Nate Silver 2012, The Signal and the Noise:


# ch10

The year 2003 was the start of the "poker boom," a sort of bubble economy in which the number of new and inexperienced players was growing exponentially and even a modicum of poker skill could be parlayed into large profits. The phenomenon had two immediate and related causes. One was the 2003 World Series of Poker in Las Vegas, which was won by a twenty-seven-year-old amateur, a Nashville accountant with the auspicious name of Chris Moneymaker. Moneymaker was the literal embodiment of the poker everyman: a slightly pudgy office drone who, through a never-ending series of daring bluffs and lucky draws, had turned the $39 he'd paid to enter an online qualifying tournament into a $2.5 million purse.
ESPN turned Moneymaker's achievement into a six-part miniseries, played on nearly continuous repeat on weekday evenings until baseball season finally came along to fill the void. It was terrific advertising for the "sport" of poker, which until that time had a reputation for being seedy, archaic, and intimidating. Suddenly, every balding, five-foot-eight accountant who had long ago given up on his dream of being the next Michael Jordan or Derek Jeter could see in Moneymaker someone who looked just like him, who had a job just like his, and who in a matter of weeks had gone from rank amateur to the winner of the biggest poker tournament in the world.
But the ESPN broadcasts presented a highly sanitized version of what reality actually looks like at the poker table. For one thing, out of the necessity of compressing more than forty hours of play involving more than eight hundred players into six hours of broadcasts, they showed only a small fraction of the hands as they were actually played. What's more, because of the ingenious invention of the "hole cam"-pinhole-size cameras installed around the edge of the table beside each player-the cards of not just Moneymaker but those of each of his opponents were revealed to the home audience as the hand was being played out, giving the audience the feeling of being clairvoyant. Poker is a pretty easy game if you know what cards your opponent holds.
Moneymaker was cast as the protagonist who could do no wrong. Hands that a sober analysis might have concluded he'd played poorly were invariably praised by the announcers-rash bluffs became gutsy ones, premature folds became perceptive ones. Moneymaker was not some slightly-above-average schmoe getting the cards of his life*1 but a poker savant who was cunning enough to have developed into a world-class player almost overnight.  [* Moneymaker has made "only" about $110,000 per year from poker tournaments since his World Series win, before accounting for his substantial entry fees into tournaments.]
The viewer was led to believe that poker is easy to learn, easy to profit from, and incredibly action-packed-none of which is true. But that didn't stop many of them from concluding that only a ticket to Las Vegas separated them from life as the next Chris Moneymaker. The number of participants in the World Series of Poker's $10,000 main event exploded, from 839 the year that Moneymaker won it to 8,773 just three years later.
I was one of those people.2 I lived the poker dream for a while, and then it died.

I lost the initial $25 fairly quickly, but the players in the Pacific Poker games did not seem much more sophisticated than the mix of ex-convicts and septuagenarians who populated the games at the Soaring Eagle. So I deposited $100 of my own. Almost all professional poker players begin their careers on winning streaks-the ones that lose at first are usually sensible enough to quit-and I was no exception. My bankroll began to grow, by $50 or $100 a night at first and them sometimes by $500 or $1,000. After about three months, my winnings hit $5,000; I began staying up all night to play, taking a cab to work at the crack of dawn and faking my way through the workday. After six months and $15,000 in winnings, I quit my job, leaving the exciting world of international tax consulting behind to split my time between playing cards and working for Baseball Prospectus. It was liberating; I felt as though I'd hacked the system somehow.

Indeed, information is so hard to come by in Texas hold 'em that players begin to make estimates about their opponents' range of hands even before any of the cards are dealt. In online games, this is often done through data mining: you'll have statistics on how loose or tight, how passive or aggressive, each opponent's play has been in previous games. In brick-and-mortar casinos, it is done through players' past histories with one another-or, failing that, through what amounts to ethnic profiling. Players from Sweden, Lebanon, and China, for instance, have a reputation for being more aggressive than those from France, England, or India. Younger players are presumed to be looser and more aggressive than older ones. Men are assumed to be more likely to bluff than women. These stereotypes, like any others, are not always true: at the hold 'em games I used to play in at the Bellagio in Las Vegas, the best players were very often women, and they were good in part because they were much more aggressive than their opponents assumed. But poker players don't have the time for political correctness. Even if the stereotype that women play more conservatively than men is false 45 percent of the time, the fact that it might be true 55 percent of the time gives them something to work with.

