In the eighties, Klaus Teuber was working as a dental technician outside the industrial city of Darmstadt, Germany. He was unhappy. “I had many problems with the company and the profession,” he told me. He started designing elaborate board games in his basement workshop. “I developed games to escape,” he said. “This was my own world I created.”

Teuber, now sixty-one, is the creator of The Settlers of Catan, a board game in which players compete to establish the most successful colony on a fictional island called Catan, and the managing director of Catan GmbH, a multi-million-dollar business he runs with his family. First published in Germany in 1995 as Die Siedler von Catan, the game has sold more than eighteen million copies worldwide. It was released in the United States in 1996; last year, its English-language publisher, Mayfair Games, reported selling more than seven hundred and fifty thousand Catan-related products. Big-box chains like Target, Walmart, and Barnes & Noble carry the game and its offshoots, such as Catan cards, Catan Junior, and Star Trek Catan. Including all the spinoffs, expansions, and special editions, there are about eighty official varieties of Catan—more if you include electronic versions—and Teuber has had a hand in creating all of them. Paraphernalia in the online Catan shop includes socks and custom-designed tables. Rebecca Gablé, a German historical-fiction author, has written a Viking-era Settlers of Catan novel. Pete Fenlon, the C.E.O. of Mayfair Games, said, “Our volume of sales will be such that, over time, Catan could, in terms of gross revenue, be the biggest game brand in the world.”

Teuber is still somewhat baffled by the popularity of his creation. “I never expected it would be so successful,” he said. Almost all board-game designers, even the most successful ones, work full time in other professions; Teuber is one of a tiny handful who make a living from games. “Going Cardboard,” a 2012 documentary about the board-game industry, includes footage of Teuber appearing at major gaming conventions, where he is greeted like a rock star—fans whisper and point when they see him—but seems sheepish while signing boxes.

Teuber left his dental lab in 1998, “when I felt like Catan could feed me and my family,” he said. He and his wife, Claudia, have three children. In 2002, they incorporated Catan GmbH and made it the family business. Teuber and his sons, Guido and Benjamin, each hold the title of managing director; Guido focusses on the English-speaking market and Benjamin controls the international side and helps with game development. (Teuber’s daughter is an actress; although she’s sometimes roped in as an unofficial game tester, she’s not formally involved with the company.) Claudia is responsible for bookkeeping and testing new games. “Luckily, she loves Catan as I do,” Teuber said.

Die Siedler von Catan is available in over thirty languages. Catan licenses the idea and prototype to publishers, who then produce and market the game and pay Catan GmbH about ten per cent in royalties. (The model works a lot like the relationship between book authors and their publishers.) Catan’s relationship with Mayfair goes deeper than a typical licensing deal: the companies have grown together, and, at this point, their fortunes are thoroughly intertwined. Catan GmbH is a shareholder in Mayfair, and Catan products make up a large portion of Mayfair’s revenue. “Collectively, all the rest of our portfolio doesn’t add up to Catan,” Mayfair’s Fenlon told me. The company originally sourced all of the materials for the game from Europe, but, when demand began to take off, the manufacturers didn’t have enough wood to keep up. Mayfair expanded to American companies for more resources. Today, every box of Catan that Mayfair produces is an international affair: the dice are tooled in Denmark; the more intricate wooden pieces are done in Germany; other wood parts are made in Ohio; the cards are from Dallas; the boxes, Illinois; the cardboard, Indiana; the plastic components, Wisconsin; finally, everything gets put together on an assembly line in Illinois.

Here’s how The Settlers of Catan works: There are nineteen hexagonal tiles, known as “terrain hexes.” Each hex represents one of five resources: brick, wool, ore, grain, or lumber. To start the game, the tiles are shuffled and laid out to create the game board, which is the island. Every hex then gets assigned a number between two and twelve; these numbers are evenly distributed across the board. Players take turns rolling the dice, and the number that’s rolled determines which terrain hex produces resources. By collecting various combinations of resources, you can build roads and settlements around the borders of these hexes, placing little wooden houses on the board to mark out turf. More resources allow you to build more or to upgrade your settlements into cities. There’s also a robber in Catan, a token that moves around to different terrain hexes. When the robber’s on a hex, that terrain can’t produce its resources, and every time a seven is rolled players with too many resources have to give some back. The robber is crucial: it forces players to trade with opponents instead of hoarding goods.

A board game with economic theory, land development, and cute little buildings: one is naturally reminded of something else. The Washington Post hailed Catan as the Monopoly “of our time.” Wired called it the “Monopoly Killer.” Meanwhile, Monopoly itself has begun to respond to the shifting tides. In 2007, Hasbro published Tropical Tycoon Monopoly, in which the original Atlantic City layout frames the perimeter while Rich Uncle Pennybags erupts from a volcanic tropical island in the center. U-Build Monopoly, released in 2010, replaces the rectangle properties with hexagonal tiles that resemble Catan’s terrain. Still, Derk Solko, a co-founder of the popular gaming forum Boardgamegeek.com, said to Wired in 2009, “If I could wave a magic wand and replace all the copies of Monopoly out there with Settlers, I truly think the world would be a better place.” Fenlon told me, “Our mission in life is to make Catan the preëminent game—to have people think of Catan instead of Monopoly when they think of a board game.”

Teuber himself is more sanguine. “I do not see that Catan will kill Monopoly,” he said. “But I hope that Catan will become a permanent classic game beside Monopoly.” In Catan, one player’s success can benefit others, and if you simply form a monopoly on one resource you’ll never win, since you have to have a combination of different elements to get anywhere on the island. (There is a “Monopoly” card in Catan, which gives its holder the power to steal all the resource cards of a declared type from opponents’ hands, but it’s a one-time, unpredictable bonanza.) Competition, Teuber believes, makes Catan better, for players and for him. Strategy and inventiveness are required in order to keep up.

Teuber was born in 1952 in Rai-Breitenbach, a small village tucked beneath Breuberg Castle, in central Germany. As a child, he set up miniature fighters and ancient Romans on the floor, using strings to create mountains and rivers and to build routes through the terrain. He rediscovered games during his mandatory military service, when he needed something to entertain his wife and young son in the barracks. He was still running Teuber Dental-Labor in 1988, when he designed Barbarossa, a game in which players mold clay sculptures and try to guess what their opponents’ figures represent. He had been reading “The Riddle-Master,” a swashbuckling fantasy trilogy by Patricia McKillip about a man who wins a game of riddles against a ghost. “I was sorry to see it come to an end,” Teuber said, “so I tried to experience this novel in a game.” It took Teuber seven years to show Barbarossa to a publisher, but when he did it was a hit. The game won the 1988 Spiel des Jahres award, the most coveted prize in the board-game world. According to Stewart Woods, a communications professor at the University of Western Australia, a successful game typically sells about ten thousand copies in Germany; a Spiel des Jahres winner can expect to sell between three hundred and five hundred thousand.