Poker Is a Game of Skill

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 Hayer

Due 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:

  1. There are different possible strategies a player could choose.
  2. Some strategies do better than others.
  3. 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.

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30 Responses to Poker Is a Game of Skill

  1. Mark Weitzman says:

    As a long time professional poker player (28 years of high limit poker), I actually have a different opinion than most professional poker players. To start, I think the wrong question is being asked – does poker involve skill: definitely. However that does not mean that it does not involve gambling. Ask any professional poker player whether they are also a professional gambler, and I think all will say yes. The fluctuations are huge (rare is the pro poker player who has not had a losing year), the edge is small (often in the range 1-2%, which is nevertheless very significant when hundreds of thousands of effective bets are made) and if you are sitting in a game with say eight players – maybe two have skill, what about the others – clearly they are gambling.

    But the key idea is that there is no economic purpose to the wagers other than entertainment and gambling. Yes a few professionals make a living, but the vast majority of players lose. Do they have skill – of course not. Unlike stock/options trading where there is an economic purpose (providing a liquid market, raising capital etc.), gambling really has no purpose other than the entertainment and perhaps providing a living to a small number of professionals.

    Unfortunately in our financial markets there has been a proliferation of products (derivatives) which have similar characteristics of no real economic purpose, and just a means for smart people to out gamble others (think Orange county) who are much less smart and who are gambling with other peoples money.

    Anyway, should internet poker be legal. It should be as legal as sports betting, blackjack, and any other form of gambling. So for me the answer is yes, but not because it involves skill, but because people should be free to engage in gambling and the entertainment (or perhaps misery) it provides to many people. Should it be regulated – definitely.

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  2. Doc C says:

    While it may be correct to call poker a game where a strategy to deal with chance events must be chosen, and choosing that strategy is a skill, the data presented could indicate that the chance events in poker overwhelm the skills used to navigate the events to gain an advantage. This might be because the amount of skill needed is so small that even the most skilled player can only gain a small advantage over a relative novice, given the random nature of the winning and losing hands multiplied over a number of deals.

    It might feel like good strategy wins, but in fact, luck could easily play more of a role in poker than skill (though I agree that this paper by no means proves it). As for online poker, there are surely no tells in the virtual world. Luck has to play more of a role.

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  3. John says:

    Nice post Sean. I’m also a pro poker player, although just starting out really. I usually object when I get introduced as a professional gambler because I think there’s no significant distinction from certain types of financial traders. There are a lot of negative connotations to being described as a gambler of course. There are certainly low-variance grinders in online poker and high-variance gamblers in finance.

    Doc C: I couldn’t really disagree more with everything you said. Why write long comments about things that you know nothing about? I’ll say one thing, there are certainly tells in online poker.

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  4. @Sean

    Blackjack:- Card counting is not “cheating”. It’s legal in the U.S. as long as no external card counting device or A.N.Other person assists the “advantage player” in counting cards. As an aside [& more for your readers since I know you are a card player] the card counting part is easy, the difficult parts are accumulating a starting bankroll large enough to make the effort worthwhile & managing to fool the casino staff for long enough to profit [very skilful mix of talents to count, carry on a conversation, not draw attention & vary bet sizes/strategies AND remain anon].

    The main casino response is to ban. They can ban anyone for no reason ~ thus a career “advantage player” has to be able to change appearance to counter the worldwide casino database sharing of cheaters & advantage players.

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  5. @ Doc C.

    I agree with what John has written ~ You do not know your subject

    There are as many tells online as live ~ they are just of a different kind. Examples:-

    1] Timing:- Many online sites allow you to decide your action ahead of your turn. An “instacall” is a huge tell.

    2] Timing:- A methodical, tight playing style with a noticeable wait before acting is often a sign of a “multitabler” [some people online play 20-30 tables at once across a few sites] . It is very easy to play back at these types because they must play ABC-style poker.

