I'm not a gambling man, but I'll bet this is going to be a controversial study.
The authors recruited 300 poker players - half were defined as 'experts' and the rest were 'average'. Players sat at tables of 6, with 3 experts and 3 average per table, and played 60 hands of Texas Hold 'em. On some tables, there was a fixed limit, on others, no limit. The stakes were fairly small, with each player having just 10 euros to start with, but there were also prizes of up to 500 euros (over $600) for the overall winner.
The trick was that the deals were fixed, with some players getting better cards than others. This was to allow the researchers to measure the effects of luck; the players didn't know this was happening. There were 3 levels of luck, and each table had 2 players of each level: 1 expert and 1 average. Like this:
So what happened? Here's the key finding: the graph is for Fixed Limit but No Limit was much the same -
The authors conclude:
It can be concluded that chance clearly dominates skill; thus, poker should be classified as gamblingBut how expert were these 'experts'? Players were defined as 'experts' if they scored above the median on a questionnaire which asked things like, "How often did you play poker on average per month within the past year?" and "How successful do you regard yourself in terms of poker?" That's obviously a pretty weak measure of expertise. It's entirely self-report, and measures subjective enthusiasm and confidence, rather than skill.
On the other hand though... if you're reading this and thinking "That's BS - but I really am an expert, I really am good at poker" - then you're the kind of person who'd have scored highly on that questionnaire.
Previous work on this question has given mixed results; Dedonno and Detterman argued that "Poker Is A Skill" and found that teaching students some basic strategies made them perform better. Fiedler and Wilcke, however, analyzed a large database of online poker games and found that, while playing about 1000 hands of poker did seem to lead to the development of skill, the majority of online players had much less experience than that, so were at the mercy of chance.
Maybe the 'experts' in this study had played less than 1000 hands?
Meyer G, von Meduna M, Brosowski T, and Hayer T (2012). Is Poker a Game of Skill or Chance? A Quasi-Experimental Study J Gambling Studies DOI: 10.1007/s10899-012-9327-8
55 comments:
The important point for health and society is to warn people that even if they consider themselves "expert poker players" they are going to lose money playing poker on the internet.
NB: Gambling on line might result in a gambling addiction and gambling addictions ( through the internet or not) are very costly on the money and relationship fronts.
"videogame addiction" might exists or not really but gambling addictions do exist.
That is really interesting, particularly how badly, comparatively, 'expert' players do with good hands. If an expert player could learn to play like a beginner when they get good cards. Hm.
I think it's undeniable that it's possible to be successful at poker if you train your self to become an expert poker strategist. It's just self evident from a complete understanding of how the game works.
The key thing about poker is how deceptive it is, it has a quality of convincing you that you're an expert at the point when you understand the rules and start to appreciate the skill aspects of the game. This is very probably an illusion, and only a very select few extremely talented and dedicated people ever actually achieve 'true' skill.
It's possible to design an experiment to show what I describe, but you'd have to go a hell of a lot further than they did in the above study. The effects of skill only bear out over many many games, each with hundreds of hands, rather than just 60.
I nonetheless think it's wise to characterise poker as gambling, and a dangerous form of it at that, for the vast majority of people, that's what it is, and it's far more seductive than roulette.
Saoili: Hmm, maybe the good players did badly with good cards, because they were too cautious.
The "good cards" remember were a set up. Maybe the experts, reasonably, thought "I'm getting good cards but this is unlikely to continue, it is just chance".
So they were conservative.
Whereas the newbies thought "Good cards! I'm on a roll! Raise raise raise" - and it worked but only in this fake setup, in a real game it would fail.
I think mixing in beginners with people who understand things like pot odds and betting strategies probably skews the results somewhat. Playing with beginners can be an absolute nightmare. They follow through on junk hands and don't consider anything but their own cards. It just becomes a lottery, so I'm not surprised by the results of this study. I'd like to see them analyse some of the later stages of WSOP or something.