Dwan was once better known by his online screen name "durrrr," which he selected because he figured it would put the other players on tilt if they lost to him.

I mostly played limit hold 'em instead, where the betting increment is fixed on each round. (Until very recently, this was the most popular game outside of tournaments; ten years ago, there were often no more than two or three no-limit games running anywhere in the United States.15) Limit poker offers fewer opportunities for creativity. Still, until practice caught up with theory, I had a couple of very successful years by exploiting an aggressive approach. In both 2004 and 2005, I made an income from poker in the six figures, with my cumulative profits from the game peaking at about $400,000 overall.

The Pareto Principle of Prediction implies that the worst forecasters-those who aren't getting even the first 20 percent right-are much worse than the best forecasters are good. Put another way, average forecasters are closer to the top than to the bottom of the pool. I'm sure that I'd lose a ton of money if I played poker against Dwan. But I'd gladly play him if, as part of the deal, I were also guaranteed a match for the same stakes against some random person I picked off the street, against whom I'd expect to make back my losses and then some.
We can test this hypothesis empirically by examining the statistical records of poker players. I evaluated the data from an online poker site, which consisted of a random sampling of no-limit hold 'em players over a period in 2008 and 2009. These statistics told me how much money the players won or lost per hand, relative to the stakes they were playing.17
Because near-term wins and losses are very much subject to luck, I applied a statistical procedure18 to estimate what the players' true long-term profitability was. I then ordered the players by their skill level and broke them down into ten equal-size quadrants. The top quadrant-consisting of the top 10 percent of the player pool*-corresponds to the best player at a typical ten-person table.19 The bottom 10 percent, meanwhile, are the biggest fish.
Figure 10-8a represents my estimate of how skilled the players in each quadrant really are, measured as money won or lost per one hundred hands in a no-limit hold 'em game with $5/$10 blinds. The figures include both money won and lost to the other players and that lost to the casino, which either takes a small percentage of each pot (known as the rake) or charges an hourly fee for dealing the game.20
I estimate that the very best player at the table in one of these games is averaging a profit of about $110 per one hundred hands played over the long run. That's a nice wage in an online casino, where hands are dealt very quickly and you could get almost that many hands during an hour or two.* It's less attractive in a traditional casino, where it might take four hours to play the same number of hands, and translates to wage of $25 or $30 per hour.
The key insight, however, is that the worst players at the table are losing money much faster than even the best ones are making it. For instance, I estimate that the worst player in the game-the biggest fish-was losing at a rate of more than $400 per one hundred hands. This player is so poor that he would literally be better off folding every hand, which would cost him only $150 per one hundred hands instead.
...In the game I just described, the one fish was feeding a lot of hungry mouths. His presence was worth about $40 per 100 hands to the other players. That subsidy was enough that about half of them were making money, even after the house's cut. Poker abides by a "trickle up" theory of wealth: the bottom 10 percent of players are losing money quickly enough to support a relatively large middle class of break-even players.
But what happens when the fish-the sucker-busts out, as someone losing money at this rate is bound to do? Several of the marginally winning players turn into marginally losing ones (figure 10-8b). In fact, we now estimate that only the very best player at the table is still making money over the long run, and then less than he did before.
FIGURE 10-8B: ESTIMATED MONEY WON OR LOST PER 100 HANDS IN A $5/$10 NO-LIMIT HOLD 'EM GAME AFTER FISH BUSTS OUT
What's more, the subtraction of the fish from the table can have a cascading effect on the other players. The one who was formerly the next-to-worst player is now the sucker, and will be losing money at an even faster rate than before. So he may bust out too, in turn making the remaining players' task yet more challenging. The entire equilibrium of the poker ecosystem can be thrown out of balance.
How, in fact, do poker games sustain themselves if the worst players are a constant threat to go broke? Sometimes there are fishy players with bottomless pockets: PokerKingBlog.com has alleged that Guy Laliberté, the CEO of Cirque du Soleil, lost as much as $17 million in online poker games in 2008,22 where he sought to compete in the toughest high-stakes games against opponents like Dwan. Whatever the number, Laliberté is a billionaire who was playing the game for the intellectual challenge and to him this was almost nothing, the equivalent of the average American losing a few hundred bucks at blackjack.
Much more commonly, the answer is that there is not just one fishy player who loses money in perpetuity but a steady stream of them who take their turn in the barrel, losing a few hundred or a few thousand dollars and then quitting. At a brick-and-mortar casino like the Bellagio, these players might wander in from the craps table, or from one of its nightclubs, or after going on a winning streak in a tournament or a smaller-stakes game.