    3] Cash game topping up:- A seasoned online player sets up their stack size parameters so they usually buy in for the maximum allowable & if their stack drops below say 90% the stack is auto topped up ~ [although actually there are seasoned players who play a short stack style]. Stack size & top up behaviour is a good way of classifying opponents.

    4] Bet sizing:- This is very important online where play is far more aggressive than live. It’s fairly easy to pick up on who’s paying attention to & reacting to the table dynamics through their “moves” & bet sizing. It’s a good way of recognising who to exploit & who to avoid or tiptoe around. There’s no point in playing “fancy poker” against a recreational player or a multitabler since they are oblivious to table dynamics.

    I could go on…

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  6. Doc C says:

    No one has provided data to show that the skill needed exceeds the randomness of the hands.

    As for “tells”, you have described general styles of play, not specific behavioral traits that can be read during a single hand. They are playing the odds, not the person.

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  7. @ Doc C.

    Quote:- “No one has provided data to show that the skill needed exceeds the randomness of the hands.” I have no idea what you’re trying to say with that. Are you referring to the study that Sean mentions? Or are you claiming that people like Doyle Brunson & Phil Ivey are not lifetime poker winners? Or are you saying something entirely different?

    To claim that there are no tells in online poker is absurd.

    Defining a tell as being ONLY about a particular behavioural trait in a hand is absurd.

    But, even if I go by your definition then tells are not just steadiness of the hands, pulse, sweat etc. ~ bet-sizing, check-raising, instachecking, instacalling & timing are all tells within the space of a hand. There’s also the online chatbox of course. Check-raising is particularly well known online & not used anywhere as often live ~ it’s a very definite tell that polarises the hand of the actor to very strong or very weak [but usually it means "very strong"] .

    ALL tells are actually “playing the odds” since any poker player behaviour can be a reverse tell or a simple misread. Then there’s the problem of deciding if that tell is a sign of strength or weakness for that player that time.

    You are not a poker player sir.

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  8. whatmeworry says:

    I make my living at the game of bridge, but I also play a mean game of neighbourhood poker! Bridge is much deeper and far more technical, but the two games broadly share the extent to which ‘luck’ plays.

    That is, for any particular hand/deal, luck plays a huge role and skill very little. However for a sufficiently large sample of deals, those contributions are reversed; the games become essentially 100% skill. Over a lifetime, I will be dealt the same number of AA hands and 72 hands as Phil Ivey, but he is a literal guarantee to clean my clock because the luck element is gradually squeezed out of the equation.

    There was a local case several decades ago where a bridge club was charged with ‘gambling’, because some of the membership were playing for money. The proprietor hired one of the top lawyers in the city to defend him, said lawyer happening to be one of the country’s top bridge players. The lawyer made approximately the argument I just made. Unfortunately for the bridge club, the judge hadn’t read Sean’s blog.

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  9. FrankL says:

    Let me first state off the bat that I am, like Doc C., “not a poker player”, although I occasionally play poker with friends and, rarely, online. I am more familiar with the game of baseball.
    Sean’s definition of a decision game of skill is:

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

    I am also a student of thermodynamics, so in that vein, I would propose that the statistical aspects be eliminated by the following (untestable) definition for ANY game of skill:

    In the limit of an infinite number of fairly played games between each player, in which each player’s overall strategy does not change, a heirarchy can be established based on average wins (or winnings, or points) per game (which may be a negative number for “losers”).

    Applying this to Sean’s definition, no such heirarchy can be established if (1) or (2) is violated, so that is good, however (3) not good – the dominant strategy may be known, but part of the “skill” is the ability to acquire the information avialable, and the ability to optimally respond to it.

    In poker, yes, the dominant strategy is not known, what with “tells” and all, the dominant strategy is an extremely complex mix of simple card statistics and human behavior. But, according to the above definition, I think its clear that it is a game of skill. Playing poker against a computer for which the only input is the cards dealt, the dominant strategy is known and practicable, and a heirarchy cannot be established for those who use the dominant strategy. Its not a game of skill for such players.

