Via the Seriously, Science? blog comes what looks like a pretty bad paper:

Is poker a game of skill or chance? A quasi-experimental study

Gerhard Meyer, Marc von Meduna, Tim Brosowski, Tobias HayerDue to intensive marketing and the rapid growth of online gambling, poker currently enjoys great popularity among large sections of the population. Although poker is legally a game of chance in most countries, some (particularly operators of private poker web sites) argue that it should be regarded as a game of skill or sport because the outcome of the game primarily depends on individual aptitude and skill. The available findings indicate that skill plays a meaningful role; however, serious methodological weaknesses and the absence of reliable information regarding the relative importance of chance and skill considerably limit the validity of extant research. Adopting a quasi-experimental approach, the present study examined the extent to which the influence of poker playing skill was more important than card distribution. Three average players and three experts sat down at a six-player table and played 60 computer-based hands of the poker variant “Texas Hold’em” for money. In each hand, one of the average players and one expert received (a) better-than-average cards (winner’s box), (b) average cards (neutral box) and (c) worse-than-average cards (loser’s box). The standardized manipulation of the card distribution controlled the factor of chance to determine differences in performance between the average and expert groups. Overall, 150 individuals participated in a “fixed-limit” game variant, and 150 individuals participated in a “no-limit” game variant. ANOVA results showed that experts did not outperform average players in terms of final cash balance…

(It’s a long abstract, I didn’t copy the whole thing.) The question “Is poker a game of skill or chance?” is a very important one, not least for legal reasons, as governments decide how to regulate the activity. However, while it’s an important question, it’s not actually an interesting one, since the answer is completely obvious: while chance is obviously an element, poker is a game of skill.

Note that chance is an element in many acknowledged games of skill, including things like baseball and basketball. (You’ve heard of “batting averages,” right?) But nobody worries about whether baseball is a game of skill, because there are obvious skill-based factors involved, like strength and hand-eye coordination. So let’s confine our attention to “decision games,” where all you do is sit down and make decisions about one thing or another. This includes games without a probabilistic component, like chess or go, but here we’re interested in games in which chance definitely enters, like poker or blackjack or Monopoly. Call these “probabilistic decision games.” (Presumably there is some accepted terminology for all these things, but I’m just making these terms up.)

So, when does a probabilistic decision game qualify as a “game of skill”? I suggest it does when the following criteria are met:

- There are different possible strategies a player could choose.
- Some strategies do better than others.
- The ideal “dominant strategy” is not known.

It seems perfectly obvious to me that any game fitting these criteria necessarily involves an element of skill — what’s the best strategy to use? It’s also obvious that poker certainly qualifies, as would Monopoly. Games like blackjack or craps do not, since the best possible strategy (or “least bad,” since these games are definite losers in the long run) is known. Among players using that strategy, there’s no more room for skill (outside card-counting or other forms of cheating.)

Nevertheless, people continue to act like this is an interesting question. In the case of this new study, the methodology is pretty crappy, as dissected here. Most obviously, the sample size is laughably small. Each player played only sixty hands; that’s about two hours at a cardroom table, or maybe fifteen minutes or less at a fast online site. And any poker player knows that the variance in the game is quite large, even for the best players; true skill doesn’t show up until a much longer run than that.

More subtly, but worse, the game that was studied wasn’t really poker. If I’m understanding the paper correctly, the cards weren’t dealt randomly, but with pre-determined better-than-average/average/worse-than-average hands. This makes it easy to compare results from different occurrences of the experiment, but it’s not real poker! Crucially, it seems like the players didn’t know about this fake dealing. But one of the crucial elements of skill in poker is understanding the possible distribution of beginning hands. Another element is getting to know your opponents over time, which this experiment doesn’t seem to have allowed for.

On Black Friday in 2011, government officials swept in and locked the accounts of players (including me) on online sites PokerStars and Full Tilt. Part of the reason was alleged corruption on the part of the owners of the sites, but part was because (under certain interpretations of the law) it’s illegal to play poker online in the US. Hopefully someday we’ll grow up and allow adults to place wagers with other adults in the privacy of their own computers.

The one and only dominant strategic skill a potential poker player can choose to never lose is a decision not to play the game (:-)

Say for instance you start going for flushes instead of straights, well a flush beats a straight because it is statistically harder to get a flush. But then how is this even possible? There are only four different suits. That means that one in four cards in the deck can give you a possible flush. On the other hand a straight has to have five particular cards in a row that only have four of each card in the deck. So then do you want to fish for only certain groups of four possible cards, or do you want to fish for any of the one in four cards in the whole deck?

