“But the difference between prejudice and Bayesian thinking is that I try to improve my assumptions as we go along. So once we start playing, if I see that the forty-year-old is a great bluffer, that might mean he’s a professional hoping everyone will underestimate him. Or, if the twenty-two-year-old is trying to bluff every hand, it probably means he’s some rich kid who doesn’t know what he’s doing. I spend a lot of time updating my assumptions because, if they’re wrong, my base rate is off.”
With Annie’s brother out of the competition, there are only two players left at the Tournament of Champions table: Annie and Phil Hellmuth. Hellmuth is a card room legend, a television celebrity known as “the Poker Brat.” “I’m the Mozart of poker,” he told me. “I can read other players probably better than anyone playing, maybe anyone in the world. It’s white magic, instinct.”
Annie is at one end of the table, Hellmuth at the other. “I had a good idea of how Phil viewed me at that point,” Annie said later. “He’s told me before that he has a low opinion of my creativity, that he thinks I’m more lucky than smart, that I’m too scared to bluff when it matters.”
That’s a problem for Annie, because she wants Phil to think she’s bluffing. The only way she can lure him into a big pot is by convincing him she’s bluffing when, in fact, she isn’t. To win this tournament, Annie needs to force Phil to change his assumptions of her.
Phil, though, has a different plan. He believes he’s the stronger player. He believes he can read Annie. “I have this capacity to learn very, very quickly,” he told me. “When I know what people are doing, I can control the table.” Those aren’t idle boasts. Hellmuth has won fourteen poker championships.
Annie and Phil have roughly equal piles of chips. For the next hour, they play hand after hand, neither gaining a clear advantage. Phil keeps subtly trying to throw Annie off, to make her mad or lose her cool.
“I would have preferred to play your brother,” he says.
“This is all right,” Annie replies. “I’m just happy to be in the finals.”
Annie bluffs Phil four times. “I wanted him to reach the breaking point where he says, ‘Screw this, she’s bluffing me hand after hand and I gotta fight back,’?” Annie said. But Phil doesn’t seem shaken. He doesn’t overreact.
Finally, Annie gets the hand she’s been waiting for. The dealer gives her a king and a nine. Phil receives a king and a seven. In the middle of the table, the dealer lays down a communal king, six, nine, and jack.
Phil knows he has a pair of kings. But unbeknownst to him, Annie has two pair—kings and nines. Neither sees what the other is holding.
It’s Annie’s bet, and she raises $120,000. Phil, thinking his pair of kings is likely the strongest hand at the table, matches it. Then Annie goes all in, bringing the pot to $970,000.
The bet is now to Phil.
He starts muttering to himself. “This is unbelievable,” he says out loud. “Really unbelievable. She might not even know how strong I am here. I’m not sure she fully even understands the value of the hand.”
He stands up.
“I don’t know,” he says, pacing around the table. “I don’t know, I have a bad feeling about this hand.” He folds.
Phil flips over his king, showing Annie that he had a pair. Then Annie strikes: She casually turns over one of her cards—but not both—showing Phil her pair of nines, but not revealing that she also had a pair of kings.
“I wanted to force him to change his assumptions about me,” Annie later said. “I wanted him to think I was bluffing with a pair of nines.”
“Wow, did you really just push in with a nine?” Phil says to Annie. “That’s so reckless, especially against someone like me. Maybe I acted too fast.”
The players ready for the next hand. Annie has $1,460,000 in chips; Phil has $540,000. The dealer gives them their cards. Annie has a king and a ten; Phil a ten and an eight. The first communal cards come out as a two, ten, and seven.
Phil has a pair of tens, with an eight backing it up. It’s a good hand. Annie also has a pair of tens, with a king, slightly better.
Phil pushes $45,000 into the pot. Annie raises $200,000. It’s an aggressive move. But Phil is starting to believe that Annie is playing recklessly. He thinks he sees a pattern he didn’t expect from her: She’s bluffing and bluffing and bluffing again. Phil’s base rate is gradually shifting.
Phil looks at the pile of chips on the table. Maybe his assumption that Annie is too scared to bluff at critical moments is wrong? Maybe Annie is bluffing right now? Maybe she’s finally overplayed her hand?
“I’m all in,” Phil says, pushing his stack into the middle of the table.
“I call,” Annie says.
Both players turn over their cards.
“Shit,” Phil says, seeing that they both have a pair of tens—and that Annie has the high card, a king to Phil’s eight.
The dealer puts a seven on the table, benefiting neither player.
Annie is now standing, gripping her cheeks. Phil is also on his feet, breathing hard. “Give me an eight, please,” he says. It’s the only card that will keep him in the game. The dealer turns over the final communal card. It’s a three.
Annie wins the $2 million. Phil is out. The game is over. Annie is the champion.
Later, she will tell people that winning this tournament changed her life. It made her, in effect, the most famous female poker player on earth. In 2010, she went on to win the National Heads-Up Poker Championship. Today, she holds a record for World Series of Poker profits. In total, she’s won more than $4 million. She doesn’t worry about her mortgage anymore. She doesn’t have panic attacks. In 2009, she appeared on a season of Celebrity Apprentice. She was a little nervous before the filming started, but not too much. There were no anxiety breakdowns. She doesn’t play in many poker tournaments these days. She spends most of her time giving lectures to businesspeople about how to think probabilistically, about how to embrace uncertainty, about how, if you commit to a Bayesian outlook, you’ll make better decisions in life.
“A lot of poker comes down to luck,” Annie told me. “Just like life. You never know where you’ll end up. When I checked myself into the psych hospital my sophomore year, there’s no way I would have guessed I would end up as a professional poker player. But you have to be comfortable not knowing exactly where life is going. That’s how I’ve learned to keep the anxiety away. All we can do is learn how to make the best decisions that are in front of us, and trust that, over time, the odds will be in our favor.”
How do we learn to make better decisions? In part, by training ourselves to think probabilistically. To do that, we must force ourselves to envision various futures—to hold contradictory scenarios in our minds simultaneously—and then expose ourselves to a wide spectrum of successes and failures to develop an intuition about which forecasts are more or less likely to come true.
We can develop this intuition by studying statistics, playing games like poker, thinking through life’s potential pitfalls and successes, or helping our kids work through their anxieties by writing them down and patiently calculating the odds. There are numerous ways to build a Bayesian instinct. Some of them are as simple as looking at our past choices and asking ourselves: Why was I so certain things would turn out one way? Why was I wrong?
Regardless of our methods, the goals are the same: to see the future as multiple possibilities rather than one predetermined outcome; to identify what you do and don’t know; to ask yourself, which choice gets you the best odds? Fortune-telling isn’t real. No one can predict tomorrow with absolute confidence. But the mistake some people make is trying to avoid making any predictions because their thirst for certainty is so strong and their fear of doubt too overwhelming.