Mr. Farnsworth said, “When you apply computer science and machine learning to an industry that we believe has lacked significant innovation, useful patterns start to emerge.” If MoviePass gets big enough, it could try to demand that chain theaters sell tickets at a discount or share a slice of their concession revenue.

Helios recently raised $60 million for the expansion of MoviePass, which expects to have more than three million subscribers by the end of next year. Monthly subscriber retention is roughly 96 percent, Mr. Lowe said. About 75 percent of MoviePass users are millennials, a group that Hollywood has struggled to turn into avid moviegoers.

“Millennials understand us because they grew up on subscription,” Mr. Lowe said.

Dan Steven, 34, signed up for MoviePass in October. Mr. Steven, who lives in Orlando, Fla., said he had gone to “maybe one movie a month” before he became a subscriber. In November, he went 12 times.

“I used to only go if it was clearly worth buying a ticket — something big-screen worthy, a spectacle or a movie with a lot of effects,” he said. “I would skip the undercard movies. I would just wait until they came out on Netflix.”

Over the last decade, theaters have spent billions of dollars to enhance the moviegoing experience. Improvements include the ability to reserve seats online, reclining seats, bigger screens, and better sound and projection systems. But the business has remained more or less the same for decades (sell ticket, serve popcorn, show movie) even as nearly every other area of media (television, music, publishing) has been forced to reinvent itself to contend with digital disruption.

As the popularity of MoviePass demonstrates, theater owners may no longer be able to avoid fundamental change. In particular, studios are expected to force exhibitors in the coming months to loosen their grip on new movies. Theaters have typically insisted on a 90-day period of exclusivity. Studios want to shorten that window and speed films to home video-on-demand services.