I would go for the flush! The last card you need for a straight could at most only have eight possible cards you could get to complete it, and that is if none of them where drawn and you can complete it by getting the next higher or lower number card. It can become fewer than getting one in four cards in the deck if you need a card in the middle of the straight or it is a high or low straight.

But, in online poker there is always some lucky guy that will complete a straight pushing most of their chips before the river. I can’t help but wonder how often they are able to pull that off. I surely can never pull it off! But then I think that most of the people at the table are just so bad, that one of them is bound to pull it off on me if they all call my “bluff”…

Anyways, I think there is a old western would be mathematician at the O.K. Corral to blame on flush and straight statistics. It seems like if you assume that the dealer evenly distributed the suits in the deal that you would have a one in four chance in landing a flush on the river. Then statistically it is most likely that the dealer would always deal an even number of each suit out of the deck.

But, then you start playing enough poker, you start to think that past situations have a factor in determining current outcomes even though they do not directly affect it. (You stop hitting your flushes) Like in the NES Practice test, it gives a problem if you role a dice and get a six twice on a six sided die, what are the odds that you will roll another six? I thought it would be six times six times six. But, then they say the correct answer is just one out of six.

I think if you took this kind of thinking to Vegas you would be bound to lose everything. You would have to roll it about six times to insure that you roll a six. Then you would have to roll it six times more to insure that you rolled two six’s in a row and six times more than that to insure that you finally got three six’s in a row.

Would it be wise to put everything on black when black has already hit five times in a row on the roulette wheel? If it took 64 (2x2x2x2x2x2 not counting the green space) spins of the wheel to get six blacks in a row, I would put my money on red every time the wheel did hit black five times in a row.

You would think that with every black in row it would be far more unlikely to hit another black the more times in a row it hit, since there is only a 50% chance that it should hit black. If over a large number of spins they will eventually come out even, there would need to be more reds in order to make up for that in the upcoming spins or you could just end up getting a lot more blacks than you do reds even though you increased the number of spins. But, over a large sample there should be 50% reds and 50% blacks no matter how many times in a row you got one color or the other.

I think it would be nice to live in a world where a roulette wheel could easily hit black a hundred times in a row and then red a hundred times on a regular basis, because it just had an equal chance to hit it every time.

Truly a game of skill and wits poker is, but it really depends on how quick you can react to the events.

Coming at it from the other direction… Even in decision-based games which are not probabilistic (like chess), in practice there is a non-trivial element of luck nevertheless — at least when it is played by humans. From a mathematical sense, of course there is not, but there are all kinds of factors outside of the players’ direct control which can affect their performance. Suppose you get food poisoning and start to feel queasy part way through a game. Or perhaps you were calculating an okay-but-subpar variation, and just at that moment a fly crosses your field of vision and draws your attention to another part of the board, where you see a superior move.

As far as poker, I suppose it’s an interesting paradox that while a single hand of poker is dominantly luck-based, a sufficiently large series of hands is dominantly skill-based. This is a difficult idea for some people to wrap their heads around, I guess.

Some interesting discussion here, especially as I only came here to find out if the Universe is a black hole. I wasn’t expecting to find any poker! I have been a professional poker player since 2006.

This is the comment I found most interesting :

“Liv Boeree is a very successful poker play. She graduated with a 1st class degree in Astrophysics only a few years ago. I dont think she would have been so successful if it was just luck. Moreover, her degree no doubt helped her to understand probability !”

I can assure you that there are _tournament_ poker players who are more successful through nothing more than luck. Tournament poker allows for the possibility of parleying a small amount of money into a large amount very quickly, for example the famous case of Chris Moneymaker winning $2.5 million in the World Series of Poker from an initial outlay of $40. Now, Chris is actually a better player than many give him credit for in my opinion, I’ve just cited him as a well-known example. With so many people trying to do this, some succeed. Brunson’s analogy comparing a big tournament to a lottery in which the better players have more tickets is apt. But sometimes the guy with one ticket wins. Not only that, he can then attract sponsorship (essentially paid buyins into future events), or at least he could until the bottom fell out of that particular market. Fooled By Randomness is indeed highly relevant to poker, as I say particularly _tournament_ poker – cash is a different animal entirely and someone with a good track record over time is far more likely to actually be a good player.

Also you really don’t need a degree in astrophysics to understand probability well enough to apply it to poker 🙂

Andy.