"Pawn Sacrifice" tells the true story of American chess champion Bobby Fischer (Tobey Maguire) as he prepares for a legendary match-up against Russian Boris Spassky (Liev Schreiber). (Bleecker Street)

Our first glimpse of Bobby Fischer in “Pawn Sacrifice” is not the chess grandmaster’s proudest moment.

The year is 1972, when Fischer took on Soviet champion Boris Spassky for the world title in Iceland. Fischer, played by Tobey Maguire, is shown ripping apart his Reykjavik hotel suite, looking for listening devices. By the time a handler arrives to check on him, Fischer bears the look of a misbehaving child, sheepish and red-handed amid toppled lamps and torn artwork.

At the movies, at least, there’s no such thing as the ordinary, level-headed genius. Perhaps that trope doesn’t lend itself to compelling drama. But Fischer — yet another cinematic example of the troubled prodigy — is worth spending a couple of hours with.

Part of the appeal is Maguire, who has grown up a lot since portraying milquetoast Peter Parker in one “Spider-Man” sequel too many. Here, he’s a fascinating contradiction, utterly lost one moment and audaciously cocky the next, baiting the press and the whole of the Soviet Union.

Like other smart recent biopics, “Pawn Sacrifice” focuses on a single key period in its subject’s life. By-the-book flashbacks show us Fischer’s 1950s upbringing in Brooklyn, where his mother (Robin Weigert) laments, “If I take the pieces away, he just keeps playing in his head.”

But the story heats up once Fischer decides to make a bid for the championship by unseating the pride of the Soviet Union, Spassky, played by a fantastic Liev Schreiber, who delivers nearly all of his lines in Russian. At first, Spassky appears as the antithesis of Fischer; he’s a cool customer, outfitted in ubiquitous sunglasses and tailed by an intimidating entourage.

Boris Spassky (Liev Schreiber), left, and Bobby Fischer (Tobey Maguire) square off in “Pawn Sacrifice.” (Takashi Seida/Bleecker Street Media)

Fischer, meanwhile, grows more erratic and paranoid as the stakes grow higher. Americans badly want to see this guy from Brooklyn show the Soviet Union who’s boss. But the stress of the match is also a constant challenge for his two handlers: enigmatic lawyer Paul Marshall (Michael Stuhlbarg) and former chess champion Father Bill Lombardy (Peter Sarsgaard).

Fischer’s demands are ever-changing. Suddenly, he wants more money, or he needs the faintly whirring cameras to stop making such a racket, or he wants the audience to be seated at least five feet away from him. “I can hear their thoughts,” Fischer complains, ominously. Then there are his bizarre, anti-Semitic statements — Fischer was Jewish — along with his habit of wearing a paper bag over his head in public.

Unlike many biopics, the tragedy doesn’t resolve itself in triumph. Those two poles are inextricably linked, making the story all the more affecting. At one point, Marshall wonders if he should take Fischer to see a doctor. They could, Lombardy reasons, but wouldn’t putting him on medication affect his chess game?

The screenplay by the talented Steven Knight (“Locke,” “Dirty Pretty Things,” “Eastern Promises”) propels the story, weaving bits of humor into the drama. Director Edward Zwick has a firm grasp on atmospherics, putting the audience in Fischer’s place with tight close-ups that verge on the claustrophobic. Peripheral sounds — coughing, murmurs — are amped up, replicating what it must have felt like to be Fischer, who was notoriously hypersensitive to noise.

“Pawn Sacrifice” includes black-and-white and grainy color cinematography, evoking earlier eras. Some instances, however, are more effective than others. It was a clever idea, for example, to splice Maguire’s Fischer into an actual clip of an interview Fischer did with Dick Cavett in 1971. But the obvious effort to emulate old footage — even with the soft focus — is distracting.

Overall, the movie presents a worthy and historical look at the link between genius and mental illness. The whole world was watching as Fischer took on Spassky in 1972, but few realized at the time that Spassky wasn’t Fischer’s true nemesis. His real adversary was himself.

PG-13. At area theaters. Contains brief strong language, some sexual content and historical smoking.
114 minutes.