Howard was concerned. Annie loved Vegas. She never turned down a trip.
“Why don’t you at least find a local poker game?” he said. “It might help you get out of the house.”
By then she was married, and so she asked her husband to make some inquiries. They learned there was a bar in Billings named the Crystal Lounge where retired ranchers, construction workers, and insurance agents played poker every afternoon in the basement. It was a smoke-filled, joyless dungeon. Annie went one afternoon and loved it. She went again a few days later and walked out fifty dollars richer. “Playing poker down there was this combination of math, which I loved, and all of the cognitive science stuff I had been doing in graduate school,” Annie told me. “You could watch people try to bluff each other and hide their excitement when they got a good hand, and all these other kinds of behaviors we’d spent hours talking about in classes. Every night, I would call my brother and talk through the hands I had played that day, and he would explain my mistakes, or how someone else had figured out my game and had started using that against me or what I should do different next time.” Initially, she wasn’t very good. But she won often enough to keep going. She noticed that her stomach never hurt at the poker table.
Pretty soon, she was going to the Crystal Lounge every weekday, like a job, arriving at three P.M. and staying until midnight, taking notes and testing strategies. Her brother sent her a check for $2,400 with the agreement that he would get half her winnings. She was up $2,650 by the end of the first month even after his cut. The next spring, when he invited her to Vegas, she drove fourteen hours, bought a seat in a tournament, and by the end of the first day had $30,000 in chips.
Thirty thousand dollars was more than Annie had ever earned in a full year as a grad student. She understood poker—understood it better than many of the people she was playing against. She understood that a losing hand isn’t necessarily a loss. Rather, it’s an experiment. “The thing I had figured out by that point was the difference between intermediate and elite players,” Annie told me. “At the intermediate level, you want to know as many rules as possible. Intermediate players crave certainty. But elite players can use that craving against them, because it makes intermediate players more predictable.
“To be elite, you have to start thinking about bets as ways of asking other players questions. Are you willing to fold right now? Do you want to raise? How far can I push before you start acting impulsively? And when you get an answer, that allows you to predict the future a little bit more accurately than the other guy. Poker is about using your chips to gather information faster than everyone else.”
By the end of the tournament’s second day, Annie had $95,000 in chips. She finished in twenty-sixth place, ahead of hundreds of professionals, some with decades of experience. Three months later, she and her husband moved to Las Vegas. At some point, she called her professors at Penn and told them she wasn’t coming back.
A full minute has passed. Annie still has a pair of tens. If the FossilMan is holding a higher pair—say, two queens—and Annie stays in the hand, it’s almost certain she’ll be eliminated from the Tournament of Champions. But if she wins the hand, she’ll become the table’s chip leader.
All of the odds and probability charts floating around Annie’s head are telling her to do one thing: Match the FossilMan’s bet. But every time Annie has asked the FossilMan a question during this tournament by placing a wager, he’s answered with a highly rational response. He’s never put everything on the line without a good reason. Now, in this hand, he’s pushed all of his chips into the pot, even as Annie has raised again and again.
Annie is aware that the FossilMan knows how hard it is for her to back down at this point. He knows that, unlike some of the other people at this table, she isn’t in the Poker Hall of Fame. This is her first time in front of a million television viewers. He might even know that she’s worried she doesn’t belong here at all, that she suspects she was only invited because the TV producers wanted a woman at the table.
Annie suddenly realizes she’s been thinking about this hand wrong all along. The FossilMan has been betting as if he has a good hand because, in fact, he has a good hand. Annie has been overthinking—or, at least, she thinks she’s been overthinking. She’s not sure.
She looks at her pair of tens, looks at the $450,000 on the table, and folds. The FossilMan takes the money. Annie has no idea if she just made a good or bad choice because the FossilMan doesn’t have to show anyone his cards. Another player leans over. You completely misread the situation, he whispers to her. If you had stayed in, you would have won.
A few hands later, Annie has already folded when the FossilMan, with a ten and a nine, bets all his chips once again. It’s a smart play, the right move, but as the other cards fall on the table, they go against him. Even the smartest poker players can be undone by bad luck. Probabilities can help you forecast likelihoods, but they can’t guarantee the future. Just like that, the FossilMan is out of the tournament. As he stands to leave, he leans over to Annie.
“I know the hand you had earlier was really hard for you,” he tells her. “I want you to know that I had two kings and you made a good fold.”
When he says that, the knot of panic in her stomach melts. She’s been distracted ever since she folded against him. She’s been second-guessing herself, turning the hand over in her mind, trying to figure out if she played it right or wrong. Now her head is back in the game.
It’s normal, of course, to want to know how things will turn out. It’s scary when we realize how much rides on choices where we can’t predict the future. Will my baby be born healthy or sick? Will my fiancée and I still love each other ten years from now? Does my kid need private school or will the local public school teach her just as much? Making good decisions relies on forecasting the future, but forecasting is an imprecise, often terrifying, science because it forces us to confront how much we don’t know. The paradox of learning how to make better decisions is that it requires developing a comfort with doubt.