There are few big problems with how they setup the study. 60 hands first of all is very few. This is especially true because more experienced players often tend to play it safer than beginners when they don't yet have any idea of how the others play. I think this shows very well in both, how little they lose with their bad hands, and why they tend to win more with their better hands.
This being said, poker definitelly is a game of luck in the short run. The skill could only be seen in the very long run of thousands or tens of thousands of hands. This ofcourse is only true when the hands are truly random so I like their idea of fixing the hands to make the required number of hands alot smaller. Unfortunately doing this they lose a big reason why expert players are expert players, they learn how other players play over a large number of hands.
Anyway, I honestly am not all that surprised of this result. It would be interesting to see them repeat the study with seasoned professional players vs. the groups shown here over more hands.
The self reporting of your skill level is very problematic. Poker definitelly is a game in which it's very easy to get pretty long good runs giving you an illusion of competence. And it's only too human to blame the bad runs on bad luck. Thus, the two groups might differ more significantly on their personalities than on their skill in poker.
You would need a LOT more data than what you can accumulate in a lab to overcome the randomness. I played poker online professionally for four years: it's entirely possible to play well and lose over 10,000 hands. Nobody takes their winrate seriously over fewer than 30,000 hands at a particular level. But really the whole luck vs skill question is a red herring. Governments will regulate and tax in different ways according to their whims and they need to offer a moral justification for it, because people really like those.
Nerkful,
Prostitutes are seldom suffering from sex addiction but their online regular clients are at an increase risk of it.
NB: I am not for prohibition at all but for information on the risks involved in playing poker online.
I have thought about this a lot since researching extensively about how to win playing texas holdem and losing loads of money!;-) Of course this study does not use enough hands played since thousands have to be played to cancel out the luck/chance element.
I have noticed that, owing to the increase in the numbers of players over the past few years the old 'experts' have disappeared to be replaced by the 'young guns' who now seem to have a very short career in the game. Which suggests luck is more important. Unlike in chess, a computer based winning program has not emerged yet. I wonder why.
Well... having played poker semi-professionally during my post-doc, I am a bit biased... but, evaluating the study from that point of view...
I think the controls are a very good idea, placed by someone who doesn't really understand poker. In fact, 1) it is crucial to have the full variety of poker options, and 2) to have MANY rounds of play, AND 3) to have an outcome the players care about.
1) Pro players make a lot of their money in conditions where everyone has a bad hand. The ability to win the pot in such situations (which are VERY common) was eliminated from this study.
2) A lot of advanced poker strategy requires reading betting patterns, which requires seeing the same player in many different types of hands, repeatedly. That is, over a long period of time the expert's advantage increases.
3) None of this matters at all unless players are really trying not to lose. Having played in real games a lot, it is very difficult for me to play in games with "just chips" or really small dollar values that people don't care if they lose. Unless the players are taking it seriously, you can't really make expert plays, and most people are incapable of taking it seriously in "just a game" situations.
Anyway, those are my initial thoughts. Good idea, but clearly not designed by someone who understands HOW experts make money.
---------
P.S. The existence of professional players seems to imply that it is a game of skill... there are no professional craps or roulette players for a reason... yet there are pro poker, blackjack, backgammon, and chess players (many of whom make money at all four).
Another problem, depending on who their "pros" were is the possibility for "fancy play syndrome". Low level pros often treat all games as if they are with similar level players, and try to do more mid and high level plays than they should. Against real novices, the best strategy is to play VERY boring, straight poker. Bet good hands, fold bad hands, the type of stuff that gets you killed in mid level games. The best pro's are there to make money, and are happy to sit there and play straightforward strategy. New pros are often there to make money and to show off how smart they are; they lack the discipline to not make fancy plays. (At that point, poker is "just" a job, and is not the sexy life they were looking for.)
