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Anyone who’s seen “Sherlock” on television knows that Benedict Cumberbatch owns the copyright on playing prickly British geniuses — but in the thoughtful drama, “The Imitation Game,” the actor brings some new ingredients to the mix. As Alan Turing, the brilliant World War II codebreaker whose life blended astonishing triumph and cruel tragedy, he’s self-conscious (watch the careful way Turing holds his mouth), cutting, and icy-cool, but there’s a sadness behind his characteristic smirk. As suited a man working in a secret industry — he and a Bletchley Park team were charged with cracking the Nazi’s supposedly unbreakable Enigma code — Turing had his own secret: he was gay, at a time when no one could know.

Graham Moore’s screenplay revolves us tidily in and out of three intercutting time periods: the 1920s, with Turing (played, uncannily accurately, by Cumberbatch mini-me Alex Lawther) as a young schoolboy in love; the war era; and the winter of 1952, in which Turing was arrested on charges of “gross indecency.” Most of the attention here is on the Bletchley Park years, which play out briskly. Keira Knightley, charmingly deploying an accent that sounds like bone china clinking, is the sole woman on the team; she and Alan act out a romance that’s really friendship in disguise. Aside from her, the most important supporting character is the computer — or, rather, the primitive version of one — that Turing devises; it’s a wonder of red wire and whirring discs, crouching in a room like a penned monster. (When this thing crunches numbers, it literally crunches.)

Directed by Morten Tyldum (and a far cry from his previous film, the gleefully bloody “Headhunters”), “The Imitation Game” may occasionally be a little too handsome for its own good — it feels like a conventional film about a very unconventional man. You wish more time were given to the events in Turing’s later life, but perhaps that’s a story for another filmmaker on another day. Nonetheless, “The Imitation Game” is both an education and a pleasure — and another chance to revel in what Cumberbatch can convey in eloquent silence. He resists any temptation to make Turing likable; instead, he crafts a complicated hero whose mind races like a computer, and lets us watch Alan run.

Moira Macdonald: 206-464-2725 or mmacdonald@seattletimes.com