There are ways, however, of learning to grapple with uncertainty. There are methods for making a vague future more foreseeable by calculating, with some precision, what you do and don’t know.
Annie is still alive at the Tournament of Champions. She has enough chips to stay in the game. The dealer gives each player their next cards and another hand begins.
II.
In 2011, the federal Office of the Director of National Intelligence approached a handful of universities with grant money and asked them to participate in a project “to dramatically enhance the accuracy, precision, and timeliness of intelligence forecasts.” The idea was that each school would recruit a team of foreign affairs experts, and then ask them to make predictions about the future. Researchers would study who made the most accurate forecasts and, crucially, how they did it. Those insights, the government hoped, would help CIA analysts become better at their jobs.
Most of the universities that participated in the program took a standard approach. They sought out professors, graduate students, international policy researchers, and other specialists. Then they gave them questions no one yet knew the answers to—Will North Korea reenter arms talks by the end of the year? Will the Civic Platform party win the most seats in the Polish parliamentary elections?—and watched how they went about answering. Studying various approaches, everyone figured, would provide the CIA with some fresh ideas.
Two of the universities, however, took a different tack. A group of psychologists, statisticians, and political scientists from the University of Pennsylvania and the University of California–Berkeley, working together, decided to use the government’s money as an opportunity to see if they could train regular people to become better forecasters. This group called themselves “the Good Judgment Project,” and rather than recruit specialists, the GJP solicited thousands of people—lawyers, housewives, master’s students, voracious newspaper readers, and enrolled them in online forecasting clas
ses that taught them different ways of thinking about the future. Then, after the training, those participants were asked to answer the same foreign affairs questions as the experts.
For two years, the GJP conducted training sessions, watched people make predictions, and collected data. They tracked who got better, and how performance changed as people were exposed to different types of tutorials. Eventually, the GJP published their findings: Giving participants even brief training sessions in research and statistical techniques—teaching them various ways of thinking about the future—boosted the accuracy of their predictions. And most surprising, a particular kind of lesson—training in how to think probabilistically—significantly increased people’s abilities to forecast the future.
The lessons on probabilistic thinking offered by the GJP had instructed participants to think of the future not as what’s going to happen, but rather as a series of possibilities that might occur. It taught them to envision tomorrow as an array of potential outcomes, all of which had different odds of coming true. “Most people are sloppy when they think about the future,” said Lyle Ungar, a professor of computer science at the University of Pennsylvania who helped oversee the GJP. “They say things like, ‘It’s likely we’ll go to Hawaii for vacation this year.’ Well, does that mean that it’s 51 percent certain? Or 90 percent? Because that’s a big difference if you’re buying nonrefundable tickets.” The goal of the GJP’s probabilistic training was to show people how to turn their intuitions into statistical estimates.
One exercise, for instance, asked participants to analyze if the French president Nicolas Sarkozy would win reelection in an upcoming vote.
The training indicated that, at a minimum, there were three variables someone should consider in predicting Sarkozy’s reelection chances. The first was incumbency. Data from previous French elections indicated that an incumbent such as President Sarkozy, on average, can expect to receive 67 percent of the vote. Based on that, someone might forecast that Sarkozy is 67 percent likely to remain in office.
But there were other variables to take into account, as well. Sarkozy had fallen into disfavor among French voters, and pollsters had estimated that, based on low approval ratings, Sarkozy’s reelection chances were actually 25 percent. Under that logic, there was a three-quarters chance he would be voted out. It was also worth considering that the French economy was limping along, and economists guessed that, based on economic performance, Sarkozy would garner only 45 percent of the vote.
So there were three potential futures to consider: Sarkozy could earn 67 percent, 25 percent, or 45 percent of the votes cast. In one scenario, he would win easily, in another he would lose by a wide margin, and the third scenario was a relatively close call. How do you combine those contradictory outcomes into one prediction? “You simply average your estimates based on incumbency, approval ratings, and economic growth rates,” the training explained. “If you have no basis for treating one variable as more important than another, use equal weighting. This approach leads you to predict [(67% + 25% + 45%)/3] = approximately a 46% chance of reelection.”
Nine months later, Sarkozy received 48.4 percent of the vote and was replaced by François Hollande.
This is the most basic kind of probabilistic thinking, a simplistic example that teaches an underlying idea: Contradictory futures can be combined into a single prediction. As this kind of logic gets more sophisticated, experts usually begin speaking about various outcomes as probability curves—graphs that show the distribution of potential futures. For instance, if someone was asked to guess how many seats Sarkozy’s party was going to win in the French parliament, an expert might describe the possible outcomes as a curve that shows how the likelihood of winning parliamentary seats is linked to Sarkozy’s odds of remaining president:
In fact, when Sarkozy lost the election, his party, the Union pour un Mouvement Populaire, or UMP, also suffered at the polls, claiming only 194 seats, a significant decline.
