This story was originally published in the March 2017 Princeton Echo.
It was Bradley Snider’s final day at the Seminole Hard Rock Poker Open in South Florida. Snider, a 21-year-old math major at Princeton University, was exhausted. By the final hours of the competition, he had been competing for four days in a row, the past three lasting 12 hours. Late nights can be disastrous for even the most disciplined poker players — fatigue can cause players to make rash decisions. Snider did his best to stay alert and attentive—just not to the quarter of a million dollars on the line.
“One thing I wasn’t thinking about was the money,” Snider says. “A lot of people not into poker might feel uncomfortable gambling for that much money, but for me to play my A-game, it requires not worrying. You have to think of it like another day at the office.”
Ignoring the money paid off. Snider took home his first career title, collecting the final pot of $246,400. This was Snider’s first win but far from his first game. He had played around 20 tournaments and had never cashed out before, meaning he lost in each game. But losing didn’t dissuade Snider from playing. “This is pretty unlucky, but also par for the course for poker tournaments,” he says.
Poker may conjure images of heavy drinking and basements shrouded in cigaret smoke and the debauched games of gangster movies. But a professional poker arena shares more in common with a chess match or math competition. “It’s a huge misconception that connects poker to drinking,” Snider says. “The only thing anyone is drinking is green tea. Green tea, water, and eating healthy. Everyone is trying to stay alert.”
Math and probability inform every move in poker, Snider says. While Snider doesn’t run through specific mathematical calculations in his head each time he is dealt a card, he is familiar with a set of guidelines on how to play certain hands and adjusts his strategy based on the circumstances of the game. Despite the importance popularly attributed to a player’s “poker face,” Snider says reading someone doesn’t really factor into his play because there’s no intuiting from someone’s expression the cards they have. While it might be possible to pick up on behavioral patterns or revealing ticks in some players, high-level players don’t usually have such handicaps.
The edge, rather than clairvoyance, is a poker player’s mathematical ability. Indeed, poker has captivated Snider for the past two years because of the intellectual challenge of the game. “There’s probability involved so you don’t get put in same situation twice,” Snider says, “You constantly have new decisions to make, and new situations to analyze.”
Mathematicians through the ages have been attracted to games of chance and the formulas that can be devised to measure those chances. In the 19th century the French mathematician Henri Poincare had offered a proof that predicting the final resting place of the roulette ball was impossible. A century later University of California math professor Ed Thorp proved that it was possible to gain an edge in roulette, as well as in blackjack and other games of chance. His book, “Beat the Dealer,” became a bestseller and set the stage for a similarly analytical and quantitative approach to investing in stocks, explained in his 1967 book “Beat the Market.”
Snider was attracted to poker because ‘it was a game about making good decisions over time.’ That kind of thinking also helps Wall Street traders.
In the 1990s another book about blackjack, the semi-fictional “Bringing Down the House: The Inside Story of Six MIT Students Who Took Vegas for Millions,” was transformed into a box office movie success, “21.”
Bradley Snider’s interest in poker started when he was growing up in Plantation, Florida. Both Snider’s parents have engineering degrees and are delighted by Snider’s interest in math. In high school Snider spent his free time poring over math textbooks and tests to train for national competitions. He searched for colleges with a strong math program and ultimately chose Princeton over MIT for reasons beyond academics.
He valued the university’s diversity, both of students and programs. “I didn’t want to be at a school where everyone was the same,” Snider says. He also discovered the Princeton Poker Club, a student-run organization that holds tournaments and teaches game techniques. Under Snider’s term as president, the club attracted 50 to 60 undergraduates to its tournaments, more than ever before.
Beyond poker, Snider plays trumpet in the Princeton wind ensemble and has helped direct the Princeton University Math Competition (PUMaC), a student-run math competition held for high school students around the country.
Snider first opened a book on poker strategy when he was 18. Gripped by the mathematical theory behind the game, he began studying and scouring the Internet for information. Compared to blackjack, which Snider describes as a “solved game” for which “ you can tell a computer exactly what is right at each situation,” poker is “a lot more complicated, by several orders of magnitude.
Snider was attracted to poker because “it was a game about making good decisions over time, and that if I could remember the strategy, I’d have a chance to make money,” he says. His father also had a casual interest in the game and would take Snider along when he played on cruise ships. But Snider says his father’s interest never developed into a passion on par with his own. Soon after Snider began studying poker, he tagged along with his father on a family cruise and played for his first time with real money at an electronic table.
Around the same time, Snider’s younger brother also became interested in poker — the two began studying strategy and playing each other for practice. “We’re competitive in that we want to do well in poker tournaments, but not competitive against each other,” Snider says. At 19, Snider’s brother, Jacob, still isn’t eligible for games in New Jersey or Las Vegas, but is able to play in Florida, where he is a sophomore at the University of Florida.
