Jen-Luc Piquant has donned her poker face today and for good reason. This morning the Spousal Unit was chuffed to find his latest online issue of Discover magazine was available -- because it contains an article by yours truly on poker-playing physicists. (November issue! Pick up a copy!) They're everywhere these days: not just the Spousal Unit, but also string theorist Jeff Harvey, particle physicists Michael Binger and Marcel Vonk (both of whom have done extremely well on the professional circuit), a former grad student of Harvey's named Eduard Antonyan, Liv Boeree and Michael Piper (both pals of Binger's), and who knows how many others? Discover loved the idea of poker-playing physicists as much as I did when I pitched it over the summer, and editor Bob Keating did a great job chopping my 3500-word monster draft manuscript into the more manageable length ultimately published in the magazine (clearly, writing books has ruined what little brevity I once possessed).
Still, I'd hate for all that effort to go to waste, plus there was all kinds of great material from the sources I interviewed for the piece that never made it past the transcript stage. That's why the Internet invented blogs: as a place to supplement the inevitable space limitations of traditional media for readers who might want a bit of "behind the scenes" bonus material. I mean, who wouldn't want to know that the first time Jeff Harvey played Texas Hold 'Em was for a fundraiser tournament in Chicago, where the role of "dealer" was played by an Albert Einstein action figure? So here goes:
Walk into one of the nicer poker rooms in Vegas, and you might be surprised by the eerie quiet, in sharp contrast to the cacophony in C major emanating from the slot machines on the main casino floor. There are tables of players studying their cards with hushed intensity, punctuated by the gentle clink of poker chips in the background and the shuffling of the cards. We've sampled most of the Vegas poker rooms over the years, and the MGM Grand is one of The Spousal Unit’s favorites, with elegant marble rims on the tables, and a clear view of the casino’s signature lion habitat. Not that the serious players spend much time watching the lions. There are odds to be calculated, bets to be made, and if all goes well, money to be won. And that requires laser focus and significant mental stamina.
In general, physicists hate to gamble. "I don't like gambling at all," says Antonyan. "I don't enjoy it and there's nothing in it for me to compensate for the clear negative EV decision of gambling." Harvey's not a fan, either: "Personally I don't like to gamble on games where the house has the odds, but I'm not critical of people who do." And while the Spousal Unit gamely learned craps with me while I was writing The Calculus Diaries (it was research, people!), he hasn't been tempted to play craps since.
Binger doesn't mind gambling, per se, but he learned the pitfalls of blackjack as an undergraduate, when he wrote a computer program to beat the game through card-counting (or, as the casinos like to call it, “cheating”) for his senior project. But then he tried to put his strategy into practice. He lost a pile of cash playing blackjack on an ill-fated trip to Reno, and was barred from six casinos in one day for card-counting in a desperate attempt to recoup his losses. “I realized I wasn’t going to get rich playing blackjack,” he recalls. Poker was different: as he studied the game and pondered the underlying mathematics, Binger realized that poker could be a “beatable game."
That seems to be the strongest lure for poker-playing physicists: it's a game of skill and strategy, not a game of pure chance (although let's face it, luck does play a role, too). Vonk has always loved games, but his love for poker rests on the combination of "math skills" and "people skills," as he puts it. "Good poker requires that you make sound game-theoretic decisions but there is still plenty of freedom to try and outsmart your opponents," he says. "Other casino games miss that second element. All you can do in blackjack or roulette is make the best possible mathematical decisions, and even then, you will still lose in the long run. I have never been attracted to those games. It's the fact that you play against other people that makes poker so interesting, and that makes it possible to actually be a winner at the game."
And poker favors a similar skill set. "The analytical thinking we develop certainly makes it easier to learn and keep improving at poker, but you also need to be very competitive, a little addictive, and need to have a pretty stable psyche," Antonyan says. "There are a lot of players who could have been really good but can't win because they 'tilt' [lose their cool and start making bad strategic decisions] too much and too often." Binger also cites the mental and emotional discipline required, qualities physicists tend to also develop. "In poker, you often have to sit there for hours, patiently waiting for your spot, and sometimes endure months on end of running bad," he says. "Similarly, in physics research, there are times when you are stuck in the middle of a lengthy calculation or project, and cannot see the end in sight. But you have to persevere and stay focused and positive to get through it."