    In baseball, the dominant strategy is known – on offense, hit the ball over the fence every time, on defense, catch the ball after it comes off the opponent’s bat, but before it strikes the ground. Teams and individual players have to back off of this strategy somewhat and adopt a strategy that is tuned to their particular limitations. Individuals have limited and varying ability to judge the speed and spin of the ball, and limited knowledge of the exact contours and nature of the ground (needed for catching a ground ball, for example). They also must adjust their individual strategy based on their skill in responding adequately to this limited information. I think its clear that a heirarchy can be established, qualifying baseball as a game of skill.

    As for whether online poker should be regulated, I think that it should be to the extent that the game rules are clearly stated and obeyed, but beyond that, no. The regulators should not be involved in the games, i.e. no state-run lotteries, etc.

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  10. John says:

    @FrankL, actually poker has only been formally solved in some extremely limited toy scenarios. Even lacking physical or timing tells there is no known “dominant strategy” even for simple variants of poker. The main issue is that the decision tree cannot be exhaustively searched because of the freedom in sizing bets and raises. In chess you can search a certain number of steps ahead but that approach just doesn’t work in poker because of sizing granularity.

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  11. Uncertainty Principle Determinism.

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  12. versus

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  13. John says:

    Just to further illustrate how much we don’t know about poker: suppose we have a poker tournament in progress with specified prizes for 1st, 2nd, etc and where each player has a specified number of chips. Also, let’s say each player is equal in skill or is implemented by an identical computer program.
    We don’t even know how to calculate how much equity ($ expectation) each player has in the tournament. Obviously more chips is more equity. Currently an algorithm called the ICM is used and does a pretty good job but has known limitations. Various heuristic adjustments are proposed. Accurate estimation of equity is critical to strategy decisions, so it’s not just for interest’s sake.

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  14. Ron Murphy says:

    “This includes games without a probabilistic component, like chess or go …”

    What about the probabilistic components in the player’s brain biology, the probability of a brain recognising a pattern or play, or remembering, or not, an outcome from a similar scenario that would cause the player to respond one way or another. How about the interaction of two brains, each with independent and mutually screened probabilistically influenced thoughts, so that when player B see’s player A’s latest move, as one of many possible moves, B has no real access to the unfolding game plan going on in A’s head.

    I don’t see why this physical brain activity is any less probabilistic than that of hand-eye co-ordination in other games.

    The interesting question is, what is skill? Is it just the ability of a physical brain to respond causally, if extremely complexly, in some accord with the extent of past experiences? Is it as much a probabilistic flipping of neurons as it is a shuffling of the cards?

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  15. Sean: You’re obviously right, as usual — except that I’m not sure whether poker fits your definition of a “probabilistic decision game.” For at least if you play it at a real table, isn’t there’s also the “physical skill” of controlling your facial expressions? :-)

    Also, your post raises the interesting question of just how nontrivial the “skill” component of a game needs to be, for us to call it “not a game of chance.” For example, how about rock-paper-scissors? If you use a dumb strategy (Bart Simpson: “good old rock! nothing beats rock!”) then you can indeed lose, but as soon as you’ve crossed the threshold where both players are randomizing each move, it’s a pure game of chance.

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  16. Steve Watts says:

    Dear Sean,

    I am a regular reader of your blog and on this one I feel the need to comment. I offer some alternative experimental evidence; 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 !
    http://livboeree.com/

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  17. John says:

    Steve, I would certainly never say a bad word against Liv Boeree, but you can’t just point to successful individuals in any field as proof of talent, skill or divine intervention. At the very least they’re statistical outliers. Even Warren Buffet is controversial when it comes to the luck versus skill debate. A fantastic exposition on this topic is “Fooled by Randomness” by Nassim N Taleb. I don’t believe it mentions the word poker, but it’s almost a bible for professional players trying to understand how variance impacts their careers.

