HHDealer between October 2009 and September 2010 across three different stakes levels in cash games — low, medium, and high.

“Our results suggest that skill is an important factor in online poker,” according to van den Assem.

He added that the study was designed to, “…inform the current worldwide debate about the legality of poker and the appropriate taxation of winnings.”

The trio have now submitted the paper to an esteemed academic journal where it will be reviewed in a double-blind process (which could take several years) before, they hope, being published in that journal. The authors say comments on the draft are highly appreciated.

The report is 36 pages long, divided into four sections — data and descriptive statistics, decile analyses, regression analyses, discussion and conclusions — and features over 50 references dating back as far as 1944.

The paper defines skill as “anything that affects a player’s performance other than chance”.

There are many interesting observations, findings and conclusions in the paper including:

• The raw data set contains a total of 76.7 million different hands (the average number of players per is 5.4, yielding 415.9 million different player-hand observations) involving over 500,000 players.
• About 375,000 players played at least one hand at a low stakes table ($0.25 big blind), 222,000 played in a medium stakes game ($2 big blind) and 34,000 played in a large stakes game ($10 big blind). Players hardly switched between these three levels.
• On average, players lost 97 bb/100 after charging of rake. The average win rate is much worse than the ratio of the average number of big blinds lost (47) and hands played (774), or 6 bb/100.
• Only 32 percent of all players in our sample achieved a positive overall result after the deduction of rake. In the absence of rake, 38 percent of all players would have made a profit.

In the regression analyses section the authors bring the following variables into play:

- SPM: the standard performance measure or “win rate”, defined as the average number of big blinds won per hundred hands after correction for rake.
- PRM: the performance robustness measure, defined as the average number of big blinds won per hand after correction for rake divided by its estimated standard error. The estimated standard error is the sample standard deviation of the rake-corrected winnings per hand divided by the square root of the number of hands.
- Hands (log): the natural logarithm of the number of hands played. This variable is a proxy for the experience of players and thus a possible indicator of skill.
- Tightness: one minus the proportion of hands in which a player voluntarily wagered money in the first betting round (“called or raised before the flop”). The degree of tightness is one of the two simple measures that are typically used to broadly categorize players’ playing styles. Generally, tighter play is thought to be indicative of a better player. Common mistakes in poker are to impatiently look for “action” and to overestimate the profitability of playing a given hand.
- Aggressiveness: the number of time a player led the betting (“bet” or “raised”) as a proportion of the total number of times the player voluntarily wagered money (“bet”, “called” or “raised”). The aggression factor is the other of the two simple playing style measures. Aggressive play is generally thought to yield a higher expected performance than passive play, because increasing the cost of playing at the right times can pressure other players to give up stronger cards or to pay off with weaker ones.


In conclusion the report says, “The results provide strong evidence against the hypothesis that poker is a game of pure chance. For a game of pure chance there would be no correlation in the winnings of players across successive time intervals. In our large database for three different stakes levels, however, we do find significant persistence in the performance of players over time.

“On average, players who rank higher (lower) in profitability over the previous subperiod perform better (worse) during the current subperiod. For example, players from the best decile over the first six months of our sample period earn about 30 to 40 big blinds per 100 hands more during the next six months than players from the worst decile.

The paper also finds that, “A player who is in the top ten percent in a given six-month period is more than two times as likely as other players to rank among the top ten percent in the next period. A top one percent player is more than 12 times as likely to end up in the top one percent the next period.

“Players who are characterized by a tight and aggressive playing style generally perform better than their loose and passive opponents. Performance is also related to the number of hands that subjects have played over the previous period: more frequent or experienced players achieve better results.

“This finding can indicate that better players choose to play more and that players learn from playing. Differences between players explain an important share of the differences in their performance”.

To view the full report visit ♠