The Power of Thinking Like a Poker Player

Keeping a poker face had never struck me as much of a feat—until I had to keep one. My pulse quickened, my cheeks felt flushed, and my eyes were desperate to dart and size up the pot. What had been a mediocre hand was transformed, after the flop came down, into something spectacular: every card from seven to jack—a straight. All that remained was to play it cool and build up my cash prize. The bets started small, and then grew. The next two cards looked innocuous enough. My beautiful straight was intact, and the pot had expanded rather nicely.

Truthfully, I’ve never been much of a gambling man. My previous experience was limited to a few college poker nights during which my friends would hastily explain the difference between a straight and a full house and then rake in my charitable contributions to their respective beer funds. You could safely call me risk-averse. In fact, the only really reckless financial bet I can recall making was deciding to become a professional journalist.

Nate Silver, America’s most famous elections prognosticator, got me to cut loose. His new book, “On the Edge: The Art of Risking Everything” (Penguin), uses poker as a model for responding to uncertainty. Having drawn the lot of reviewing it, I realized that I couldn’t do it justice without learning more about poker—specifically Texas hold ’em. “On the Edge,” like his previous book, “The Signal and the Noise,” is a hefty set of meditations on probabilistic thinking, only this time the author is taking in broader horizons. Silver left FiveThirtyEight, the statistics-based news site that he founded and sold to Disney, but is still in the business of predicting election results. Yet his first love is poker—he once played it professionally—and “On the Edge” sees him return to that passion.

“I still feel more at home in a casino than at a political convention,” Silver writes in the new book, a treatise that extends the lessons of poker and modern gambling to arenas like artificial intelligence and ethics. He has spent time interviewing such notables as William MacAskill, the philosopher-evangelist of effective altruism; Sam Bankman-Fried, the now disgraced cryptocurrency billionaire; and Sam Altman, the C.E.O. of OpenAI. The people changing the world are doing it by thinking like poker players, Silver contends. If we want to keep up, we’ll have to learn the mind-set of the successful gambler.

My chronic risk aversion aside, I figured I had the right foundations to do so. Chess had always been my game of choice; I squandered many afternoons of my adolescence playing, move by move, through Alexander Alekhine’s best games and “Dvoretsky’s Endgame Manual.” My college years contained less chess, but lots of problem sets in math, economics, and statistics—many of them involving probability theory. I graduated knowing my martingales from my Markov chains. Among my first assignments as a journalist was to build forecast models for British and French elections. If I applied myself to poker, I thought, I’d probably be decent: I could multiply fractions fast enough in my head to calculate the probability of, say, drawing a flush on the river. (I was also picking up the lingo.)

After giving myself a crash course, I decided that I was ready for some real action. I set up a family game, recruiting my wife and my teen-age brother. That may have been my first mistake. Somehow, I’d forgotten that my wife had once been a foreign-exchange trader, and I later learned that my brother, fresh from a summer camp for academically talented students (a.k.a. nerd camp), had spent the season card-sharking his camp mates. I’d also forgotten to get poker chips; we played with pie weights for puny stakes. Things started badly. Baby brother, barely old enough to hold a driver’s license, bluffed me out of a decent hand, and then he smugly called my audacious revenge bluff. (Brat summer, indeed.) Finally, my straight arrived, a chance at redemption. In a spousal showdown, I confidently displayed my hand—only to find that my wife had a straight of her own, and that hers ranked higher. My once proud pile of pie weights was reduced to a pittance.

Probability and gambling have always been intimately intertwined. The mathematics of probability can be traced to a well-known stumper about how best to divide a pot, which a seventeenth-century gambling enthusiast posed to two leading mathematical luminaries of the time, Blaise Pascal and Pierre de Fermat. Their inquiry would spawn the powerful idea of “expected value”—the average outcome of an uncertain event, calculated by multiplying the outcome in every possible state of the world by the chance of it happening. How powerful? The once alien notion that humans could be precise about uncertainty gave rise to the discipline of statistics. A model in which people were treated as rational actors trying to maximize the expected value of their utility became the cornerstone of modern economics. And systems based on feeding statistical prediction models with gargantuan helpings of data and computing power have already started to roil this century.

Silver’s book falls into a long tradition of using games to model real-world decisions. John von Neumann, whom some consider the greatest genius of the twentieth century, was working at the Manhattan Project when he published, together with his frequent collaborator Oskar Morgenstern, a book titled “Theory of Games and Economic Behavior” (1944). The work, which included a detailed chapter on “Poker and Bluffing,” essentially gave birth to game theory, a field that, neatly enough, would provide the basis for contemporary doctrines of nuclear deterrence. Decades before artificial neural networks could generate personalized poems and wacky images, computer scientists were using them to build backgammon programs.

