World War II involved more than two dozen countries spread across six continents and tens of millions of soldiers. But according to ‘The Imitation Game’ the entire conflict hinged on the actions of half a dozen crossword puzzle enthusiasts in a couple of huts in the South of England. It was there that a team of cryptographers created a revolutionary machine that could decode Nazi messages and turned the tide of the war for the Allies. Their leader was Alan Turing (Benedict Cumberbatch), a mathematician who was rude, disrespectful, and socially awkward in the extreme—and also one of the most brilliant minds of the 20th century. ‘The Imitation Game’ considers his life: His great achievements, his most-closely hidden secrets, and the ways in which the latter may have helped inspire the former.

Every day during the war, the German military sent its orders via ordinary radio transmission. Anyone with a receiver could hear them—but only those with a sophisticated encryption device called an Enigma machine could understand them. In the early days of WWII, the British acquired an Enigma, but because of the gadget’s complex inner-workings, each code had 159,000,000,000,000,000,000 potential solutions. And every night at midnight, the cipher reset, rendering the previous day’s work useless. Even for the brilliant men assembled by the British government to crack the Enigma code, solving this puzzle was a nearly impossible task.

Faced with this dilemma, Turing posed a provocative question: “What if only a machine can defeat another machine?” He’s referring to the enormous device—essentially one of the world’s first computers—he would design and construct, but it’s implied that Turing is also referring to himself. Turing has no close friends, finds it difficult to communicate with others, struggles to understand obvious jokes, and feels little loyalty or camaraderie with the rest of his team. After Winston Churchill gives him power over the cryptography unit, Turing instantly fires two members he finds deficient. His subordinates, even the ones that like him, call him “inhuman.” Imagine if Drax the Destroyer from ‘Guardians of the Galaxy’ was a brilliant mathematician ordered to lead and motivate a group of Earthlings, and you sort of get the idea.

‘The Imitation Game’’s structure is elegant, if not particularly sophisticated; no elaborate deciphering is required. Director Morten Tyldum tells Turing’s story in three distinct time periods. While Turing and his team race to break Enigma, the pre-teen Turing (a very good Alex Lawther) is ostracized and bullied at prep school and learns about cryptography from a classmate named Christopher (Jack Bannon), and an older Turing is investigated by a Manchester police officer (Rory Kinnear) who believes he’s hiding something. (He is, of course, but not what Kinnear’s character suspects.)

Turing refers to the Enigma as a game or puzzle, which is exactly how ‘The Imitation Game’ treats Turing. Rather that delving deeply into Turing’s private life, Tyldum (whose previous movie, the Norwegian thriller ‘Headhunters,’ explored similar themes of deception, identity, and secrecy) treats it as another inscrutable piece of information to be decoded; the movie only discusses Turing’s proclivities after Kinnear’s cop character discovers them for himself in 1951. While that decision does lend ‘The Imitation Game’ an added layer of mystery, it also reductively boils down a man’s life to a cinematic riddle. This defining component of his personality is treated as an unseen theoretical, as if Turing himself was a simple equation with an algebraic variable waiting to be solved.

What complexity is found onscreen comes primarily from the talented cast, led by the cultishly popular Cumberbatch. A lot of Cumberbatch’s American film roles to date have tested his range, and not always in flattering ways. The part of Turing is a lot closer to his star-making turn on British television’s ‘Sherlock,’ and lets Cumberbatch work in that brilliant-but-prickly sweet spot he’s already carved out as his singular niche. Though the film is very much defined by his performance, he’s surrounded by very good actors doing solid work with limited material. Keira Knightley provides a humanizing element as Joan, Turing’s intellectual equal and potential love interest, and Matthew Goode exudes charm as the rakish, roguish cryptographer Hugh Alexander. The other standout in the cast is Mark Strong as a mysterious and slyly charismatic member of MI6. It’s a typical role for Strong, who plays a lot of devious functionaries and administrators, but one he imbues with tons of scene-stealing charm and droll wit. Someone give this guy a spy movie to headline.

‘The Imitation Game’ is handsomely made, respectably acted, and reveals an interesting and important piece of world history. In other words, it’s a standard Hollywood biopic of the kind that fills movie theaters every fall. It’s hard to fault an effective piece of classical entertainment, though one could argue that a movie about a singular and unique genius deserves a movie that can be described the same way—and ‘The Imitation Game’ is anything but singular or unique. A line that is repeated throughout the film, referring to Turing or his fellow outcasts, says that “sometimes it’s the people no one can imagine anything of who do the things no one can imagine.” The worst you can say about ‘The Imitation Game’ is that this is exactly the movie you imagine someone would make of this material.