Lucky And Good

A few months back I came across a study performed by Citigal and funded by PokerStars set up to examine the relationship between skill and luck in poker.

Here is the report.

Here is Cigital’s write-up.

And finally, a column about it in The Wall Street Journal.

I wouldn’t know where to begin in describing the flaws with the “science” behind this “study,” but when you’ve got a major online poker site footing the bill for such a thing, you know right off the bat that good science wasn’t their first priority, and that there may be the teensiest of biases in its construction.

In any case, both the methodology employed, and the conclusions reached on the basis of the methodology, are grossly simplistic.

Even as someone who loves the game, and even though I disagree with some of the arguments they present, I find myself closer to siding with the detractors quoted in the Wall Street Journal article than with those who supported the study. Cigital did not, as the quoted Harvard professor opined, ask or answer “just the right questions.”

Silly Data

Poker is a game with a chance element and a skill element. This can be conclusively demonstrated with the most basic logic, and much more easily, directly and effectively than the study did.

The real question is how much of one and how much of the other are involved. On that front, the study was a bust. Noting that most Texas holdem hands end without a showdown is not exactly a watershed discovery, and makes only the most elementary of statements about the relationship between luck and skill in the game.

But then, even if Cigital wanted to demonstrate some constant and fixed relationship or ratio, they couldn’t, because there IS no such thing.

Assembling a large sample of online real-money Texas holdem hands above microstakes and noting that 75% of them ended without a showdown says this: that a large number of hands end without a showdown in one particular form of poker, in real-money online games.


If you assembled a hundred million hands of the play money games, or just about any low stakes live game, or Omaha games, or stud games, or five card draw, you’d get the opposite result – 75 to 95% (or more) of hands WOULD go to showdown.

The study even acknowledges a determined shutout of play money and microstakes games from the sample. Why? Because they were afraid there’d prove to be “more luck” in the play money games? What about live, low-limit games? Or Omaha, stud, or draw games? If the study seeks to make a blanket statement about poker, then avoiding poker games of certain stakes, classes, and categories stands in direct opposition to that goal.

Ratio, Shmatio!

The truth, despite beliefs to the contrary and the efforts of amateur theoreticians on poker discussion boards to try to break it down: there IS not, and cannot, be a fixed ratio between “skill” and “luck” in poker.

Skill and luck are moving parts that depend totally on context. The factors of the game, including the rules of the form of poker being played, the players involved in the game, the forced bet structure, and a lot more, determine what the ratio will be.

For example, in a pot limit Omaha 8 game where Player X and Y are making very good decisions, and Players, A, B, C, D, E, F, and G are all clueless players who make extremely bad decisions (they don’t understand hand values, they call pot-sized bets with weak hands when X and/or Y have fearless bets with nut hands time and time again), Player X and Y will have an enormous edge over Players A-G. They will absolutely destroy the game, and quickly too. Luck will be as much of a factor as ever in any one hand, but over a (brief) span of hands, luck will have virtually no impact on X and Y’s superior skill.

But in a PLO8 game where ALL the players – A-G plus X and Y – are each about equal in skill and making very good, near-optimal decisions, no player will have much of an edge, if any, over the others. (This is a reality that many in today’s grinder-versus-grinder online environment are in grave denial of, because they have a vested interest in believing in their own edge.)

Meanwhile, in a fixed-limit, high ante seven card stud game where Players X and Y are up against a weak field of Players A-G, X and Y are going to be there a while, and luck will have a louder voice. Luck works differently in each of the games.

The Operative Factor

Inherent differences in structure/form aside, luck is more of a factor among uniformly skilled (or unskilled) players, because when the skill is equalized, there’s nothing left but the luck. In the long term though, even that will vanish, since there is no such thing as “long term luck.” Everyone will eventually get the same cards and situations. And any one or two players who actually have some small edge will need to play tens of thousands of hands for this to emerge in their results and for the “noise” of short term luck to disappear.

But the larger the skill differential in poker, the less of a factor luck is, and the more quickly and surely skill will crush non-skill. This is why a very bad player (relative to his opposition) loses all of his money nearly every time he plays, and why less-bad players lose more slowly, and why, among the more equally-matched players, the money tends to seesaw.

It’s also not just a matter of how skilled or unskilled players are relative to one another, but the particular ways in which they are skilled or unskilled. A very aggressive and unpredictable but in many ways unskilled player is going to cause a skilled player a lot of trouble. The superior player’s earn may take a long time to stabilize. Whereas luck will exert virtually zero influence in a match between a skilled player and a milquetoast who calls all bets to the river and folds when he does not have the nuts.

So, the skill:luck ratio completely depends on the game and the opponents. A skill edge gives one a huge advantage against an unskilled field, but among all good players, skill often plateaus, and nobody has much, if any, advantage.

Over the past few years, with the availability of books, training, discussion, and accelerated experience, poker games everywhere (particularly online) have suffered from this “plateauing” of skill.

Poker—once a game of “find and fleece the suckers”—is often nowadays more of a tic tac toe match between the proficient, with short-term luck, and ego, obscuring what’s really happening. When everyone knows the optimal moves, it’s essentially one tied game after another, except that in poker every hand must have a winner, so it takes longer for the “meta-tie” to work itself out.

In any case, whether or not poker is a skill game is not up for debate. Since decisionmaking is involved, it’s a skill game by definition.

The question of the conditions under which skill can prevail over inferior skill, and to what degree—that’s the relevant one, requiring a far more complex methodology. Try again, Cigital.

(Note to PokerStars: if you’re looking to pay someone to do another study of this kind, anyone with a copy of PokerTracker and a hand history database could get this exact data in a matter of minutes. Hit me up next time.)

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