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  18. Sean Carroll says:

    Scott, it’s a good point; in most games where you are dealing with a real opponent in situations of incomplete information, there is an obvious element of skill involved in reading the opponent. That’s even true for rock-paper-scissors, which has live competitions. Not to mention computers that will usually beat a human. The point, of course, being that it’s very hard for people to truly randomize.

    So let’s imagine I was talking about idealized situations in which such skills were somehow rendered moot. (You know how to program a computer to play a dominant strategy in rock-paper-scissors or blackjack; for poker, nobody knows.) Adding them in only makes the conclusion stronger, of course.

    We could turn it around: if someone someday solves chess, so that the best possible strategy is known and people can commit it to memory, chess will no longer qualify as a game of skill.

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  19. sjn says:

    In defense of Doc C above, Nate Silver, who played poker professionally for awhile, makes a similar point. Using Silver’s metaphor of signal and noise (see his book by that title), even when the noise (due to the randomness of the draw) is significant, a skillful player can identify the “signal” and win in the long run, but given that the signal-to-noise ratio is much smaller than 1 for a single hand, it may take a long time before the difference in skill levels among players becomes evident, e.g., thousands of hands. The interesting question is how long does it take to “pull the signal out of the noise.” Clearly the statistical expectation of winning for a skillful player will be higher than that of an unskilled player, but how much does this difference in expectation compare to the size of the fluctuations (or variance) in winnings due to the randomness of the draw. To some extent these statistical questions could be studied by running simulations using an optimal strategy, or any strategy, although the psychological component would be missing. The latter, as Silver notes, is very important, e.g., a key part of it is identifying unskilled opponents.

    I had a friend in grad school who was determined to make money playing blackjack and spent many hours perfecting his game. He did succeed in making money, but soon realized the time required to win much money was unreasonable given his small statistical advantage.

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  20. Tienzen (Jeh-Tween) Gong says:

    Hidden due to low comment rating. Click here to see.

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  21. Hacking the casino’s video feed on every blackjack table, then sending the data to a card counting program which directs you casually to the tables with the best odds…takes skill :)

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  22. JollyJoker says:

    @sjn

    You’re touching on a legal definition of skill vs luck I remember seeing that went something like “Skill should be more important than luck for a majority of players”. Whether poker is a game of skill according to that definition crucially depends on how many hands the average poker player plays and if it’s reasonable to count over months or even years.

    To put some numbers on variance; iirc in online full table no-limit holdem a common win rate for professional players is 5 to 10 big blinds per 100 hands, plus or minus 100 to 200 depending on play style.

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  23. FrankL says:

    John – would your comment also apply if each player had a known, finite amount of funds to play with?

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  24. Austin Frisch says:

    As a semi-serious player, I’d like to echo the comments of those above who know what they are talking about. I’d also like to add: the edge that comes from recognizing tells, live or otherwise, is WAY over ephasized. Although there are situations where this advantage can be enormous, they are rare and usually don’t last for long (the player giving up a tell will inevitably wise up, lose their money, or leave for another game), and this holds even in live poker.

    On the other hand, the edge of a skilled player over an unskilled one can be almost as large. There are many heads up players who refuse to play anyone who has even a slight idea what they’re doing, we call them “bummunters”, and although they don’t get to play as many hands, their win-rates are comparitively enormous. Furthermore, the very best players can sometimes extract enormous edges even against other highly skilled professionals. See Tom Dwan circa 2009 for an example.

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  25. JeffH says:

    60 hands, what a joke. I think we can safely conclude that the journal that published this nonsense is not a serious scientific journal.

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

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  27. John says:

    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.

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  28. Rodney Ness says:

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

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  29. James Sweet says:

    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.

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  30. Andy Ward says:

    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.

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