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I just read a NY Times article which claims that a US Judge ruled that poker is a game of skill and not one of chance.

In a ruling that goes to the heart of what it means to play poker, Judge Jack B. Weinstein tossed out the conviction and vacated the indictment of the man who ran that gambling business. The judge’s reason: poker is more a game of skill than a game of chance, so game operators should not be prosecuted under the federal law the prohibits running an illegal gambling business.

Is there any evidence to support that poker is a game of skill and not luck?

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    This is a largely meaningless question. (a) There are clearly strong elements of chance. (b) There are clearly elements of skill, including betting strategies, bluffing strategies, evaluating probabilities, observation. (c) There are lots of forms of poker, with varying reliance on chance. (d) Over long periods, small skill tend to overcome luck. If you have a 1% advantage PER HAND over an opponent, chance is more important than skill. Play 10,000 hands, and the situation reverses. – Oddthinking Dec 22 '12 at 7:04
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    John Hodgman, in his definitive book 'More Information Than You Require', points out that "Poker isn't a game of luck, poker is a game of chance" – Richard Terrett Dec 22 '12 at 7:16
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    @Oddthinking, blackjack also clearly has (a) strong elements of chance, and (b) elements of skill, however the game is ultimately one of luck, because even with perfect play, you will lose the game unless you are lucky. – Kenshin Dec 22 '12 at 8:12
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    @Chris: I'm afraid the BlackJack analogy isn't helping. Your argument seems to be "If the expected outcome is negative, it is luck-based, by definition." That isn't a sensible definition of luck-based (or to Richard's point: chance-based). (I'm ignoring card-counting in Blackjack as an unnecessary distraction.) – Oddthinking Dec 22 '12 at 8:21
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    Yes, I fail to see the connection - because there isn't one. A skilled (non-card-counting) Blackjack player (playing "basic strategy") under typical casino rules has a negative expected value (around the -0.5% mark, depending on the rules). A non-skilled Blackjack player will make sub-optimal decisions, and will (on average) lose at a much higher rate. Therefore, Blackjack has a strong element of skill. It also has a strong element of chance - but the impact of chance tends to even out over time. – Oddthinking Dec 22 '12 at 8:29
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In tournament play, which is not a particularly long trial, there seems to be evidence that skill plays an important role:

Examining the performance in the 2010 World Series of Poker group of poker players identified as being highly skilled prior to the start of the events. Those players identified a priori as being highly skilled achieved an average return on investment of over 30 percent, compared to a -15 percent for all other players. This large gap in returns is strong evidence in support of the idea that poker is a game of skill.

The Role of Skill versus Luck in Poker: Evidence from the World Series of Poker, Levitt & Miles, 2011.

I don't know that it's valid to claim that the influence of skill is more than that of chance but it's interesting to note that the ROI magnitude for "highly skilled" players (30%) is greater than the magnitude (15%) of others.

In table play, I cannot find a reference to something I recall, which is that skill only begins to statistically dominate after several thousand hands (~2000-3000 IIRC). I believe that is only relevant to "correct" play based on pot odds and ignores psychological aspects, betting and bluffing strategies, etc.

  • While both answers were good, the reference provided was very interesting in this one. – Kenshin Dec 26 '12 at 2:57
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There is no doubt there is an element of chance involved in Poker. (Extreme example: If you are dealt a Royal Flush, you cannot lose.)

I am taking the question to mean "Is there ANY skill involved in Poker?".

I have to admit I find the answer to be blindingly obvious.

To give an extreme example, if a player had a sub-optimal strategy of betting 80% of their bank on every hand, no matter what its strength, would be quickly defeated by a moderately skilled competitor who merely folded when their cards were below the median strength.

Nonetheless, it has been studied:

  • MICHAEL A. DEDONNO AND DOUGLAS K. DETTERMAN, Poker Is a Skill, GAMING LAW REVIEW, Volume 12, Number 1, 2008, DOI: 10.1089/glr.2008.12105

They looked at a somewhat tighter question - could simple instruction improve the expected outcome of some non-expert players?

The unequivocal finding is that poker is a game of skill. In both studies, participants who were instructed outperformed those who were not instructed. Given that poker is a complex skill, it is somewhat surprising that even elementary instructions and limited practice had an effect.

The reason that poker appears to be a game of luck is that the reliability of any short session is low. In a casino game of poker, about 25 hands are dealt per hour. In Study 2, participants played 720 hands equivalent to about 30 hours of casino play. Study 2 met the psychometric qualification for moderate reliability of a psychometric task. What this suggests is that obtaining accurate estimates of poker ability may not be easy. Luck (random factors) disguises the fact that poker is a game of skill. However, as these studies show, skill is the determining factor in long-term outcome.