Oh... and (sorry for the bandwidth), the edge a pro player has can be remarkably small, and the variance is quite large. (My obsession with poker started when I realized how many layers of statistical coolness was involved.) It would be common for a successful pro's edge to be one or two big blinds an hour in mid-level games. At the highest levels it is a fractional big blind per hour.* Over 150 hands this would often not show up. If the novices were really bad, and were trying, 150 might be enough. Otherwise, flat results are not too surprising. (There are some great professional mathematicians / pro players who have written about this stuff.)
* In a mid-level game with, say, $20 big bets, a 1 bet advantage per hour makes you on par with an assistant manager at a mid-range restaurant. When you are playing in a game with $4,000 big bets, a 1/4 bet per hour edge makes a pretty good living.
Researchers should be embarrassed at publishing such tripe.
60 hands isn't even pretending to be anything close to anything vaguely similar to a usable / valid sample size.
Anything the study says after "60 hands" is 100% irrelevant. It's not a quasi-experimental study - there's nothing experimental about it at all.
You might as well show people 60 seconds from 10 different genres of film and use their reactions to determine which type of films people like the best.
Eric, 150 hands is not nearly enough. Pro players don't consider results to be an assessment of ability until they get to tens of thousands or even 100,000 hands.
So, the power of this study is really miniscule; a null result tells us nothing. This would be like running a study which would require 20 subjects, 50 trials each to have adequate power, but only running 1 trial from 1 subject and publishing the results. Yes, that bad.
The number of hands completely and overwhelmingly overshadows any conclusion and any other potential criticism of this study. It's a joke, basically.
It's a game of skill. Skill to control the situation and not leave it to chance or be interpreted as chance. The difference between a novice and an expert boils down to control. That's what should've been measured and not the other way around. It's not just in poker faces but in public officials. The expert politician doesn't leave much to chance despite the odds in their favour.
Not a very good paper. Poker is a game of high variance, Expected value is positive only over the long run. 60 hands is an insult to anyone with basic statistical literacy. Learning the bias in the lucky and unlucky hands cannot be done in so short a hand - by not updating too wildly the better players (which I suspect were still beginners but better than mean < median) showed better intelligence.
Poker is also a non-deterministic incomplete information game. There are employable strategies that do better than random that take into account not just hand strength but psychology, history and position. Bankroll management is even more important than the game itself. Top players are not even fully human, they use tools to record and analyze all of past history, optimize deviations from optimal play, track opponents and manage income.
In short, this paper was ignant.
Thanks for the comments people. Sounds like there's a consensus that a lot more more hands would be needed for a definitive study.
I think Eric also makes a good point that the existence of professional poker players makes it likely that you can develop poker skills, although it may be that the vast majority of players never get to that level (and if it takes 10,000 hands to demonstrate your skill, a lot of people are just going purely by luck.)
Good lord, there are already poker bots for limit holdem heads up that beat the best human players. Poker surely has a luck factor vs. chess, but it is a game of skill. And "swings", fluctuations due to bad/good cards sometimes last for thousands of hands like in pot limit omaha, where often all money goes into the middle. Here you need discipline, the math is not that tricky, but not giving up a winning strategy in spite of bad swing is key factor of success.
Also playin for your own real money is completely different than play money.
Seems like you can publish anything thats is falsified for years and no one cares, peer-review doesnt work here. Sokal-affair comes to my mind.
This whole "science" paper is not really worth to blog about, sry
NS 17 08 12 at 18:31 wrote:
///I think Eric also makes a good point that the existence of professional poker players makes it likely that you can develop poker skills///
I would rather think that in order to make a living out of "playing" poker some personality traits are mandatory. I suspect antisocial personality traits would be good candidates for a research on that topic thanks to omg 's fascinating comments on that topic.
I must admit I was not very much impressed by the paper in itself but I suffered from the paywall and couldn't read it: the authors may have presented it as a pilot study.
Anyway, any clinician should welcome the publication of studies on poker in an " addiction journal".
This is an awful "study." Deconstructing it would give it far too much credit. This was obviously done by people who don't understand poker, and I question any "expert" who would agree to a play analysis over 60 hands.
