Young man with a pawn: "Bobby Fischer Against the World"

"Bobby Fischer is to chess what Muhammad Ali is to boxing," asserts one of those being interviewed in the archive footage that makes up Liz Garbus's smart and absorbing documentary portrait Bobby Fischer Against the World. Yet while this may have seen true at the time of Fischer's ascendancy, in personality terms, the introverted, obsessive Fischer was to the chessboard what Glenn Gould was to the keyboard. Just as Gould often appeared to be seeking out notes beyond notes, reaching for a sound nobody but himself could hear, so Fischer was caught up in games beyond the one set out in front of him: he finished up off the board, much as Gould ended up going off the grid.

In some ways, as Garbus's film sets out, this was an inevitability for a kid who'd spent all his waking hours thinking about defence strategies: alternately encouraged and ignored by his polymath working mother Regina (even mom had something of the queen about her, taking to the battlefield of civil rights), Bobby took up the game at the age of six, was first publicly hailed as a master at 14, and became the all-American champion the following year. The bulk of the documentary is a case study, turning on Fischer's July 1972 encounter with Soviet then-champion Boris Spassky in Iceland, an epochal showdown in which the weight of the free world itself was heaped on this awkward young man's shoulders.

Fischer's opening gambit was to turn up late, alienating the Icelandic public even as his extreme individualism enthralled those watching back home; he fidgeted his way through the first game, and forfeited the second outright, before getting his act together. This was chess's own Rumble in the Jungle - or its go-slow on the ice floe - and Garbus is on sure ground documenting the way Fischer's vacillations caught the imagination of the American public: momentarily, Cold War chess topped even Watergate on the nightly news, in much the same way the pastime sparked a renewed interest in the UK when Channel 4 took a chance on screening live coverage of a handful of Nigel Short games back at the turn of the 1990s. (Like the channel's sponsorship of kabaddi and Chinese football, both far less sedentary pursuits, it couldn't last.)

Ali, though, was a born crowdpleaser. Fischer (variously described as "eccentric", "difficult" and "intransigent" by the interviewees) was too much his own man, a prisoner to his unrelenting mental processes: he insisted on having TV cameras and reporters removed from the venue of this Championship showdown, convinced they were interfering with his thoughts. Already, at what would be the moment of his greatest achievement in the game - in life, even - there were clear and unmistakable signs of the isolation and paranoia Bobby Fischer was heading into.

Produced by HBO, here affording chess the same heady status as their other pay-per-view sports, the material gets a nicely brisk, straightforward treatment, letting this singular personality reveal as much of itself as it cared to in the to-camera testimony of those who knew Bobby best, and period news and chatshow interviews with the man himself. It's telling indeed to hear Fischer, at the end of his intellectually draining 20-odd sessions with Spassky, promising "I'm going to play more chess; I feel I haven't played enough chess"; it also makes it all the more ironic to learn Fischer defaulted his title to the young challenger Anatoli Karpov three years later by refusing to play - in marked contrast to the acknowledged good sportsmanship Spassky displayed throughout their earlier encounter.

Garbus is rigorous in her inquiries, digging out Fischer's personal trainer and even his chauffeur in Reykjavik to get their memories of the man: I'm not so sure she succeeds in making chess itself as involving to sit down and watch as it may well be to sit down and play, but then the real story here is away from the pawns and bishops, and in its final half-hour, the film makes intriguing connections between chess's seemingly infinite permutations of movement and the insanity it has cause to engender in its less stable practitioners. The pay-off's a genuine kicker, tracking Fischer's subsequent, diagonal meanderings across the planet, from the former Yugoslavia (where he played his first game in twenty years, and became a wanted man because of it) to the Philippines (where we hear him cackling as the Twin Towers fell), and then his entry into exile in Iceland (as Gould retreated to the snowy Canadian north) as a bearded, raving crank.

There is a reason an earlier (fiction) film on the chess theme went under the title Searching for Bobby Fischer, and similarly why that feature had to change its title upon its release in the UK: Fischer remained, right up until his death in 2008, an elusive, scarcely known and barely knowable presence, and even the better filmmakers on his case, like Garbus, are as mere rooks in pursuit of a dark knight. However fascinating the man or the biography he inspires, this was a subject who repeatedly shied away from study: yet the poignancy of Bobby Fischer Against the World derives from its understanding that no one move, no one movie, could bring us as close to Fischer as somebody really needed to be. Like the man said: madness in great ones must not go unwatched.

Bobby Fischer Against the World is on release in selected cinemas.