Bobby Fisher's one of those names like O J Simpson or Josh Duggar. You might know the area of life he came from in and that it all ended badly, but you don't know the specifics.

Tobey Maguire – who's been very selective about projects lately – depicts the former world chess champion as an enigma, part spoiled-brat rock star, part genius, part social misfit.

The fact that you never quite get a handle on Bobby is an upside. Maguire (and the film around him) never quite plays his hand, leaving you with a complex portrait as a result.

History (and the film itself, seemingly) tells us Fischer was somewhere on the autism spectrum before anyone knew what such a thing was. Much like Dustin Hoffman's Raymond in Rain Man, what he lacks in social grace he makes up for in his gift for mathematically rigid constructs – in this case, chess.

Fischer falls in love with the game as a boy in Brooklyn in the late 50s, and by the time he's in his 20s he's a legitimate prodigy. When he's old enough, he sets about deposing the Russians as the reigning champions of the chess world – particularly world champ Boris Spassky (Liev Schreiber, speaking in very authentic-sounding Russian).

Chess fever springs up around this kid from the mean streets of Brooklyn and he becomes a proxy Cold War figure as he takes on the Evil Empire of the Soviet Union on the early 70s.

But while Bobby gets closer to his goal and more famous for it (sparking a chess craze the likes of which the world has never seen since) his handler (Michael Stuhlbarg) and coach (Peter Sarsgaard) are having an in increasingly hard time keeping him on the straight and narrow.

Bobby's demands get more ridiculous, his belief he's being bugged and followed more paranoid, and when his behaviour threatens to derail his own rise to the top, one of the themes of the film emerges. Bobby seems to be completely without fear or emotion – he's already virtually cut himself off from his family by this point – but in reality he's as terrified of winning as he is of losing. Like Alexander the Great before him, he'll weep when there are no more worlds to conquer.

But even that resolution isn't the full story. Early on when Bobby's still a boy, we see his mother entertaining friends from the radical left at one of their many dinner parties, talking about unions and revolutions while FBI agents sitting outside the Brooklyn apartment take pictures, something that's become routine to Bobby and his sister.

So it turns out Bobby isn't paranoid at all. He is being watched and bugged. The extent to which it followed the real man throughout his life isn't known, but in the film it seems to both drive him mad and come to define him as he grows up.

It asks one of the more interesting questions in the film that's left to your interpretation. Was there something wrong with Fischer (who ended up living out his days in Iceland, ranting and raving about the US government like a lunatic) or was there something wrong with the world around him, driving him to be the way he was?

Seeing Maguire in the role makes you realise what a distinctive appeal he has in the right film. When he looks over his shoulder at the barely-audible noises in the auditorium during matches that he claims are driving him nuts, his huge, angry eyes simmer with what looks like murder and violence about to burst forth, a stark contrast to his stiff movements and soft-spoken voice.

Performance-driven films like this suit him much more than his brief early 2000s flirtation with superhero stardom, and he's the focal point for a movie that's surprisingly gripping considering the showdown is a chess match.

We know director Ed Zwick much more for big, sweeping epics like Brad Pitt's Legends of the Fall, Tom Cruise's The Last Samurai and Leo DiCaprio's Blood Diamond. Here he zeroes in on characters and story on a much smaller scale with just as much confidence.