LOS ANGELES — Kathryn Bigelow’s well-reviewed “Detroit” arrived to about $7.3 million in North American ticket sales over the weekend, a limp result for a wide-release movie that cost at least $55 million to make and market.

“Detroit,” a harrowing account of the riots that engulfed that city in 1967, with a focus on the killing of black teenagers by the police, was not Hollywood’s most expensive new offering. That distinction belonged to “The Dark Tower,” a troubled adaptation of Stephen King’s book series that cost Sony and Media Rights Capital about $60 million to make and tens of millions more to market. “The Dark Tower,” which most critics disliked, took in $19.5 million, a soft total that was nonetheless enough for No. 1.

But “Detroit” was the release that Hollywood was watching most keenly, partly because it represented an effort by Annapurna Pictures to join the movie-business big leagues.

Founded by 2011 by the Oracle heiress Megan Ellison, Annapurna has been a successful producer of prestige-minded dramas like “American Hustle” and Ms. Bigelow’s “Zero Dark Thirty.” But Ms. Ellison, until now, has always relied on experienced studio partners to market and distribute her movies. “Detroit” was Annapurna’s first attempt to go it alone.