Intuition

Hand 1: A player calls a raise out of position with seven-deuce offsuit. He flops a full house and cracks his opponent's aces, winning his whole stack. After the hand he says, "You gotta play when you're feeling it."

Hand 2: The player bets twice the pot on the river. After a long think, his opponent folds. "I knew he didn't have it," he says.

Was either of these plays justified? Both? Neither?

Since most situations in poker cannot be analyzed conclusively, it is both necessary and important to make some decisions intuitively. Equally important is knowing when intuition is valuable and when it is not.

My answer would be that the play in Hand 1 was unequivocally bad, while the play in the second hand may (or may not) have been justified. As usual, thinking in terms of ranges of hands clarifies the issue. 7-2 is the worst hand in poker, so when you call with it, what you're really saying is that you would call with any two cards. It's very, very rare for the game conditions to indicate a call with any two. As far as "feeling" that you would hit the flop, unless you're cheating, you don't have access to any information about what the next card will be, so it's hard to see how you could feel it.

Hand 2 is less clear. While you don't have any information about what the next card will be, you have a lot of information about what your opponent might do when you bet: his previous actions in this hand; how he's played past hands in this session; age, attire, posture...and much more. Any piece of information might be the key to the puzzle, or it might not be. This is where experience becomes incredibly valuable. Without experience, you won't pick up on most of the clues, or know how to interpret those you do see. But if you have a lot of experience, you may be able to synthesize all the information available to you to come to a better decision.

Hand 1 and Hand 2 are completely different situations, but people seem to confuse the two. When someone is able to make a good intuitive decision in a situation like Hand 2, all they see is the result, not the previous work that went into it. They conclude that analysis is unnecessary or even counterproductive, that the way to make good decisions is with your "gut." But intuition isn't a replacement for hard analytical work, it's a reward for having done a lot of it.

The Q Words

Alone on the rack, the Q stared at me. All his brothers had leapt to the board and in the process built for me a solid lead, but the Q would betray me. He would take 10 of my points and give them to someone else. I looked over the board again. There was nowhere to put it. The Q was going to make me lose. I resolved to look up all the Q words when I got home.

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Here is the list of words in the Scrabble dictionary that have a Q but no U:

QI
QAT
QIS
QADI
QAID
QATS
QOPH
FAQIR
QADIS
QAIDS
QANAT
QOPHS
TRANQ
FAQIRS
QABALA
QANATS
QINDAR
QINTAR
QIVIUT
QWERTY
SHEQEL
TRANQS
QABALAH
QABALAS
QINDARS
QINTARS
QIVIUTS
QWERTYS
QABALAHS
MBAQANGA
QINDARKA
SHEQALIM
MBAQANGAS

I haven't memorized them yet. When I saw the list I began to have second thoughts, not because of the tedium of memorizing it, but because of what it would do to the game. The joy of Scrabble, at least for a novice, is in the way it combines culture and competition. It's an opportunity to dust off long-forgotten stores of knowledge, deploy them in a new context, and to show off.

That part of the game dies when you start playing mbaqanga, because despite what the Scrabble Dictionary says, mbaqanga is not a real word. You would never know it if you hadn't learned it specifically for Scrabble. It doesn't signify anything, it's just a token in a game. I was afraid the mbaqanga attitude would infect my whole experience of the game.

The problem is not unique to Scrabble. I've found that becoming expert often impoverishes games from a meaning standpoint. For most, chess is a ruminative pastime, a meeting of the minds between two white-haired men smoking pipes. But what happens when you realize both of them are making blunders, practically throwing the game away on nearly every move?

Scientists have the same problem. As their research becomes more and more specialized, they struggle to make it understandable and relevant to non-scientists. To master something means appreciating the smallest minutia, but finding meaning is all about abstraction.

Levitt on luck vs. skill in poker

Steven Levitt, the well-known author of Freakonomics, just came out with a paper about the role of skill versus luck in poker. He looks at the performance of skilled players and unskilled players in the World Series of Poker and concludes that the role of skill and luck in poker is comparable to that of professional baseball.

As an unemployed poker player hoping online poker eventually gets legalized, I appreciate the plug from a source as celebrated as Levitt. As he observes, "the single most important factor in determining the legality of poker is whether poker is a game of skill or a game of luck." But as someone who's grappled extensively with the questions he examines in the paper, I don't find many original insights in his approach.

In short, Levitt compiles a list of "skilled" players based on rankings from some poker magazines and past tournament finishes. Then he compares the performance of those players to that of other, presumably "unskilled" players and finds "a substantial role for skill in poker over the time horizon examined."

While this methodology is adequate to establish the presence of at least some skill in poker (as any reasonable approach would be), it has obvious problems. Magazine rankings and past finishes are far from perfect indicators of skill. For example, an unskilled player who rode a streak of good luck to a recent tournament victory could be identified as "skilled," but a highly skilled online professional who rarely plays live could be identified as unskilled.

The comparison to Major League Baseball doesn't say much about the rewards for skill inherent in poker and baseball, because the levels of competition are so different. While the WSOP features the best against the rest, MLB is more a case of the best against the best. You have to be one of the very best baseball players on the planet to play in the Major Leagues at all. A closer baseball analog to the WSOP would be to pit the New York Yankees against your intramural softball team.

While Levitt refers to previous academic research, he never mentions the work of poker players themselves. This is odd because while baseball players, for example, are not typically experts on the statistics of baseball, skilled poker players are experts on the statistics of poker. Understanding statistics and probability is a poker player's bread and butter. So when Levitt says his data set allows him "to compute ROIs for individual players, allowing us to measure poker skill more directly than in previous research," while this may be true of the academic research, he's way behind the game in the poker community (ROI stands for "return on investment," essentially the amount a player expects to profit when he enters a tournament). Professionals track their ROI obsessively over thousands of tournaments. A search for posts titled "ROI" on the poker internet forum 2+2 returns 250 threads. Sites such as sharkscope track the tournament results of online players and display average ROI as a basic statistic for each player. In short, Levitt's paper is a perfunctory stab at something poker players have been mapping extensively for years.

