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.
Now the expert player can compare those odds by imagining this hand one hundred times. The expert doesn’t know if she is going to win or lose this hand, but she does know that if she played this exact same hand one hundred times, she would, on average, win twenty times, collecting $100 with each victory, yielding $2,000.
And she knows that playing one hundred times will cost her only an additional $1,000 (because she has to bet only $10 each time). So even if she lost eighty times and won only twenty times, she would still pocket an extra $1,000 (which is the winnings of $2,000 less the $1,000 needed to play).
Got it? It’s okay if you don’t, because the point here is that probabilistic thinking tells the expert how to proceed: She is aware there’s a lot she can’t predict. But if she played this same hand one hundred times, she would probably end up $1,000 richer. So the expert makes the bet and stays in the game. She knows, from a probabilistic standpoint, it will pay off over time. It doesn’t matter that this hand is uncertain. What matters is committing to odds that pay off in the long run.
“Most players are obsessed with finding the certainty on the table, and it colors their choices,” Annie’s brother told her. “Being a great player means embracing uncertainty. As long as you’re okay with uncertainty, you can make the odds work for you.”
Annie’s brother, Howard, is competing in this Tournament of Champions right alongside her when the FossilMan is eliminated. Over the past two decades, Howard has established himself as one of the finest players in the world. He has two World Series of Poker bracelets and millions in winnings. Early in the tournament, Annie and Howard lucked out and didn’t have to directly compete for many big pots. Now, however, seven hours have passed.
First the FossilMan was eliminated by that bit of bad luck. Another competitor named Doyle Brunson, a seventy-one-year-old nine-time champion, was knocked out by a risky attempt to double his chips. Phil Ivey, who won his first World Series of Poker tournament at twenty-four, was eliminated by Annie when she drew an ace and queen against Ivey’s ace and eight. Over time, the players at the table have dwindled until there are only three players remaining: Annie, Howard, and a man named Phil Hellmuth. It is inevitable Annie and Howard will butt up against each other. The contestants spar over chips and hands for ninety minutes. Then Annie gets a pair of sixes.
She starts tallying what she does and doesn’t know. She knows she has strong cards. She knows, from a probabilistic standpoint, that if she played this hand one hundred times, she would do okay. “Sometimes when I’m teaching poker, I’ll tell people there are situations where you shouldn’t even look at your cards before you bet,” Annie told me. “Because if the pot odds are in your favor, you should always make the bet. Just commit to it.”
Howard, her brother, seems to like his hand as well, because he pushes all of his chips, $310,000, onto the table. Phil Hellmuth folds. The bet is to Annie.
“I’ll call,” she says.
They both turn over their cards. Annie reveals her pair of sixes.
Howard reveals a pair of sevens.
“Nice hand, Bub,” Annie says. Howard has an 82 percent chance of winning this hand, collecting chips worth more than half a million dollars, and becoming the table’s dominant leader. From a probabilistic perspective, they both played this hand exactly right. “Annie made the right choice,” Howard later said. “She committed to the odds.”
The dealer turns over the first three communal cards.
“Oh, God,” Annie says and covers her face. “Oh, God.”
The six and the two queens in the communal pile give Annie a full house. If Annie and Howard replayed this hand one hundred times, Howard would likely win eighty-two of those contests. But not this time. The dealer puts the remaining cards on the table.
Howard is out.
Annie jumps from her chair and hugs her brother. “I’m sorry, Howard,” she whispers. Then she runs out of the studio. She starts sobbing before she makes it to the door.
“It’s okay,” Howard says when he finds her in the hall. “Just beat Phil now.”
“You have to learn to live with it,” Howard told me later. “I just went through this same thing with my son. He was applying to colleges and he was nervous about it, so we came up with a list of twelve schools—four safety schools, four he had an even chance of getting into, and four that were stretches—and we sat down and started calculating the odds.”
By looking at the statistics those schools had published online, Howard and his son calculated the likelihood of getting into each college. Then they added all those probabilities together. It was fairly basic math, the kind even English majors can manage with a little bit of Googling. They figured out that Howard’s son had a 99.5 percent chance of getting into at least one school, and a better than even chance of getting into a good school. But it was far from certain he would get into one of the stretch schools, the ones he had fallen in love with. “That was disappointing, but by going through the numbers, he felt less anxious,” Howard said. “It prepared him for the possibility that he wouldn’t get into his first choice, but he would definitely get in somewhere.
“Probabilities are the closest thing to fortune-telling,” Howard said. “But you have to be strong enough to live with what they tell you might occur.”
III.