The GJP’s training modules instructed people in various methods for combining odds and comparing futures. Throughout, a central idea was repeated again and again. The future isn’t one thing. Rather, it is a multitude of possibilities that often contradict one another until one of them comes true. And those futures can be combined in order for someone to predict which one is more likely to occur.
This is probabilistic thinking. It is the ability to hold multiple, conflicting outcomes in your mind and estimate their relative likelihoods. “We’re not accustomed to thinking about multiple futures,” said Barbara Mellers, another GJP leader. “We only live in one reality, and so when we force ourselves to think about the future as numerous possibilities, it can be unsettling for some people because it forces us to think about things we hope won’t come true.”
Simply exposing participants to probabilistic training was associated with as much as a 50 percent increase in the accuracy of their predictions, the GJP researchers wrote. “Teams with training that engaged in probabilistic thinking performed best,” an outside observer noted. “Participants were taught to turn hunches into probabilities. Then they had online discussions with members of their team [about] adjusting the probabilities, as often as every day….Having grand theories about, say, the nature of modern China was not useful. Being able to look at a narrow question from many vantage points and quickly readjust the probabilities was tremendously useful.”
Learning to think probabilistically requires us to question our assumptions and live with uncertainty. To become better at predicting the future—at making good decisions—we need to know the difference between what we hope will happen and what is more and less likely to occur.
“It’s great to be 100 percent certain you love your girlfriend right now, but if you’re thinking of proposing to her, wouldn’t you rather know the odds of staying married over the next three decades?” said Don Moore, a professor at UC-Berkeley’s Haas School of Business who helped run the GJP. “I can’t tell you precisely whether you’ll be attracted to each other in thirty years. But I can generate some probabilities about the odds of staying attracted to each other, and probabilities about how your goals will coincide, and statistics on how having children might change the relationship, and then you can adjust those likelihoods based on your experiences and what you think is more or less likely to occur, and that’s going to help you predict the future a little bit better.
“In the long run, that’s pretty valuable, because even though you know with 100 percent certainty that you love her right now, thinking probabilistically about the future can force you to think through things that might be fuzzy today, but are really important over time. It forces you to be honest with yourself, even if part of that honesty is admitting there are things you aren’t sure about.”
When Annie started playing poker seriously, it was her brother who sat her down and explained what separated the winners from everyone else. Losers, Howard said, are always looking for certainty at the table. Winners are comfortable admitting to themselves what they don’t know. In fact, knowing what you don’t know is a huge advantage—something that can be used against other players. When Annie would call Howard and complain that she had lost, had suffered bad luck, that the cards had gone against her, he would tell her to stop whining.
“Have you considered that you might be the idiot at the table who’s looking for certainty?” he asked.
In Texas Hold’Em, the kind of poker Annie was playing, each player received two private cards, and then five communal cards were dealt, faceup, onto the middle of the table to be shared by everyone. The winner was whoever had the best combination of private and communal cards.
When Howard was learning to play, he told Annie, he would go to a late-night game with Wall Street traders, world-champion bridge players, and other assorted math nerds. Tens of thousands of dollars would trade hands as they played until dawn, and then everyone would get breakfast together and deconstruct the games. Howard eventually realized that the hard part of poker
wasn’t the math. With enough practice, anyone can memorize odds or learn to estimate the chances of winning a pot. No, the hard part was learning to make choices based on probabilities.
For example, let’s say you’re playing Texas Hold’Em, and you have a queen and nine of hearts as your private cards, and the dealer has put four communal cards on the table:
One more communal card is going to be dealt. If that last card is a heart, you have a flush, or five hearts, which is a strong hand. A quick mental calculation tells you that since there are 52 cards in a deck, and 4 hearts are already showing, there are 9 possible hearts remaining that might be dealt onto the table, as well as 37 nonheart cards. Put differently, there are 9 cards that will get you a flush, and 37 that won’t. The odds, then, of getting a flush are 9 to 37, or roughly 20 percent.*1
In other words, there’s an 80 percent chance you won’t make the flush and could lose your money. A novice player, based on those odds, will often fold and get out of the hand. That’s because a novice is focused on certainties: The odds of getting a flush are relatively small. Rather than throw money away on an unlikely outcome, they’ll quit.
But an expert sees this hand differently. “A good poker player doesn’t care about certainty,” Annie’s brother told her. “They care about knowing what they know and don’t know.”
For instance, if an expert is holding a queen and nine of hearts and hoping for a flush, and she sees her opponent bet $10, bringing the total pot to $100, a second set of probabilities starts getting calculated. To stay in the game—and see if the last card is a heart—the expert needs only to match the last wager, $10. If the expert bets $10 and makes the flush, she’ll win $100. The expert is being offered “pot odds” of 10 to 1, because if she wins, she’ll get $10 for every $1 she bets right now.
Smarter Faster Better: The Secrets of Being Productive in Life and Business Page 18