Nonsense all around.
Ivana,
Quite right regarding personality! But let's add two caveats:
1) Of course, personality develops.
2) Many pro players are very good at turning that personality on and off. A really early book by Erving Goffman talked about this as an "interaction membrane". Basically, when they are at the table, it is a job, and "I would bust my own grandmother", but when they get up from the table (many) are totally normal people. This isn't too much different from being a pro-athlete (and no, I would never call poker a "sport", but that particular mindset is the same). On the golf course, at a for-money match, the players are going to try to win no matter who their opponent is. Even if seconds afterwards they would generously make sure the same person could cover rent for the month. There are some genuinely "antisocial" players, to be sure, but fewer than you might expect, especially amongst pros who play live.
Regarding time-to detect differences: In the internet world, where you can play multiple tables and afford a smaller edge relative to your average opponent, 10,000 hands is an absolute minimum before you make a conclusion, and probably you want to be closer to 100,000. However, you can get up to that number pretty quickly. Online one can typically play a hand per minute per table, and have multiple tables open (at the lower $ tables). When playing seriously, I could get 10,000 hands in 5 days, no problem. In person, the game is much slower. Say 20 hands an hour, and only one table. In that context you need a much bigger edge, and can probably start to make reliable conclusion about profitability over a thousand hands, a few thousand at most. In either case, the other comments are right that looking for a reliable difference over 60 hands is just being silly.
The variability is just huge. Bankroll management, the discipline to sit down with a small enough percentage of your available money to ride out the variation, is one of the final hurdles that differentiates "mere" skilled players from pros. (Did I mention before the many, many layers of statistical coolness?)
For a low-level introduction, see Chris Ferguson's strategy for building a bankroll (i.e., this). Chris is a top pro with a Ph.D. in computer science, and his father teaches game theory at UCLA. Chris has done some awesome analyses of poker strategy (specifically for two-person play, e.g., this).
Dave W, while I agree with what you're saying, I could see exactly why a professional poker player would want to participate in this study despite it's obviously horrid flaws.
What's better than convincing the general public that poker is a mere game of luck and supposed professionals aren't all that good? I suspect more people may be more willing to part with their money at the table ;)
If Tiger Woods and I played one hole of golf, and he hit it in the water and made a 4, and I made a hole in one, would that mean I'm a better golfer than he is?
According to this study, yes it would.
@laderdragon. And poker would be more dangerous to most people precisely because people overweight both their own skill and the weight that skill itself plays in winning -- both of which are less likely to be assumed in roulette.
I have no idea how someone could write such an article; a no-clue blogger would of done a better job researching the topic than these people.
The way the candidates were chosen and the amount of hands is laughable.
Also, the fact that the hands were "rigged" means nothing as the researchers obviously have no clue how to play the game.
A 5 minute search on Google would have given them a better idea of how to set up an appropriate experiment.
@Ivana Fulli MD
"I suspect antisocial personality traits would be good candidates for a research on that topic thanks to omg 's fascinating comments on that topic."
Anti-social? What? I believe when OMG mentioned "control" he meant "pot-control" (Google it).
And please, don't make baseless assumptions. Phil Galfond, Vanessa Selbst, Phil Gordon, Antonio Esfandiari, Phil Laak, Doyle Brunson, and of course, Daniel Negreanu aren't anywhere near "anti-social". (I missed a bunch.) Granted that's a bit biased because anyone who is winning and isn't a jerk instantly gets TV time.
"gambling addictions (through the internet or not) are very costly on the money and relationship fronts."
This is very true.
"video game addiction"
It exists.
Gosh I've been awfully lucky these last few million hands. To give some context to the comments on variance, in my current database my winrate for no-limit holdem is ~8 big blinds per hundred hands, while the standard deviation is 87bb/100 (it has been shown that the distribution is roughly normal). For those numbers it would take 45,000 hands just to demonstrate difference from zero to a 95% confidence level. For 60 hands the 95% CI is +/-220bb.
