Ariana Greenblatt will play Tiny Tina, the teenage explosives expert, in Eli Roth’s adaptation of the video game phenomenon “Borderlands.” She joins a cast of heavyhitters and A-listers that includes Cate Blanchett as Lilith, Kevin Hart as Roland, Jamie Lee Curtis as Dr. Tannis and Jack Black as Claptrap.

The history of movie versions of video games can be a bit spotty — “Sonic the Hedgehog” was a hit, as was “Lara Croft: Tomb Raider,” but there are also lots of duds in the “Super Mario Brothers” and “Assassins Creed” vein. But there’s a reason that “Borderlands” is hotly anticipated. It’s one of the world’s most successful video game franchises, with more than 68 million units sold worldwide, including over 24 million units of “Borderlands 2” and 12 million units sold for “Borderlands 3.”

Greenblatt has already racked up some impressive credits despite her relative youth. She starred in “Love and Monsters,...