There’s something deeply satisfying, cozy almost, about The Imitation Game, a WWII spy thriller with a biomovie underpinnings centered around a crack performance by Benedict Cumberbatch (Sherlock, Star Trek Into Darkness) as the brilliant analytical mathematician but socially inept Alan Turing, who, with a motley crew of cryptologists, broke the Nazis’ shipping codes, crushed the Enigma machine, and helped win the war. The brilliant, verbally agile Turing’s achievements were astonishing but because he was homosexual, then a criminal offense, the British government suppressed his fame and heroism. In 1954, mercilessly hounded and neutered by Brit authorities, Turing ended his own life.

The posh, pacey, beautifully shot movie, directed by Morten Tyldum from a spry screenplay by Graham Moore, is anything but a dirge, though. In fact, it feels like it ought to be viewed by a roaring fire with a fine wine. That doesn’t mean it’s fussy or musty but it does err in being too tidy. It smooths over and almost buries Turing’s gayness, his bullying at school, his love for a fellow student, and the torment ignorance and bigotry made of his life.

Cumberbatch does what he can to fill in the blanks and he is the real thing here — all shyness, rudeness, acid comments, pathos, dazzling intellect and aching melancholy, while suppressing his velvety star charisma. He dazzles alongside costars like Keira Knightley (better than ever as a wizardly member of the Bletchley Park team and Turing’s abortive love interest) and Matthew Goode as a womanizing chess champ cryptologist who radiates a haughtiness that recalls the glory days of old time movie cads like George Sanders.

The movie opens with Cumberbatch snapping, “Are you paying attention?” In the smart, gripping The Imitation Game, the stakes are so high, the level of craft and art so solid that it’s impossible not to pay attention. *** ½