In the middle of our interview, Snider’s phone rings—it’s his brother, calling after his first break in a poker tournament, to chat with Snider. Snider tells his brother he’ll call back. “Don’t worry, he’s fine,” Snider says smiling, when I tell him to take the call. “The game’s just started—we’ll talk at the next break.” Snider explains that he and his brother regularly call each other during breaks in poker tournaments to discuss the game, evaluate their play so far, and strategize. “It’s good to get the validation or the correction about your play, so we know we’re playing our best,” Snider says.
The Snider brothers also provide each other with an important support network. Most poker players, particularly professionals who constantly deal with the emotionally draining aspects of the game, rely on other players who can understand and provide emotional support during periods of cash loss. A professional tournament player’s income fluctuates during the course of year, usually a repeated cycle of small losses followed by large wins. Many poker players find themselves in a down swing, or a period of time in which, despite the logic of their play, they lose money.
Because of the element of chance, skilled players could make strategically optimal decisions and still end up losing cash. “It’s par for the course to go and lose lots of tournaments. It’s a statistical unlikelihood, but it happens. I don’t find it too demoralizing — unless I’m playing bad. If I’m playing well and just getting unlucky, that’s a lot easier,” Snider says. In poker, players can’t attribute a single win to superior skill; they may have just been lucky. That’s why Snider explains he isn’t results oriented and doesn’t attribute the success or failure of a single game directly to the merits of his strategy. “If I lose 20 poker tournaments in a row, but I think I was making good decisions, because I’m not results oriented I don’t feel as upset as a normal person would,” Snider says.
In early November Snider took advantage of Princeton’s fall break to compete in a PokerStars tournament at Resorts in Atlantic City. The event featured 40 tournaments over the week. Snider didn’t make any money in the main event, but won some cash during a few of the side events. “I was definitely feeling more confident after my win over the summer,” Snider says. In January, during the winter break, Snider was in the Bahamas competing in another PokerStars event.
Now in his final semester at Princeton, Snider studies probability and game theory in the math department. Snider’s thesis is on “methods for equilibrium finding in Texas Hold’em Bounty Tournaments.” It will not be a handbook on how to play a winning hand but rather an analytical discussion.
‘Poker has helped me to be more rational when it comes to risk, so I will be more willing to make trades that have positive expectation, even if they might sometimes result in a loss.’
Snider plans to compete in the World Series of Poker in Las Vegas this summer. He anticipates preparing for the six-week tournament will be a bit like training for a marathon. “My parents are concerned if I’ll have the endurance,” Snider says, laughing. “It will require a good routine of eating healthy and exercising.”
The poker profession’s inconsistent paycheck is a big reason Snider doesn’t plan to play professionally. “When I’m playing poker it’s with money I can afford to play with, so I don’t feel bad about losing lots of games in a row, which might seem crazy to some people because it’s real money,” Snider says. “Poker is a hard way to make an easy living. Even though I won this tournament, I did get very lucky. I can’t expect to win like this in the course of the year.”
Although Snider is eager to explore his interest in poker, he already has a job offer with an investment firm. While Snider doesn’t think the specific mathematics of poker will be useful for the job, he believes some of the mindset he has developed through the game will be relevant.
For instance, in poker Snider cannot be results-oriented, focusing on the outcome of each game, but rather must focus on his big-picture strategy — decisions that might not work out in the short term may be correct in the long term. “Poker has helped me to be more rational when it comes to risk, so I will be more willing to make trades that have positive expectation, even if they might sometimes result in a loss,” Snider says.
In a Power Point presentation he prepared to introduce fellow students to the joys of poker, Snider observes that poker can be played either as a game of chance or a game of skill.
As Snider sees it, even for the best players poker offers some valuable insights:
- Good decisions still yield a bad result quite often.
- Bad decisions still yield a good result quite often.
- Professional poker players must remain analytical and not let the result affect their view of their decision.
- This is really hard for lots of smart and motivated people, who like setting results-oriented goals.
Those attributes, it turns out, are also some of the traits possessed by the leading players on Wall Street, which is always on the lookout for bright new talent. Snider’s pamphlet for the Princeton Poker Club has two sponsors:
Optiver, a Chicago-based company that describes itself as “a leading global electronic market maker, focused on pricing, execution and risk management.”
Jane Street, described by the New York Times as a secretive firm that “specializes in trading strategies to capture arbitrage profits by buying and selling (using its own capital) large amounts of E.T.F. (exchange-traded funds) shares.”
Like poker it’s a risky business, and a good poker face won’t be enough to win.