Once Party Poker shut Americans out, however, and I shifted my play to tougher sites like PokerStars, I found that I wasn't winning anymore. In fact, I was losing-a lot: about $75,000 during the last few months of 2006, most of it in one horrible evening. I played through the first several months of 2007 and continued to lose-another $60,000 or so. At that point, no longer confident that I could beat the games, I cashed out the rest of my money and quit.
My conclusion at the time was that the composition of the player pool had changed dramatically. Many of the professional players, reliant on the game for income, had soldiered on and kept playing, but most of the amateurs withdrew their funds or went broke. The fragile ecology of the poker economy was turned upside down-without those weak players to prop the game up, the water level had risen, and some of the sharks turned into suckers.26
Meanwhile, even before the new law passed, my play had begun to deteriorate, or at least cease to improve. I had hit a wall, playing uncreative and uninspired poker. When I did play, I combined the most dangerous trait of the professional player-the sense that I was entitled to win money-with the bad habits of the amateur, playing late into the evening, sometimes after having been out with friends.
In retrospect, things worked out pretty fortunately for me. The extra time I had on my hands-and my increased interest in the political process following the passage of the UIGEA-eventually led to the development of FiveThirtyEight. And while it wasn't fun to lose a third of my winnings, it was better than losing all of them. Some players who continued in the game were not so lucky. In 2011, the "Black Friday" indictments filed by the Department of Justice shut down many of the online poker sites for good,27 some of which proved to be insolvent and did not let players cash out their bankrolls.
I've sometimes wondered what would have happened if I'd played on. Poker is so volatile that it's possible for a theoretically winning player to have a losing streak that persists for months, or even for a full year. The flip side of this is that it's possible for a losing player to go on a long winning streak before he realizes that he isn't much good.
...What this means is that even after literally tens of thousands of hands are played, a good player might wind up behind or a bad one might wind up ahead. In figure 10-11, I've modeled the potential profits and losses for a player with the statistics I just described. The bands in the chart show the plausible range of wins and losses for the player, enough to cover 95 percent of all possible cases. After he plays 60,000 hands-about as many as he'd get in if he played forty hours a week in a casino every week for a full year-the player could plausibly have made $275,000 or have lost $35,000. In essence, this player could go to work every day for a year and still lose money. This is why it is sometimes said that poker is a hard way to make an easy living.
...The Bayesian method described in the book The Mathematics of Poker, for instance, would suggest that a player who had made $30,000 in his first 10,000 hands at a $100/$200 limit hold 'em game was nevertheless more likely than not to be a long-term loser.
...Another player, Darse Billings, who developed a computer program that competed successfully33 against some of the world's best limit hold 'em players,* put it even more bluntly.  "There is no other game that I know of where humans are so smug, and think that they just play like wizards, and then play so badly," he told me. "Basically it's because they don't know anything, and they think they must be God-like, and the truth is that they aren't. If computer programs feed on human hubris, then in poker they will eat like kings."