(FORTUNE Magazine) – FARGLED ANYONE LATELY? You just might have. Whether you call it fargling, Roshambo, or jankenpo, if you've played Rock Paper Scissors, you've done it.

Of course, if you're a typical American, you associate Rock Paper Scissors (or RPS, as it's known to aficionados) with school playgrounds, frat houses, dive bars, and the like--where it's used to decide such supremely banal things as who goes first, who takes out the trash, or who buys the next round. But last January, Takashi Hashiyama, president of Maspro Denkoh Corp., a Japanese electronics company, used it to decide a rather weighty matter: whether Christie's or Sotheby's would sell his company's multimillion-dollar art collection. A single round of RPS settled the question. (Christie's scissors beat Sotheby's paper. Ouch!)

If you're asking yourself why anyone would use RPS to make a major decision such as who should sell a Cézanne (the centerpiece of Maspro Denkoh's collection, "Les Grands Arbres au Jas de Bouffan," went for a cool $11.8 million), perhaps a better question would be, "Why not?" After all, RPS is one of the oldest decision-making devices known to man.

RPS is easy enough to play: Each of two opponents makes a fist. They count together, "One, two, three," while simultaneously bouncing their fists. After "three," each player changes his fist into one of three weapons: paper, rock, or scissors. The rules--paper covers rock, rock blunts scissors, and scissors cuts paper--determine the winner. The game is beautiful in its tripartite simplicity.

Though anthro- pological documentation of the game is lacking, it is generally accepted that it originated in Asia. The Official Rock Paper Scissors Strategy Guide (yes, there is such a thing), a cleverly written handbook by Douglas and Graham Walker, leaders of the World RPS Society (again--yes, there is such a thing), offers the theory that the game migrated to Europe from the Far East, where it is known by many names (jankenpo in Japan), during the mid-1700s growth in trade between the continents.

In France the game became synonymous with Jean Baptiste Donatien de Vimeur, comte de Rochambeau (1725--1807), who commanded the French forces during the American Revolution, and at some point in America, Roshambo became a common name for RPS. (Today, the South Park kids are quite the little Francophiles, regularly playing I'll Rochambeau You for It--though their game is a bit simpler and crueler than RPS: You kick your opponent in the crotch, and the first to fall loses.) Roshambo became a common name for RPS in the U.S. A less common name is fargling, whose origins are, alas, obscure.

You may ask, "Why not just toss a coin?" The difference is that while coin-tossing relies solely on random odds, RPS, despite what many people think, doesn't. What's fascinating about RPS is that it's a competition to simultaneously read your opponent's mind and prevent him from reading yours. And unlike other games that involve reading and misleading your opponent (like poker), you can't win RPS by bluffing alone. Eventually you have to show your hand.

Winning at RPS is all about knowing what your opponent is going to do. Successful strategizing involves a series of mental questions: "If you know that I know that you know that I know ..." The popular name for this strategy is Sicilian Reasoning. Part of the trick is knowing when to stop the series; otherwise you risk overestimating your opponent's intelligence (and outwitting yourself). Another part is knowing where to start: Ask yourself, "Deep down, is my opponent rock, paper, or scissors?" Guess right and you've probably guessed his first throw. Douglas Walker of the World RPS Society offers a rough guide to personality types: rock, Muhammad Ali; paper, Mohandas Gandhi; scissors, Leonardo da Vinci. Asked who would win in a match between Superman and Lex Luthor, Walker didn't hesitate: Superman's rock beats Luthor's scissors. Elsewhere on the evolutionary chain, he predicts that a match between Bart Simpson and Eric Cartman would result in a draw: a perpetual string of rocks.

RPS's value as a tiebreaking tool for deciding everyday matters is less well recognized in the U.S. than in Asia, but at least one domestic company is using it. ThoughtWorks Inc., a Chicago-based IT services company with offices around the world, says RPS gives its 700 or so employees an easily translatable way to break ties and make decisions. The company's U.S. people-support director, John Hundreiser, says the most expensive round of RPS he ever lost was over who would pay the dinner bill for 22 people at a restaurant in Bangalore that didn't accept credit cards.

If the World RPS Society's brothers Walker have anything to do with it, this side of the planet just might catch up to the East. Their mission began ten years ago on a cold night at the Walker family's cottage in Canada, when Douglas and Graham, after a few drinks, played a best-of-13 match of RPS to decide who would go outside to get more wood for the fire. After the match was over (Douglas lost), they discussed their strategies and the patterns they observed in each other's play and quickly realized that there was a lot more to playing RPS than random chance.

The Walkers did a bit of sleuthing and discovered a "pretty much defunct" organization called the World RPS Society, Douglas says. They got involved, took things over, and in 2002 held the organization's first major public tournament.

The 2002 International Rock Paper Scissors World Championship was held in a bar in Toronto. The sold-out event offered a $1,200 grand prize, which was won by local "Master Pete" Lovering, who was wearing a green bathrobe and a blue-straw cowboy hat at the time.

By 2003 the tournament had nabbed a corporate sponsor, Molson, and upped its grand prize to $5,000. More impressively, it achieved that über-cool benchmark of near-mainstream success: It became the subject of a film documentary. That's right, Rock Paper Scissors: The Movie will be released later this year.

Mike McKeown, 28, a documentary filmmaker based in Calgary, Alta., served as writer, director, and producer. Lest you think the film is a mockumentary, let's make this point clear: The events it chronicles are very real. "Once people see the bright lights and cameras and hard-core competitors and giant checks, they really want to win," says McKeown. "It truly is just as exciting as any world-championship event. Maybe even more so, since not many events allow the fallen competitors to come back and heckle the winners in their final rounds."

Current RPS World Champion Lee Rammage describes the atmosphere as "WWF meets chess meets Star Trek." Since winning, Rammage, who entered the contest on a whim, has never been more awesome in the eyes of his daughters, ages 7 and 9: Walt Disney World invited the whole family down to Orlando, threw a parade, and named him grand marshal. Japan went into a minor media frenzy over Rammage.

The uses of RPS aren't unlimited, of course--Douglas Walker points out that it wouldn't be much use settling political arguments, for instance, because "the backbone of the game is the honor of the people playing it." So what's the biggest thing Walker himself has ever played for? A house, against his wife (Douglas lost again). And what's the biggest matchup he could imagine? Jesus vs. Darwin. "Frankly," he says, "I would like to have the evolution-creationism debate resolved once and for all." ■