What Silver offers is a tour of what he calls “The River”—the community of people (often based in Silicon Valley, on Wall Street, and in Las Vegas) who think about the world in terms of expected value and comfortably use words like “Bayesian prior”—and its face-off with “The Village,” basically the political and media establishments. The River’s name is an homage to the river card, the fifth and final card revealed in a game of Texas hold ’em. Where the Village gets its name is left unexplained, though it’s presumably meant to convey a sense of conformity. The dichotomy is not a particularly illuminating one, but this detracts little from the stimulation of each individual subject. Silver’s meandering itinerary through the River and all its oxbows makes for an enjoyable ride.

He begins with the world of gambling, where being “degen,” or degenerate, is something of a badge of honor. My homemade humbling helped me grasp the grand scale of Silver’s own poker achievements. At one point, he was in the top three hundred of the Global Poker Index rankings; he has also won eight hundred and fifty-six thousand dollars in high-profile tournaments (and presumably further significant sums in private games). It’s understandable that he sees poker as a model for the game of life. Poker calls for properly calibrating risk in the face of very imperfect information—and recalibrating it as you gain more information about your companions. In that respect, it is a decidedly human undertaking.

Even so, the computer—having already established its dominance in other classic games (chess, Go, StarCraft II)—has come to surpass the best human players in poker. Just as chess grand masters rehearse their opening lines with superstrong programs, the best poker players, Silver reports, now spend hundreds of hours honing their skills with computer-based “solvers.” Unlike chess—in which the solution is deterministic and there’s always a best move—the solution to poker is stochastic and requires you to play identical hands differently, because once you’re predictable you’re beatable.

In recent years, the game has been swept up by what’s known as the “game-theory optimal,” or G.T.O., approach. It has been accepted that the best way to play—to maximize expected value—is to randomize between calling, folding, and raising according to a computer-calculated list of probabilities, which serious players memorize. As for randomizing? “The player wasn’t just staring out into space—she was probably looking at the tournament clock,” Silver writes about one G.T.O. adept. “She could randomize by taking an aggressive action if the last digit was an odd number or a passive action if it was even.”

When you read about the lengths to which poker sharks, shrewd sports bettors, and savvy slot-machine players (they do exist) must go in order to scrape together a narrow edge—to get “positive expected value,” or “+EV,” against the house or their fellow-gamblers—you realize what a slog big-time gambling actually is. Even if you’re exceptionally talented, you will find it hard to make serious money, and you may have to spend seventy or eighty hours a week to achieve it. There are reasons that the house always wins: identifying a real edge is hard to do, that edge tends to be thin (as in less than one per cent thin), and the house is constantly trying to shove you off the precipice. Casinos will politely but firmly ask you to leave if they notice you counting cards. The major sports-betting sites will sharply curtail your wagering privileges once they figure out that you are playing to win. Big edges are fleeting, and usually exist only for gigantic events like the Super Bowl, or Presidential elections, in which the sheer volume of dumb money resists correction by the sharks.

So Silver is justifiably proud that, in 2016, his statistical model gave Donald Trump a twenty-nine-per-cent chance of winning, when the betting markets put his odds at seventeen per cent. His results made it rational to bet on a Trump victory: assuming that Silver’s model was accurate, the expected value of the bet was high. Because the markets were giving odds of roughly five to one, if you risked a hundred dollars betting that Trump would win, and he did, you’d earn five hundred dollars of profit. The value of a twenty-nine-per-cent chance of getting five hundred dollars outweighed the seventy-one-per-cent chance of losing a hundred. The expected value of your bet was a seventy-four-dollar gain on what you’d wagered. How often would you find such a sizable edge? By Silver’s calculations, even an outstanding poker player, one in the top two hundred in the tournament play, has even odds of finishing in the red in any given year.

As an experiment for the book, Silver, a basketball fanatic who developed his highly regarded statistical model for player performance, took up betting on N.B.A. games. Despite being limited by many major sports books, he managed to place $1.8 million in bets a year. His profit: $5,242, a return of about one-third of a percentage point. That wasn’t for lack of trying. “Sports betting took more mental bandwidth than I expected, even when I wasn’t on the clock,” Silver writes. “Checking betting lines was often the first thing I did when I woke up and the last thing I did before going to bed.”

