Warren Buffett and Sandra Day O’Connor walk onto a fairway…

Mark Zuckerberg tees off against Biz Stone….

Bill Gates plays Arnold Schwarzenegger.

These are among the 32 fantasy match-ups in the Fab Foursome Bracket Challenge, a new app that Golf Magazine launched on Facebook today.

Golf Magazine publisher Dick Raskopf says that his group came up with the app after actor Will Ferrell, who appeared on the cover of Golf‘s big fall issue last year, offered to help with a grander promotion scheme this year. The Golf folks considered various ideas around social media. Since Sports Illustrated–which, along with Golf and Fortune, is owned by Time Inc. –had scored with March Madness bracket-style promotions for its annual Swimsuit issue, the folks at Golf thought, why not apply bracketology to our game?

The Fab Foursome Bracket Challenge is no elite club. Ferrell and actress Halle Berry, competing in the “Artists & Entertainers” bracket, are hackers–actually worse at the game than their 36 handicaps (the max, by golf rules) imply.

Charles Barkley is a famously bad golfer–tragic since he loves the game and works hard at it.

Other than the “Icons of Golf”–Palmer vs. Mickelson, Woods vs. Nicklaus, Paula Creamer vs. Michelle Wie–the pro athletes, no surprise, are among the best golfers in the fantasy lineup. Pittsburgh Steeler Ben Roethlisberger has a 3 handicap, according to Golf estimates. Peyton Manning, of the Indianapolis Colts, has a 4.6. The non-golf pro in the game: Michael Jordan, whose handicap is 1.2.

Among the “Leaders & Influencers,” who would be the top player? Donald Trump, with a 4 handicap and a reputation as the King of the Gimme. Given that daughter Ivanka’s handicap is 29, she doesn’t stand a chance against Daddy Donald in the Fab Foursome’s first round.

Closer matches in the “Leaders & Influencers” field: Gates (27) vs. Schwarzenegger (24), and Bill Clinton (15) vs. Rush Limbaugh (18).

As for Buffett’s match with former Supreme Court Justice O’Connor (13), we’ll predict here and now that the Oracle of Omaha will lose in his first round.

In his youth, Buffett was a golf fanatic. I emailed him this morning to ask how his game is these days, and he replied: “Lucky to break 100 would be a very generous appraisal of my current abilities.”

Added Buffett, who is 80: “In a fantasy matchup game, the only spot I would qualify for is caddy (probably would only last nine holes).”

Go to Golf.com or Facebook.com/SI.Golf  to vote in the Fab Foursome Bracket Challenge and enter the sweepstakes. The winner gets to put together a foursome to play in the Will Ferrell Invitational at Pebble Beach, benefiting a scholarship program called Cancer for College.