In the past half-century, backgammon tournaments—like backgammon itself—have undergone a profound transformation. The game, which has been around in some form since the time of the Pharaohs, is most popular in the Near East, and in the 1920s it became a popular club game in the West. In the sixties, the game acquired a certain glamour. Lucille Ball played, and so did Paul Newman. The world championships were black-tie—though many competitors were mediocre, a condition that soon attracted the attention of genuine gamblers, who set out to unlock the game’s moneymaking potential. Backgammon is far more mathematical than chess, but, while chess has a literature that dates back centuries, backgammon had no real theory until the 1970s, when gamblers at New York’s Mayfair Club began to take the game apart systematically. Chess players can visualize what the board might look like 20 moves ahead, but in backgammon the dice offer 21 random possibilities at each turn. The game must be encountered frame by frame. The players at the Mayfair drew up tables: If one checker is 12 slots from another, there are three ways to attack, and an 8 percent chance of doing so successfully. They rolled out positions, playing every permutation to identify the best move. Rollouts could take hundreds of hours. Players attempted to calculate, at each position, their game “equity”—the more the better. By shaving off any trace of error, they could hedge against the chaos of the dice. To the uninitiated, they undoubtedly seemed astoundingly lucky. The Mayfair denizens won a lot of money, until their skill became too conspicuous.
For players of Falafel’s generation, the early theories were given a tremendous advance in the 1990s, when an engineer at IBM figured out how to apply neural-network computing to the game. The laborious rollouts were no longer necessary. One of the old Mayfair hands, Jersey Jim Pasko, a bodybuilder with a math degree, told me, “I’m spoiled. I want to do a lot of mathematical analysis, and I don’t want to allow anybody else to do any.” He said that many new players came into the game with a single-minded desire to make money, and lacked any sense of style and social grace, so he had dropped out of the circuit.
In San Antonio, while Kostadinov and O’Laughlin played, an official observer with a laptop computer entered their moves into a program that can roll out thousands of possibilities in seconds and calculate errors to three decimal points. Many younger players assume that its judgment is close enough to perfect. Michihito Kageyama, a former McDonald’s employee from Japan who is now fourth on the Giants of Backgammon list, told me that he had created a database of 10,000 positions. He reviews 30 a day on his Kindle, as a morning exercise.
Falafel has no patience for memorization. Because he is undisciplined, he regularly makes small mistakes early on, but in the complex middle game—where checkers are spread out in ambiguous arrangements, and the differences between plays can be hard to measure—he excels. “He’s very special,” Kageyama told me. “He doesn’t calculate equity. He’s just seeing it.” Perry Gartner, the president of the United States Backgammon Federation, put it this way: “Truthfully, out of the top 64 players that I know, there isn’t anyone who has his intuitive understanding of the game.”
I should have bet on Falafel: by the time the main tournament in San Antonio began, he and The Bone had arrived. The event was held in the Menger’s Grand Ballroom, though most of the attendees—130 people—were middle-aged men in T-shirts or casual wear. “Backgammon used to be a lot more glamorous,” one of the few women there told me. Falafel was wearing red Air Jordan sweatpants, a black-and-white plaid shirt, a green hoodie, and his yellow cap. His first opponent was Carter Mattig, a sound engineer from Chicago and a jocular trash-talker. Looking at Falafel, he said, “That’s quite a color combination he’s got today,” and that afternoon he posted a photograph online of Falafel in the ensemble, titled “The Angriest Elf.” Falafel was sore about it for days.
The two men found an empty spot at one of the folding tables that filled the room. When Falafel plays, his manner is casual but focused—unless he is losing, in which case his head droops as if it were filled with sand, and his body curls over the board. If an inferior player beats him, he might say, “He played horribly.” When Falafel wins, he is not always gracious, and he often seems unaware of his lack of tact. Once, on a backgammon forum, Mattig wrote, “I do vomit a little in my mouth when he speaks of his ‘modesty.’”
As a few spectators looked on, Falafel played Mattig, who put in earbuds and listened to music—to block out Falafel’s “crying,” he said. The play was brisk, and with each move Falafel, like all the Giants, was looking for fractional advantages. For most people, it is difficult to see the difference between a superlative player and a very good one. Later in the tournament, Jeremy Bagai, who is number 40 on the Giants list, pulled me aside during a game between two competitors who were playing at an exceptionally high level. “I haven’t seen anything like this,” he said. As a computer made clear, each move was just marginally better than the one Bagai would have made, but the aggregate effect was undeniable. Backgammon is a game of nano-distinctions.