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Tuesday, July 19, 2011

The Role of Skill and Chance in Poker

Skill Or Chance In Poker: Legal Perspectives

By Ingo Fielder Phd. and K. Preston Oade J.D. 

Most gambling opportunities are driven by chance. Poker is not. Skill affects results, but how large are these effects? And does this make any difference for the legislator or the juror?

One way to identify games to be regulated is the so-called “predominance test”: If a game’s skill elements predominate over the chance elements, it is considered a “game of skill” and – in many jurisdictions - usually not subject to any restrictions.

Many jurisdictions outside the U.S. use some form of the “predominance test” with various results. In the U.S., however, the legal issue of whether poker is “gambling” depends on state law, and many states do not use the predominance test, making the skill/chance debate legally irrelevant[1]. Most of those approaches are neither coherent nor sophisticated but instead lump too many things together. The result are laws which are constantly under debate.

Criteria are needed to distinguish between different games. Arthur Reber, a psychology professor, made a good step in the right direction by pointing out that every game has two dimensions: expectation and flexibility. Expectation is a game’s expected value; flexibility is the possibility to modify the payoffs. While most gambling has negative expectation and no flexibility, poker can either be played with positive or negative expectation and flexibility exists. But is the flexibility in poker sufficient to make it a game of skill?

Until now nearly all efforts to answer this question were qualitative. Courts and legal scholars listed various reasons for poker being a game of chance or skill, but did not quantify the relative amounts of skill and chance. However, Ingo Fiedler and Jan-Philipp Rock of the University of Hamburg, recently published the first quantitative analysis in Gaming Law Review and Economics.

They compared the relative skill, represented by players’ net expected value with the chance elements, represented by the standard deviation of the outcomes. Their approach makes clear that there is a third dimension involved in games: repetitions. While the expected value increases in proportion to the repetitions (n), the standard error of the mean increases only in the square root of n: skill adds up, chance cancels out.

If only one hand of poker is played, chance dominates skill; if poker is repeated infinitively, skill dominates chance. In between, there is a threshold where the outcomes (gains or losses) of a poker player are 50% due to skill and 50% due to chance. It’s called Critical Repetition Frequency (CRF) and is different for every player. The higher his expected value (positive or negative), the faster he reaches CRF.

The answer to the question of predominance therefore depends on 1) the relative skill of the players, 2) the chance elements of the game, and 3) repetitions. Legislators should consider all three dimensions. The best way is to target the average player and determine if he reaches his CRF or not.

Based on a 51,761 player sample Fiedler and Rock showed that the CRF for the median no limit midstakes online cash game player is about 1,000 hands. When he plays more than one thousand hands, the outcome is dominated by skill and not by chance.

This number is surprisingly low because the median player is a big loser. In 100 hands he loses 32 big blinds! This lack of skill quickly dominates chance.  For a player winning 10BB/100h it takes much longer, about 30,000 hands. But legally,the average player should matter. The crucial question is whether the average poker player plays 1,000 hands. If yes, that limit holdem cash game is a game of skill under the predominance test.  

In tournament poker the CRF is not as easy to calculate. The effect of skill varies depending on the amount of starting chips, blind structure and length of the rounds. The skill component rises monotonically in the proportion of stack sizes to the blinds. A tournament with 5-10 big blinds is basically push or fold and therefore involves only one betting decision, which leaves little room for skill.  A tournament with an effective stack of 250 big blinds requires much more skill.

The degree of skill relative to chance also varies between cash games and tournaments. In every tournament, the proportion of stack sizes to blinds decreases constantly and eventually reaches a very low level.  In this final stage of the tournament – which is most important for the overall result – the outcome of the game often depends mostly on chance. 

The impact of skill therefore varies highly according to the tournament structure and there is no general answer for tournaments. But as a guideline, most online tournaments are played with small stakes and therefore involve less skill than cash games. But tournaments with very large stacks relative to the blinds usually involve considerable skill.     

Poker’s situational nature therefore seems to preclude any sweeping generalizations about whether it is primarily a game of skill or chance. It depends on the nature of the particular game, the players’ skill, and the number of hands actually played. 

This seems to be confirmed by jury verdicts which have applied the predominance test.  These verdicts – which set no legal precedent precisely because each case is based on its own unique facts – vary from case to case.  In a 2006 U.K case, London’s Gutshot Club was  found quilty by a jury of violating a law against operating a poker club taking a rake without a license. The law contained an exception, however, for any games that are “predominately based on skill.  The jury, however, was not persuaded.[2]

The predominance test does not legalize poker. It just provides a defense to a charge of gambling if you can prove that the particular game favored skill over chance. This fact must be proved like any other disputed fact. The answer depends on the factors discussed here and how particular judges and juries interpret them.. 

Defining and prohibiting “gambling” by reference to the role played by chance is largely a moral and social judgment made by each state legislator. Juries often make the same judgment when presented with the issue of whether the outcome of a particular game is determined mainly by chance or skill. When deciding this issue, the moral and social values of each jury member can easily prevail over math or statistical models presented by expert witnesses. 

Whether poker is defined as “gambling” under the various laws of the 50 U.S. States has historically depended on religion, morals or politics – not math or logic. And it remains to be seen if it ever will. It is a mathematical fact, however, that skill will eventually dominate the chance elements in poker. The only question is how many repetitions are required. The answer depends on the different players and the structure of each individual game.

Copyright by Ingo Fielder and Preston Oade, 2010.  All rights reserved.  

[1] See Recreational Gambling Laws State by State; Pennsylvania to Wyoming, Hartley Henderson, http://majorwager.com/index.cfm?page=27&show_column=578
[2] See Hartley Henderson, Major Wager.com, 02-17-2008. Recent verdicts in some U.S. states have gone the other way. 

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