The effort to improve one’s rationality as a gambler easily approaches the irrational. Even my own study of poker became moderately obsessive. I watched hours of poker-strategy videos and long montages of televised poker tournaments with commentary; I went through the lecture notes of a class taught at M.I.T. called Poker Theory and Analytics. Learning about pot odds—it turns out that you can confidently meet an opponent’s call with positive expected value (that is, money-making on average) if your chance of winning is greater than the share of the pot you’d be contributing—made me understand where I’d erred. The concept of “fold equity” could help me decide how big my bluff ought to be. The concept of “blockers,” or cards one possesses that limit the winning combinations available to one’s opponent, further refined the rudimentary calculations I had been trying to make. I spent a few hours playing against a G.T.O. poker program and analyzing my play with a solver. All this because of losing forty ceramic balls and some of my dignity.

Silver acknowledges the paradox here. Although poker is an arena that prizes decision-making, most pros would, he writes, be better served financially doing something else for a living. Clearly, its rewards aren’t fully reflected in the +EV models. The dopamine rush that follows a successful bet will trump the slow-burning satisfaction of contributing to your Roth I.R.A. The first time Silver played a poker game with two-hundred-dollar stakes, he recalls, “I literally felt like I was on the sort of narcotics that I used to do a lot of in my twenties.” Our understanding of the mathematics of gambling has never been greater, but no one captured the psychology of gambling quite like the great Russian writers of the nineteenth century. Alexander Pushkin’s short story “The Queen of Spades” tells of a Russian officer who is obsessed with gambling but able to contain himself until he hears about an unbeatable card trick. He scares an old woman to death in order to learn it, but she has the last laugh: the officer ends his career in an asylum. Fyodor Dostoyevsky was himself a roulette addict. (“I pawned both my ring and my winter coat and I lost everything,” he wrote in a letter to his wife, begging her for fifty francs to settle his hotel bill.) His novella “The Gambler,” one of the finest studies of the compulsion to gamble, was written in less than thirty days to pay off his own debts. He had wagered a prominent publisher to whom he owed money that he would complete a novel and an edition of writings by a specific date, or else he would surrender the rights to all his works—past and future. He finished the manuscript with only hours to spare.

What about the games of chance that Silicon Valley venture capitalists play when they stake millions of dollars on tech startups that have a roughly one-in-ten chance of making it? Success comes when the returns on a breakthrough firm more than make up for their losses elsewhere, so venture capitalists have to be thoughtful about their bet sizes. Being good at this game is different from being good at founding a company, Silver argues. He sees it as the difference between the fox, who, proverbially, knows many things, and the hedgehog, who knows one big thing. The venture capitalist is a fox: risk-tolerant, probabilistic, adaptable, and comfortable with complexity. The founder in whom the V.C. invests is a hedgehog: risk-ignorant, stubborn, drawn to order. V.C.s, spreading their bets, will acquaint themselves with multiple markets and try to adjust their exposure on the basis of the latest information. Founders, committed to their company, will persevere through setbacks and fight for their singular vision. The genius of Silicon Valley, Silver maintains, is in creating a symbiotic relationship between the two: the founders get to take their shots, and the venture capitalists get their positive expected value in returns.

In Silver’s account, large language models like OpenAI’s ChatGPT or Anthropic’s Claude are like poker players, too. The job of a large language model is to maximize the chance that the next word it outputs makes sense given its previous output and the user’s query. (For the latest version of ChatGPT, this has involved training on a vast Internet corpus and fine-tuning a trillion or so parameters.) The linguist Noam Chomsky described these models as “a kind of super-autocomplete,” and, though he meant it dismissively, it’s a fair description of the mechanics. Super-autocomplete can do more than just solve high-school homework problems. It has already revolutionized computer programming, in which co-piloting with A.I. is now routine, and you can imagine lots of white-collar tasks getting more efficient with its use—up to the point where they are automated away.

Silver finds a cautionary tech-industry parable in Sam Bankman-Fried, who granted him several interviews after FTX, his cryptocurrency exchange, went bust but before he was sentenced to twenty-five years in prison. Although Silver thinks the stodgy Village types are too risk-averse, Bankman-Fried shows what happens when you’re a compulsive gambler without limits. He had “hacked the VC algorithm and catered to some of its worst biases,” Silver writes. Because Bankman-Fried looked the part, had the right pedigree, and had placed himself in the right networks, nobody cared to examine the financial details of FTX too closely. Silver’s take on his rise amounts to a mini-book within the book, and an enlightening one.

Still, Silver might have spent more time exploring domains where expected-value thinking may be even more consequential. One involves the government’s role in funding and fostering scientific innovation, which requires balancing the reality of repeated failure with the huge potential of success. It could do with a serious reboot. That probably means taking more chances rather than rewarding scientists for their ability to fill out labyrinthine grant applications and channelling money toward the gerontocrat who coasts on a discovery made decades ago while the next generation languishes unfunded.