Is the math really enough to be a poker badass at the professional level? Binger fields this question a lot, and says the probability and equity calculations and statistical analysis he applies give him an edge in the game. Vonk finds that his post-game analysis of how he played specific hands benefits from his mathematical skills. But both Vonk and Binger admit that there are also plenty of other players who really don't know much about the underlying math; they have a good feel, or instinct, for how to play the game. "There are many people who hate math but are great poker players, but there are hardly any players who lack the people reading abilities and still manage to be good poker players," says Vonk. "Mathematical knowledge can to a large extent be replaced by intuition and experience. After a player has played a million hands of poker, even if he does not know the math at all, he will have a decent feeling about when it is profitable to draw to a flush and when it is not."
That said, knowing the math means you can acquire this kind of knowledge much more quickly, and those skills can give an edge in very rare situations that don't often occur in a poker game. "To be a great player, you need both!" Vonk insists. Chris "Jesus" Ferguson is one of the best players in the world, and definitely relies on math and game theory when he plays:
Antonyan estimates that the game of poker is "90% simple math/general strategy, and 10% understanding the dynamics of the table and/or the attitudes of one or more players towards you as they develop." The math part rests on basic probability theory, and as the article makes clear, the probabilities of poker are a bit more complicated because there are many more possible combinations of hands -- and you're working with incomplete information. Vonk breaks down the process to a few basic questions: What cards do I have? What range of cards do I think my opponent has? Given these, what is the probability I will win the hand after all cards have been dealt? And most important: given that probability, will I make money in the long run when I pay the bet? The best one can do, most of the time, is "make a very broad guess," he says. Per the Spousal Unit (blogging at Preposterous Universe way back in 2004):
"Texas Hold 'Em is so popular because it manages to accurately hit the mark between 'enough information to devise a consistently winning strategy' and 'not enough information to do much more than guess.' The charm in such games is that there is no perfect strategy, in the sense that there is no algorithm guaranteed to win in the long run against any other algorithm. The best poker players are able to use different algorithms against different opponents as the situation warrants."
To get a sense for how the probabilities can play out in poker, consider the following three possible pairs of hole cards:
Pair of sixes
Sean posed this question on his blog, Cosmic Variance, back in 2006: Which hand is most likely to win if you choose to stay in the pot all the way to the showdown, against other pairs of randomly chosen hole cards? The answer took a whole 'nother blog post to delineate. Mathematically, it depends on the number of opponents. The probability that you will win goes down as the number of opponents goes up, because there are more ways for you to be beaten. That said, some hands play well against very few opponents, while others play well against many opponents. It all depends on the circumstances.
Against one opponent, the sixes will win 62.8% of the time, versus 57.3% for Ace-7 and 56.2% for Jack-10 suited. Against four opponents, those odds are reversed: Jack-10 suited will win 27.3% of the time, versus 20.7% for Ace-7 and 17.9% for the pair of sixes. Why does this happen? “Against only one randomly-chosen pair of hole cards, there is a substantial chance that the sixes won’t need to improve; likewise the ace can often come out on top just by itself, so the Ace-7 is second-best,” Sean explains. “But against four randomly-chosen pairs of hole cards, chances are excellent that someone will improve, and Jack-10 suited has the best chance.”
The probabilistic outcomes change again if we pit these three hands against each other, two at a time. In that case, sixes are slightly more likely to beat Ace-7, and Ace-7 is likely to beat Jack-10 suited, but Jack-10 suited is likely to beat a pair of sixes.
The sixes are the best starting hand all by themselves. For one of the latter two to win, favorable community cards must appear on the flop, turn, or river. The only way for the Ace-7 to beat paired sixes is for either an ace or a seven to turn up -- or, less likely, for just the right combination of four cards to land on the board to make a straight or flush.