"I would rather think that in order to make a living out of "playing" poker some personality traits are mandatory. I suspect antisocial personality traits would be good candidates for a research on that topic thanks to omg 's fascinating comments on that topic."
That's actually quite perceptive. Most of the professionals I've known both online and in real life display some mix of psychopathic, narcissistic, autistic and schizoid traits (myself included) and playing definitely produces some personality changes, although people seem to react in two different ways. Also, oddly enough, informal surveys seem to show that about half of professional players are ENTP on Myers-Briggs, with many of the rest being INTP and almost all being NT-types, which surprised me as I never gave Myers-Briggs much credit.
'surveys seem to show that about half of professional players are ENTP on Myers-Briggs, with many of the rest being INTP and almost all being NT-types, which surprised me as I never gave Myers-Briggs much credit.'
and you still don't need to. Or are you being ironic?
Since when are 60 hands enough to really identify a trend? One of the major skills of experts in poker is probably that they recognize and use the patterns in other players way faster.
No joke; this was a terrible study, just for the simple reason the "expert" group was composed of people who judged themselves "experts". That is a supreme failing of an experiment. Dunning-Kruger effect, unreliable witness, etc. There sure are some ignorant "scientists" out there who probably think they're quite "expert."
Zach,
Paywall made me trust Neuroskeptic's writing:
///The authors concluded:
It can be concluded that chance clearly dominates skill; thus, poker should be classified as gambling But how expert were these 'experts'///
I really believe that this study is very interesting and useful-be it only because you conclude with others "poker experts" that, unless you play indeed a lot, poker on line is about chance.
This is important since gambling addiction is not something you can cure easily.
It is unregognised as such when so many people shout loud about videogame addiction who might not even exist.
Eric,
Thanks for the compliment and the informations on poker. Coming from you, I appreciate both greatly.As precious omg will put it : I am a great fan of your blog.
In France, the director of the Paris VI University "Laboratoire de Probabilités et Modèles Aléatoires (LPMA)", Pr Gilles Pagès,
http://www.proba.jussieu.fr/dw/doku.php?id=users:pages:index#publications_et_travaux
uses his strikingly good and smart looks and intelectual gifts in math but also in the teaching art and with the French language -for a mathematician academic that is- trying to educate the public on the probability to win money at the loteries. He spoke on television and even wrote a book on the subject:
///En passant par hasard, les probabilités dans la vie de tous les jours/// Gilles Pagès with C. Bouzitat (collab. F. Carrance, F. Petit)Vuibert 1999 (3è édition 2003)
On his own admission (one of my sons was lucky enough to haver him as a teacher as an undergrad)his efforts have not been yet rewarded by a general public awareness of the no win probabilities of "chance money gaming" and not even by his all his readers increased awareness judging by the letters he received asking for tips to win at the lottery...
And poker on line is just chance money gaming with very few exceptions like yourself and the "professional quality players".
My brief initial thoughts:
The sample size of 60 hands seems like it can't possibly be enough. It would depend on the rest of their methodology.
More important, potentially, than the number of hands played is the manner in which the hands were constructed. In particular, I'm curious as to how the rigged "better-than-average" and "worse-than-average" cards are defined. Did they just rig the preflop distributions to be more favorable starting hands for the good-cards case? Or does better-than-average mean they are literally rigging the deal of the entire hand such that the 74s dealt to the good-cards UTG seat ends up rivering trips? (Yeah, you can see how one of these would quite decisively favor the player making demonstrably bad decisions.) The fact that the average player outperforms the expert only in the good-cards would lead me to strongly suspect that the authors of the experiment have unintentionally built this rigging condition in a way that favors incorrect play.
Alternatively, as other commenters have noted, there's a lot of reason to doubt the validity of a self-identification of participants as experienced or not, as most poker players have inaccurate assessments of their ability and success.
