Not everyone has found the online world of Minecraft so hospitable. One afternoon while visiting the offices of Mouse, a nonprofit organization in Manhattan that runs high-tech programs for kids, I spoke with Tori. She’s a quiet, dry-­witted 17-year-old who has been playing Minecraft for two years, mostly in single-­player mode; a recent castle-­building competition with her younger sister prompted some bickering after Tori won. But when she decided to try an online server one day, other players — after discovering she was a girl — spelled out “BITCH” in blocks.

She hasn’t gone back. A group of friends sitting with her in the Mouse offices, all boys, shook their heads in sympathy; they’ve seen this behavior “everywhere,” one said. I have been unable to find solid statistics on how frequently harassment happens in Minecraft. In the broader world of online games, though, there is more evidence: An academic study of online players of Halo, a shoot-’em-up game, found that women were harassed twice as often as men, and in an unscientific poll of 874 self-­described online gamers, 63 percent of women reported “sex-­based taunting, harassment or threats.” Parents are sometimes more fretful than the players; a few told me they didn’t let their daughters play online. Not all girls experience harassment in Minecraft, of course — Lea, for one, told me it has never happened to her — and it is easy to play online without disclosing your gender, age or name. In-game avatars can even be animals.

How long will Minecraft’s popularity endure? It depends very much on Microsoft’s stewardship of the game. Company executives have thus far kept a reasonably light hand on the game; they have left major decisions about the game’s development to Mojang and let the team remain in Sweden. But you can imagine how the game’s rich grass-roots culture might fray. Microsoft could, for example, try to broaden the game’s appeal by making it more user-­friendly — which might attenuate its rich tradition of information-­sharing among fans, who enjoy the opacity and mystery. Or a future update could tilt the game in a direction kids don’t like. (The introduction of a new style of combat this spring led to lively debate on forums — some enjoyed the new layer of strategy; others thought it made Minecraft too much like a typical hack-and-slash game.) Or an altogether new game could emerge, out-­Minecrafting Minecraft.

But for now, its grip is strong. And some are trying to strengthen it further by making it more accessible to lower-­income children. Mimi Ito has found that the kids who acquire real-world skills from the game — learning logic, administering servers, making YouTube channels — tend to be upper middle class. Their parents and after-­school programs help them shift from playing with virtual blocks to, say, writing code. So educators have begun trying to do something similar, bringing Minecraft into the classroom to create lessons on everything from math to history. Many libraries are installing Minecraft on their computers.

One recent afternoon, I visited the Bronx Library Center, a sleek, recently renovated building in a low-­income part of the borough. A librarian named Katie Fernandez had set up regular Minecraft days for youths, and I watched four boys play together on the library’s server. Fernandez had given them a challenge: Erect a copy of the Arc de Triomphe in Paris in 45 minutes. Three of them began collaborating on one version; a younger boy worked on his own design. The three gently teased one another about their skills. “No, no, stop!” shouted one, when he noticed another building a foot of the Arc too wide. “Ryan, this — like this!” They debated whether command blocks would speed things up. As the 45th minute approached, they hadn’t quite finished their Arc, so they gleefully stuffed the interior with TNT, detonated it and hopped onto different games.

Over in the corner, the fourth boy continued to labor away at his Arc. He told me he often stays up late playing Minecraft with friends; they have built the Statue of Liberty, 1 World Trade Center and even a copy of the very library he was sitting in. His fingers clicked in a blur as he placed angled steps, upside-­down, to mimic the Arc’s beveled top. He sat back to admire his work. “I haven’t blinked for over — I don’t know how many minutes,” he said. The model was complete, and remarkably realistic.

“I’m actually pretty proud of that,” he said with a smile.