Pit those same sixes against Jack-10 suited, and the situation is reversed. In that scenario, there are more ways for Jack-10 suited to improve. The cards are “connectors,” so there are more possible cards that would give low straights (7-8-9) and high straights (Q-K-A), plus the hole cards are suited, making it much easier to make a flush.
So Jack-10 suited will usually beat a pair of sixes. But it won’t usually beat Ace-7 if the ace is of the same suit. For instance, if four more suited cards come up, the Jack-10 suited will have a flush, but the Ace-7 will have a higher flush, and will win the hand.
See? Poker is a very complicated game. And even more complications arise during the betting process: "what happens after the first two cards are dealt and after each card thereafter," the Spousal Unit once wrote.
If determining the edge and the odds were all there were to succeeding at poker, probability theory would suffice, and if it were a purely logical game like chess, it would merely require impressive feats of calculation to determine the winning series of moves.
But remember that poker is a game of limited information, where players must deduce what cards their opponents are likely to have based on their knowledge of the odds and clues from other players’ behavior. There may not be a single answer. As Harvey -- ever the string theorist -- puts it in the Discover article: “Chess is like classical mechanics. Poker is like quantum mechanics. In chess, there is only one right move. In poker, there is a probability distribution of right moves.” Harvey admits that one of his classic errors is "calling wen I think I am beat for other reasons (betting patterns, tells, and so on)," but he calls anyway because "the math says I should. At times like that, I need to pay less attention to the math."
Yet another complicating factor is that human beings aren't always predictably rational, particularly when it comes to poker: if you assume your opponent is skilled and rational, and he isn't, your strategy could backfire and fall victim to "beginner's luck." I found this enlightening analysis over at Cardplayer.com, outlining the different between an optimal strategy and an exploitive strategy (Ferguson's favorite) in No-Limit Texas Hold 'Em (and note the very specific circumstances described throughout: change even one element and it might call for a different strategy):
"Let's say you're playing no-limit hold 'em against a calling station who never folds pre-flop no matter what the bet is, but will sometimes fold after the flop if he misses completely. He just insists on seeing the flop. Now say you're dealt two aces and you each have a few thousand blinds in front of you. The optimal strategy is probably to make a small raise, both building a pot and disguising your hand. But with this player in the game, a much better play is to move all in, knowing he'll call you. To take maximum advantage of this terrible opponent, you need to employ an exploitive strategy. The optimal strategy would still win you money but against bad players, other strategies might win you more money. ... An optimal strategy is designed to protect you against opponents who play well. But when we can find ways to do better than optimal strategy against certain players, we do it."
The article also mentions mathematical/computational great John von Neumann, who with Oskar Morgenstern (an economist) wrote the definitive treatise on game theory and poker -- specifically the art of bluffing, which fascinated von Neumann -- in 1944: Theory of Games and Economic Behavior. It wasn’t a bestseller, but it did yield an intriguing insight into the art of the bluff: you should always bluff with your worst hand, not a mediocre “bubble” hand. If betting is slow, it might be worth calling, or “limping” into the game, with a mediocre hand, because your chances of winning are pretty good against other mediocre hands. A bad hand won’t win unless everyone else folds, so an aggressive raise is the best strategy.
Indeed, there are rare cases where game theory dictates you should fold pocket aces before the flop when playing a tournament. In non-tournament play, the goal is not just to win the hand but to make the most money. In a tournament, you want to outlast your opponents to win it all. That might entail intentionally opting not to maximize your monetary gains on one specific hand to remain competitive in the tournament. You sacrifice short-term gain to achieve the long-term goal.
It doesn’t pay to be too consistent in Texas Hold ‘Em. I once played poker with a group that included Harvey. I consistently bet when I had a strong hand, checked when I had a “bubble” hand, and folded when I had a bad hand. So when I made trip aces after the flop, I pushed all-in, going heads-up with Harvey. He had pocket Queens, an otherwise strong hand had there not been an ace on the board. It’s hard to fold pocket Queens but that’s just what Harvey did. He correctly analyzed his chances, based on my all-too-predictable style of play, and he had the discipline to stick to his strategy. I won the hand, but didn’t win much money because Harvey folded before he’d committed many chips to the pot.