Did the subjects know about the rigged conditions, and whether or not they were in good or bad seats? If they did, then the different types of players may have approached this information in different ways. If they didn't, then more experienced poker players would be more likely to continue to play correctly even if they were in the good-cards seat, whereas a less-informed poker player would "play a rush".
Overall, I see a lot of opportunity for potential misdesign by an experimenter who wasn't careful or wasn't deeply familiar with poker. The authors should expect significant scrutiny on both their methods and their credentials. That's as far as I'll speculate from this information.
I'd love to read the full study, but I'm not going to pay for it. I'm working on a broad essay on skill vs. luck in poker myself and would be grateful for the opportunity to better-understand the details of this study, if the authors were willing to share it with me.
It's pretty laughable that people who study gambling can consider 60 hands per table to be a meaningful sample size. Look at the studies that analyze databases of 600,000,000 hands and determine that players some players win money in the long run over a sample that almost cannot possibly be luck. You took a game that has an enormous amount of variance, rigged the cards and played for about an hour and a half and concluded that, even though there are 1000s of people who have played for a living for between 5 years and a decade on the internet, poker is dominated by luck and should be considered gambling. Seems like a really lazy study to be honest.
Mike Stein,
Have you tried to send an e-mail and ask politely for the article?
You have credential to do so that I haven't
There's a reason no sports leagues play one game, and call it the end of the season. There's variance in everything, and in poker there's more than in most other forms of competition.
If an NFL team misses a field goal due to a gust of wind, and exits the playoffs because of it, that doesn't mean they are the worse team. They just got unlucky
You need to run at least 50,000 hands for each player, before having any idea about their skill level.
You have no idea what you are talking about, but thanks for the standard royal flush 5-card draw poker hand picture, that always accompanies poker articles written by people who don't understand the game.
Don't tell me... some of the winning players didn't even make a royal flush, in any of their 60 hands? Poker must be about luck then.
ha ha - if anything this study actually proves that there is skill in poker. There are far more bad hands than good hands - not an equal amount as portrayed in the study. The skilled player with the more cautious and selective approach loses less on the bad hands that are the majority, but due to caution wins slightly less than the poor player on the minority of better hands. Overall though he shows a profit.
Anonymous said...29 August 2012 09:25
/// ha ha - if anything this study actually proves that there is skill in poker. There are far more bad hands than good hands - not an equal amount as portrayed in the study. The skilled player with the more cautious and selective approach loses less on the bad hands that are the majority, but due to caution wins slightly less than the poor player on the minority of better hands. Overall though he shows a profit.///
Thank you for your useful comment.
People should be warned that unless they are very talented and very good at playing poker they will lose money playing poker on the internet where ptofessional players will make a living with their money.
Poker (online or not) is a game of skill in the long run. Poker online is more skill dependent than live. You can play much more hands online and you can also have software to analyze your sessions to identify leaks in your game.
You have to play at least 100.000 hands in cash games to figure out if you are a winning player or not.
To become a winning poker player you have to work hard, study the game, adapt to your opponents and be willing to improve your game on a daily basis.
Like I said, poker is a skill game in the long run.
Just to make some irony and fun to this joke study, will had what someone write on a forum about this study (attention this has a lot of irony!!):
"Well, at least I know that Ivey, Durr, Galfond, etc are just lucky. Probably means I'll be shipping the main in '13 obv. If anyone wants to trade, i've got 13 poker books. Will trade for a lucky rabbit's foot. Must provide a 60 hand sample to prove rabbit's food is one of the lucky ones."
This test is too nice. Poker is ALL luck. You either have the best hand or you don't. It's 50/50. Science overthinking things again. Condolences from kazhakstan. Amen
This test is too nice. Poker is ALL luck. You either have the best hand or you don't. It's 50/50. Science overthinking things again. Condolences from kazhakstan. Amen
Hey anonymous you play anything but poker, right?
If poker was all luck and 50/50 then professional poker players were losing players.
