New Study Suggests Poker Is Game Of Skill

Three academics from the Erasmus School of Economics, Erasmus University Rotterdam, Holland have 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,

They concluded that,“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 http://ssrn.com/abstract=2129879.

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