The optimal strategy can also depend on what type of poker is being played: your strategies will be different for No-Limit Texas Hold-Em, for a No-Limit tournament, a Limit Texas Hold 'Em "ring game", and different again for online poker. "The only people playing online are serious," says Harvey. "They also use software to keep track of their opponents' statistics, which is consistent with the rules of the site, even if it seems a bit like cheating." Here's the difference: in a live game, you have to remember/keep track of opponents' style of play yourself, i..e, when they raise and in what position. The online software can analyze thousands of hands being played at the same time, and that larger sample space makes for a more accurate statistical analysis. Antonyan excels at online poker, and has won a tidy sum to date, although he rarely plays more than four hours a day. He's since left physics, but not to pursue poker: he's putting his quantitative abilities to work on Wall Street as a "quant" with a high frequency trading group.
"It's much more about modeling, statistical analysis and game theory at that level," says Harvey. "I'd have to spend as much time learning and playing poker as I do on physics." And to date, he's been unwilling to do that, unlike, say, Binger, who took time off from physics after scoring big in the 2006 Wold Series of Poker. Despite winning around $4 million through his third place finish, and an extra 2 million since, Binger still lives pretty simply: he uses his winnings to bankroll his travels and more poker tournament action, going to Australia, New Zealand, South Africa, Monte Carlo, London, Venice, San Remo, Aruba the Bahamas, and all over the US. That's a lot of frequent flyer miles! (You can follow his exploits on Twitter: @mwbinger.) And check out the stats: six tournament wins, second place in Bluff player of the year in 2008, and currently ranked sixth worldwide in the Bluff Power Rankings.
The mathematicians have had a good run when it comes to analyzing poker, but the Spousal Unit is (rather cheekily) on record predicting that physicists will prove to be the better poker players in the future? His reasoning? No-Limit Texas Hold 'Em is such a complex system that "we cannot derive a dominant strategy in a closed form. Game theorists and mathematicians study simplified systems about which they can actually prove theorems," he wrote. This is a decent strategy for two players going heads-up, but for a full table, pre-flop, "it becomes a question of which approximations to make and which models to choose for your opponents." Physicists, let's face it, are often pretty adept at choosing the best models.
He also had a corollary: "Phenomenologists and astrophysicists will be better poker players than string theorists." I expect Harvey to respond in kind to the obvious throw down. In fact, I think Discover magazine should sponsor a tournament in Vegas pitting the poker-playing physicists against each other -- or against mathematicians like Ferguson. Just to keep things interesting...
There’s a saying that Texas Hold ‘Em consists of long stretches of boredom punctuated by three minutes of sheer terror. Poker never lacks for suspense: you can play a hand flawlessly from a probabilistic standpoint, but there is still the possibility you’ll lose; statistical anomalies do happen. Even with pocket aces and a flop of 9-9-2, your chance of winning a heads-up showdown against pocket queens is only 92%. Harvey recently faced just that scenario – and a third queen appeared as the very last card. His opponent “sucked out on the river.”
So poker also requires nerves of steel, and an emotional equilibrium that Harvey, for one, admits he does not possess. “You need to be unflappable,” he says. “Bad luck can’t bother you. It’s too easy to get ‘tilted,’ and start playing looser, more erratic, or too passive.” More often than not, he says, “My emotions get the better of me.”
I dug up anecdotal evidence to support that. That same Chicago game where Harvey "read" me and folded his pocket queens also included Peter Sagal, host of NPR's "Wait Wait Don't Tell Me." He, Harvey and another pal, Chris Lackner, once went to a riverboat casino in Indiana to play poker. Sagal recalls harvey "getting a really hot hand and betting on it. I remember his hand was actually shaking as he pushed in the chips." And alas, Harvey lost to a bad beat. But it made me feel better, since I suffer from the same display of nerves whenever I play poker. Some of us just don't have what it takes, in the long run, to be truly world-class players. But I'll be working on perfecting my poker face. You can count on it.