An empirical test of luck versus skill in poker

You can read the full research report here: http://www.liebertonline.com/doi/pdfplus/10.1089/glr.2008.12105

or the newsy summary of it here: http://www.sciencedaily.com/releases/2008/03/080321125835.htm.

The fundamental conclusion: "The question at the start of this study was Is poker a game of luck or skill? The unequivocal finding is that poker is a game of skill. In both studies, participants who were instructed outperformed those who were not instructed."

Well, yeah, but....

I'm confident that the same would be true of blackjack--those receiving, say, printed cards instructing them in the mathematically optimum strategy for each combination of their cards and the dealer's shown card would surely do better than those given no instruction at all. But they would simply lose less, rather than actually being winners over the long run. In fact, the same is undoubtedly true of slot machines; the simple expedient of pointing out to a new player that typically there are proportionately higher jackpots available when you play the maximum amount of money at a time rather than the minimum would produce a statistical edge for the player following that advice (though you'd have to watch for a long time to see it emerge). Even with craps and roulette, there are bets that have larger or smaller house edges. Just teach a new player which are the bets with the smallest house margins, and you've got a player that will lose his money to the casino more slowly than somebody who is given no instruction.

Does the fact that one can learn to lose less, all by itself, make something a game of skill rather than luck? I don't think so.

Annie Duke argued, in a column for Bluff magazine last year (http://www.bluffmagazine.com/magazine/Is-there-really-any-luck-in-poker%3F-Annie-Duke-830.htm) that there is, in reality, no luck in poker, not even in the short run; it's all skill. This is based on a theoretical computerized player that makes each move randomly from among the legal options available--her definition of a zero-skill player. OK, but then by the same argument you would have to accept that blackjack is a game of all skill and no luck, too, because any player trained in the basic strategy would do far better than a computer player that simply chose to hit or stay randomly. Especially considering the political consequences, does Duke really want to be stuck with the conclusion that blackjack is 100% skill and 0% luck just the way poker is? Wouldn't that logically mean that online blackjack is just as deserving of legal protections and/or exemptions as poker is?

There's also a problem with Duke's definition of "short term." Her argument is based on the fact that the random player would never win even such a short-term game as a single-table tournament. (I don't think that's correct; given enough trials, it would eventually win at least once. But that's just an academic point that I don't think is really important.) But even if that's true, it's a very convenient definition of "short-term." What if "short-term" is considered, instead, to be one hand? Would she argue that her zero-skill player will never win even one hand? I doubt it. Readers who follow this kind of stuff in ridiculous detail, as I tend to do, may recall the idiotic court decision last year in North Carolina in which a court determined that poker was predominantly skill, on the evidence provided by one "expert" about one televised poker hand in which a player was something like a 9:1 dog when the money went in, but still won the hand. In other words, I think Duke's argument breaks down when you don't let her set the definition of "short-term" to one that proves her point.

Duke has also argued (http://www.annieduke.com/journal.php?journalID=1708) that the fact that one can deliberately lose at poker shows that it is a game of skill rather than luck, because one cannot deliberately lose at, say, roulette or baccarat. The obvious rejoinder to that, again, is that by that criterion, blackjack must also be all skill and no luck, because one can certainly lose every blackjack hand on purpose, should one care to do so. One can also lose money on every spin of the roulette wheel by simply betting the same amount on every number as well as the 0 and 00; one of them will hit and you'll get paid $35 on that spot, but it costs you $38 to put down this assortment of bets. You lose. By Duke's argument, roulette is therefore a game of pure skill.

Still, I think she's right (even if only in a way that's fairly obvious to experienced players) in saying that the smaller the difference in skill level between two players, the longer it will take for the skill difference to show itself in tangible results, and the more luck will control (or I think she would say, appear to control) the results in any one session.

I have still not found anything that persuades me away from what seems the only rational conclusion: luck can be (though isn't always) the dominant factor over skill in any one hand, but as the time frame is increased, the importance of luck diminishes and skill becomes the dominant factor in determining who is a long-term winner or loser. At some undefinable point of sufficiently long duration, luck has been rendered very small, perhaps even negligible--though never truly zero--as a factor.

I wish courts would follow Mark Twain's lead on this question. Back in about 1867 he wrote about a group of men criminally charged with playing a game of chance, known as "old sledge" or "seven-up." Their attorney convinces the court to convene a jury of six experienced players and six novices. When the novices lose all of their money to the better players, over the course of a night of playing, they unanimously conclude that it's a game of skill, and the defendants are acquitted. (See http://www.readbookonline.net/readOnLine/1540/.)

That's the essence of what happened in the study with which I started this post, though without the judicial aspect. The outcome is hardly a surprise. The "unequivocal" conclusion, though, that poker is a game of skill is, or should be, subject to the caveat about the time frame of the observation. I think it is reductio ad absurdum ever to state that the game is either all skill or all luck.