But maybe this is all beside the point. While the paper is a head-scratcher from a statistical perspective, it makes perfect sense as PR. The examples seem selected less for statistical relevance than cultural resonance. Hence the WSOP (poker's most visible event) and MLB (America's pastime). Overall the paper seems designed to demonstrate a non-trivial element of skill in poker to total outsiders, using the most familiar possible reference points, and it does a pretty good job of this.

What then about the original question: is poker a game of luck or a game of skill? Well, it's not at all clear what this means. Implicit in the question is the assumption that a game is made up of some combination of luck and skill, and if you add some of one you must subtract some of the other. This turns out not to be the case.

As the game designer Richard Garfield points out,

"The reward for skill depends on how much luck there is in a game, but a game that is mostly determined by luck can have an enormous amount of skill.

A couple of examples will demonstrate this. The first is rando-chess, which is played as standard chess, but after each turn you roll two dice. Roll 12 and you win! This game has as much skill as chess, but also a lot more luck and much less reward for skill. The second example is pikanumber, in which each player holds out a number of fingers; whoever holds out more wins. There isn't any luck in this game and not much skill, but there is a very high reward for what little skill there is—you never lose. Skillful players will always draw (unless one has more fingers than the other)."

It is obvious to anyone with even a passing familiarity with poker that it contains a great deal of both skill and luck. Identifying the best play is far from easy, but in any given hand luck is likely to overshadow skill.

When measuring skill against luck, a better question than "How much?" is "How long?" Meaning, how many times would you have to play for the better player to be confident of coming out ahead? Clearly this is a matter of degree - how confident is confident? But it does allow us to get a sense for how games compare to one another. In chess, if one player is significantly more skilled than the other one game would be adequate. For poker it becomes more confusing, because it's not clear what our unit should be. A single hand isn't a self-contained unit like a chess game is -- it's more like a possession in basketball. But larger units like a session or a match don't have a fixed duration. In general, online poker players consider 100,000 hands to give a reasonable idea of your expected win rate in a particular game. For reference that would take almost 140 days playing round-the-clock without breaks in a brick and mortar casino. But the 100,000 number applies to tough games where you have at most a small advantage over your opponents. Against weaker players, a few thousand hands might be enough.

Andriy Slyusarchuk's Wikipedia Page

You probably haven't heard of Andriy Slyusarchuk -- he's not yet widely known outside of his home country. But he's become a sensation in the Ukrainian media for astonishing displays of mental prowess: memorizing 30 million digits of pi, 20,000 books, and defeating Rybka (one of the strongest chess-playing computer programs) in a blindfold match.

Let's dispense with the obvious. He's a phony, of course. Reciting 30 million digits of pi at the rate of one per second without breaks would take about a year. If you're interested in the history of computer chess (and why Slyusarchuk's claims are implausible), grandmaster and commentator Sergey Shipov has written a pretty good summary.

What's more interesting is Slyusarchuk's reception. Why would anyone believe his claims? He seems to be taken quite seriously in Ukraine, where he even secured a meeting with the President.

In general, his audience can be divided into skeptics and believers. The conflict between the two sides makes for a schizophrenic wikipedia page. Multiple authors are evident in the tone, which alternates between fawning and scathing:

Novy Channel (Новий Канал—one of the major TV channels in Ukraine) has hosted a few TV events in which Andrity Slyusarchuk demonstrated many of his extraordinary abilities...

When he tried to fake Chess position memory on TV, his scam was revealed by chess experts.

But more interesting still is the "talk page" documenting conflicts about what should appear in the Wikipedia entry. It seems that the original, overwhelmingly credulous article is the work of a user called NazarK, who turns out to come from the same town as Slyusarchuk. There seems to be some hometown sentiment at work. When one commenter suggested, "Only some nationalist Ukrainians can believe in that circus," NazarK fired back, "The above unsigned comment seems to come from some nationalist Russians (check IP location) who just hate to accept any human achievement if it comes from Ukraine."

So maybe some people in Ukraine are desperate for a national hero. At the same time, claims about mental achievements may be easier to swallow for many than other kinds of claims. If someone claimed to run a 30-second mile, no one would believe him. But if someone claims to remember 30 million digits of pi, sure, why not? The accepted world record, 67890 digits, is already unbelievably big (although more than 40 times smaller than Slyusarchuk's claim). Likewise, if you don't know much about the history of chess, his claim to beat Rybka in a match seems plausible enough. By making claims at the edge of the average person's range of knowledge -- about things that they are passingly familiar with, but not expert in -- Slyusarchuk manages to seem both plausible and extraordinary.

Obama's Poker Face

On Sunday American forces stormed a compound in Afghanistan and killed Osama Bin Laden. Barack Obama gave a comedy speech at the White House Correspondents' on Saturday night. Which is to say, he knew. He had to do a comedy routine having given the order for the world's most notorious terrorist to be killed the following day in a risky, complicated operation, the outcome of which would have a great effect both on world politics and his personal legacy.

That to me seems hard. If I fear I've offended someone in an email, I lie down for an hour. I don't think I could have done the comedy speech.

The President has an obligation to oversee weighty decisions, but he also has no end of commitments to trivial fluff. Maybe it is that part of the job -- putting on a placid, confident face -- not the actual decision-making that is hardest. Or at least hardest to fathom.