  • You support posting evidence of a claim in "meta", but you seem to have blatantly disregarded the link that I posted in the question. The Judge declared that poker is not a form of gambling because of the skill involved. Many forms of gambling have components of skill, but I'm sure no judge is going to say that blackjack shouldn't be classed as gambling. The issue is thus, whether or not the skill element is greater than the element of luck. – Kenshin Dec 22 '12 at 8:40
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    Ahh... maybe your question isn't "Is the skill element greater than the luck element?" (which I maintain, is meaningless) but is "Does US Law consider it a form of gambling?", which would be resolved by posting a link to the court papers with a decision made by the judge? If this is a question of scientific fact, what an arbitrary authority decides is not definitive evidence. If it is a question of law, then it is the only thing that matters. (Note: I am still flailing, trying to figure out what the question means.) – Oddthinking Dec 22 '12 at 8:48
  • @Chris: Doesn't this answer the question in the comment "Is it possible for a poker player to gain a long term-edge over his opponents?" – Oddthinking Dec 22 '12 at 8:49
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    Good try, Chris, but I have explained several times why there is a problem with the question. The issue isn't that I am naive about the field and don't understand the question. The issue is that I understand the field and the question needs clarifying. – Oddthinking Dec 22 '12 at 9:07
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    I think your sub optimal strategy approach is a bit flawed. It's along the same line of arguing that coin toss is a game of skill because you could swallow the coin while trying to flip it. – MrDosu Feb 13 '15 at 17:02
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I think the "more" part of the (title) question is difficult to answer. You need a metric for "more".

Several papers have used the metric proposed in "On a relative measure of skill for games with chance elements": a scale of 0 to 1 for the skill element, calculated as

skill = (potential learning effect) / (potential learning effect + random effect)

For a single-player game, this comes down to:

skill = (Gm - G0) / (Gu - G0)

where the G's are the expected net gains of three players

  • '0': a beginner who plays the game in the naive way of somebody who has just mastered the rules of the game.

  • 'm': a real average player who can be thought to represent the vast majority of players.

  • 'u': a virtual average player whom we tell in advance (i.e. before he has to decide) the outcome of the chance elements.

As examples, they give for American Roulette Gu = 35 and Gm = -1/74 and G0 is -1/37 assuming the beginner won't play a simple strategy, which gives a skill of 0.0004. If the beginner does play a simple strategy like just red/black, then the skill is 0 (there's nothing more to be learned about Roulette than that). Using computer simulation, for Blackjack they determined Gm = 0.11, Gu = 27, and take G0 = -0.057 for a "mimic the dealer" beginner strategy, which gives a skill of 0.002.

Unfortunately, this metric is difficult to calculate for more interesting games, like any full-fledged poker variant. Several papers have calculated this skill value for simplified versions of poker.

The papers emphasise however that the exact skill value depends on the definition/assumption of beginners’ behavior.

Another way to tackle this problem is experimentally as in the accepted answer, but do note that the NBER paper discussed there is using a proxies for skill past winning and measures derived from that (like rankings), so it is measuring more of an autocorrelation (past winnings predicting present ones). What's more important (see figure 1 in that paper) is that the cash structure of the tournament is highly convex, so won 30% more money doesn't really mean would win 30% more games.

So, a slightly older paper has results I think are worth mentioning.

"Quantifying Skill in Games—Theory and Empirical Evidence for Poker" analyzed two on-line Poker sites' data and came up with this summary:

enter image description here

The median winrate in that table is an absolute value and expressed in BBs (big blinds) adjusted for rake, so that the numbers are comparable across different-BB (stake) groups. The sigma is the standard deviation of that winrate with the odd twist that they say the could not compute it except for the last group, so that's why the entire column has the same value. The two CRFs are calculated simply as 4sigma/winrate^2 and respectively 9sigma/winrate^2. The theoretical interpretation of the CRF is the number of games it would take for a player to reach his 50%/50% chance-vs-skill cut-off point, illustrated below

enter image description here

From the table, it's obvious that whom one is playing against makes a big difference in winrate and thus CRF. Absolute winrate goes down pretty fast (and CRF goes up) with the experience group because the big losers go away quickly. So rather than having a theoretical discussion as to the beginner's behavior, now one has to decide how clueless of a player one allows into the sample. The authors note that playing 1,000 hands may seem like a big number, but can be reached in 13 hours of online play (and about 33 hours in a brick-and-mortar casino).

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The supreme court of Sweden decided that poker (texas holdem) is a game of both skill and chance.

  • The article headline and subtitle are:

    HD: Både tur och skicklighet i poker

    Pokerspelet texas holdem handlar både om tur och skicklighet, slår Högsta Domstolen (HD) fast i en ovanlig dom.

  • Which in English via Google translate:

    HD: Both luck and skill in poker

    Poker game texas holdem matter of both luck and skill, hitting the Supreme Court (HD) caught in an unusual sentence.

The court decided that while the game is a game mostly of chance in a tournament form it is a game of skill.

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    This appears to be pretty much a repeat of the claim - the evidence is no stronger than original claim. (I maintain my objection the claim is meaningless.) – Oddthinking Feb 13 '15 at 8:42
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More than most card games, poker is a game of psychology and reading other people.

There is an element of chance to each individual hand, but the game isn't just one hand, it's a whole series. The winner isn't the person who won the most hands, but the one who wins the most money.

The best players learn to read cues from their opponents, to gauge just how strongly that person feels about their hand. Maybe how they hold their cards, their posture, nervous gestures, maybe just their eyes... do they have a strong hand, or are they bluffing? How strongly do you raise when you have a good hand? Enough to up the ante, but not so much you scare off the other players. You want to win the hand after they've matched your raises, not after they folded. And, how do they meet your raises? Hesitantly, or confidently and topping your raise? And... are they bluffing with that confident response, or are they holding aces over kings, and just luring you in? It will cost you the next raise, to find out.

There is definitely skill, and possibly even a bit of innate ability involved in being a top poker player. The best ones know when to meet a challenge, and when to fold, by reading their opponents.

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