If poker was all about having the best hand then all the books about poker were only one page.
I think there are a lot of people who are jealously about the winning poker players.
Hard work and dedication pays off in the long run. I had played more than 300.000 hands in cash games and I have a 6bb/100 win rate (6 big blinds per 100 hands).
Poker is all about probabilities and bankroll management, is a mathematical game where variance exists, so you will losing cycles sometimes, it's part of the game. In the long run poker is a skill game.
Just to give an ideia of some concepts behind poker theory: Expected value, Mathematical expectation in poker, pot odds, implied odds, reverse implied odds, tournament odds, set mining, SPR (Stack Pot Ratio), Equity, cold equity, stack size, effective stack, metagame, hand reading, pot control, position, fold equity, (...)
Do you guys master those concepts?? Do you guys have ever read anything about those concepts?? I don't think so, if poker was all about luck and 50/50 situations, then we were playing a cards game only. The thing is, poker is more than the cards you hold in your hand.
@luis
I'm pretty sure that was a troll post.
First i wanna sorry for my bad english.
I play poker in low levels (very low) to pay my bills (university, books, food)i play like 4000 hands a day. Somedays i win a lot , others i dont win, other i breakeven, in the end of the month i have my winrate (that is positive) and i widrawal my money. Just had like 2losing months in 3years... My WR its big (the levels are easy for me. I play 16tables SH online (80 hands per hour) i play like 1300 hands per hour. 60 hands its absoluty nothing. This study its a big, big, big joke.
Go see nanonoko graph (now PTR its closed)... its just 2 Million USD in a 5M hands sample + bonus.
^^
But.. for me its ok that everyone thinks that poker its just luck (its the best thing - one of the biggest secret of poker its that (ppl thinking they lose all their money everyday cos bad luck; so they sit again and again ;) they dont realize why.
What you will notice is that the sample size is extremely small, only 60 hands.
If poker is just luck, how is Phil Ivey still winning so much money after all these years?
it cannot be good for poker when apparently legitimate institutions put this stuff out. people put a lot of trust in authority, but it is players who truly have the authority to speak on this subject.
justin
Just a quick follow-up, I did in fact correspond with the lead author of this paper, and he is willing to share the paper with anybody who is curious to read it if you contact him directly.
He was also open to constructive criticism and was very aware of the limitations and shortcomings of the study overall, though it does seem to be specifically-tailored towards German law which defines whether a game is skill or luck based on the playing habits of the "average player" (and perhaps the average poker player, depending how it's defined, plays for such a short amount of time that skill does not have time to "overtake" luck in the Central Limit Theorem sense). I don't think this is a good definition or approach overall, but it seems to be the right context for Germany.
Wow, thanks for the info Mike!
By that particular, German legal criterion things are quite different. So, the goal was not, as we had suspected, to really be about the "skilled" players?
Still, we might ask what a fair criterion would be for testing the average player. For an average player against a bunch of other average players, you will get a normal distribution of success, which could be interpreted as luck. Or, it could be interpreted as the logical result of a game played by people who all have equal skill levels. (Imagine a chess tournament in which 100 people each play 40 matches, but everyone has the same ranking.)
If that is your criterion, and you wanted to show that poker was a game of skill, you might have average players pitted against someone making moves (bet, check, fold) at random. I would wager quite a large amount of money that even an "average" poker player does a lot better than a completely unskilled opponent.
Thanks for the comments. That's interesting info.
The problem with the "luck" graph is that inexperienced players will play good hands way too aggressively. The other donks call them with worse cards and in the short run the average players might have won more money. However, this "skill" of the players is wrongly measured. It doesn't necessarily matter that the average players won more money with the good hands, it just matters who makes the long-term profitable decision.
Funny how all the gamblers protect their favorite game of luck.
No No you need lots more hands, the good players were too cautious.
And the funniest comment of them all - When you play against beginners it's like a lottery - wow really - it's a game of luck after all loooooool
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