(FORTUNE Magazine) – DO YOU BELIEVE in luck? Let David Wittig, the former co-head of investment banking at Kidder Peabody, tell you why you should. One evening in 1986, Wittig says, he was having dinner at the Manhattan apartment of Marty Siegel, the infamous Wall Streeter whose indictment on charges related to insider trading was still a few months away. Siegel was trying mightily to woo Wittig, 31 at the time, over to Drexel Burnham. "Siegel was giving me the big schmooze," Wittig recalls. "He told me to ask him anything I wanted.

"I said, 'Okay, Marty. Dennis Levine is in trouble, and there are rumors that Ivan Boesky is next. You once told me you talked to Ivan Boesky every day. Marty, are you clean?'

"Siegel looked me straight in the eyes and said, 'David, I haven't talked to Ivan Boesky in two years.'

"With that, the phone rang, and the housekeeper came into the room. 'Mr. Siegel,' she said, 'Mr. Boesky for you on line one.' "

(Through his lawyer, Siegel recalls meeting with Wittig but denies the rest of Wittig's account.)

The lucky Wittig did not move to Drexel, which later collapsed, nor did he follow Siegel to prison. Instead, he went on to become a managing director at Salomon Brothers and retired from Wall Street earlier this year, a very wealthy man. In May, at age 39, Wittig began a second career, with the goal of running a major company. His first stop: back to his home state of Kansas as head of corporate strategy at Western Resources, a publicly owned utility in Topeka.

For those of us who believe we are the masters of our fate, the captains of our soul, the notion that a career might hinge on random events is unthinkable. Self-made men and women are especially touchy on this subject. If they get all the breaks, it's because they're smarter and harder working than everyone else. If they know the right people, it's because they network the nights away. Luck? Many successful people think it diminishes them.

Hard workers do get ahead, no doubt about it. So do people with charisma, uncommon ability, and great legs. But then there are folks like Ringo Starr. One day he was an obscure drummer of limited talent from Liverpool; the next day he was a Beatle.

Nobody demonstrates better than Ringo that true luck is accidental, not inevitable. Warren Buffett, who helped seal the $19 billion deal this summer between Disney and Capital Cities/ABC, likes to say he was lucky to run into Disney's Michael Eisner just as he (Buffett) was on his way to play golf with Cap Cities chief Tom Murphy. In fact, Buffett's encounter with Eisner at Herbert Allen's 13th annual media-mogul bash in Sun Valley, Idaho, was elephant bumping at its best-the predictable result of "hanging out where luck happens," as Harvard B-school professor John Kotter puts it. "Some people are very clever at figuring out what lake has a lot of fish in it," he says, "and then knowing how to get the boat out there at the right time of day."

Chance may favor the prepared mind, but to one degree or another, chance happeneth to us all. As Northwestern sociologist Christopher Jencks wrote in his seminal work Inequality, financial success often depends on "chance acquaintances who steer you to one line of work rather than another, the range of jobs that happen to be available in a particular community when you are job hunting, the amount of overtime work in your particular plant, whether bad weather destroys your strawberry crop, whether the new superhighway has an exit near your restaurant, and a hundred other unpredictable accidents." In the broadest sense, then, luck is the great "but for" in life: But for this or that bit of luck--good or bad--you would have married a different person, had a different career, lived in a different city.

In reporting this story, FORTUNE ignored the mundane "but fors" that we all love to talk about, and tried to isolate spectacular, career-making moments of blind, dumb luck. We interviewed a number of smart, rich, charming, beautiful, happy people. Among those willing to admit that another force might have been at work in their success was economist William Sharpe, 61. Sharpe won a 1990 Nobel prize for his research on how to price risky assets. He says that luck ultimately elevated him above his peers. "There are lots of people who are just as smart and worked just as hard as I did," says Sharpe. "But they picked topics that were intractable or may not have had sweeping enough implications."

Were it not for an embarrassing meeting early in his career, Sharpe too might have been just another economist. In 1959 he gave his adviser the first 50 pages of his doctoral thesis on transfer pricing, a study of what one division of a company charges another for its services. To Sharpe's dismay, the professor found the work uninspiring. "Had he not criticized my original thesis, I might be the world's greatest authority on transfer pricing--known to maybe eight people."

USING census data and a 20-year longitudinal study of 5,000 families, Jencks and other social scientists controlled for all sorts of variables that might pave the way to wealth and power, including parental income, the neighborhood a person grows up in, education, occupation, and test scores. Concludes Jencks: "We can account for no more than 50% of a person's success. The rest is a combination of our inability to measure things--and luck."

Part of what Jencks can't easily quantify is personality, and that, we know, can make or break a career. But isn't it also a matter of luck whether or not your particular personality suits the task at hand? "An administrator is quite likely to earn more money if he or she is good at pouring oil on troubled waters," says Jencks. Then also, someone who can downsize without a hint of remorse will be highly valued in a top-heavy organization. And it might not be stretching it too far to suggest that had MCA President Sid Sheinberg not been such a confrontational fellow, he might have gotten along better with his Japanese bosses at Matsushita. But lucky for him, the Japanese grew weary of the Hollywood power struggle and unloaded MCA on Seagram. Sheinberg is now the happy head of his own production company, called the Bubble Factory, in which MCA has a stake.

Even if things do come down to whom you know in this world, luck definitely figures in whom you meet. Bob Eaton might never have gotten the top job at Chrysler were it not for the fact that his wife once taught grade school with the wife of Chrysler finance man Fred Hubacker. Thrown together at a teachers' party, the husbands hit it off. Thirty years later, when Lee Iacocca was looking around for a successor, Hubacker suggested he take a look at his old buddy Eaton, a career engineer at GM.

Luck falls on rich and poor alike, though not in equal measure: People born into poverty are less likely to succeed than those who aren't. "There is stickiness at the bottom, just like there's stickiness at the top," says Mary Corcoran, a professor of public policy at the University of Michigan. Her data show that children raised in a family whose income is below the poverty line end up earning 30% to 40% less than those whose parents' income is two to three times that at the poverty line. Breaking the cycle is tough, but not impossible: The poor have to either work a lot harder than most people do--or get a lot luckier.

Golf's blue-collar hero Lee Trevino, whose career earnings exceed $9 million, did both. At 55 he still practices several hours a day, 365 days a year, and is famous for the remark, "The harder I work, the luckier I get." But fate did smile on him early in life. He grew up in a dirt-floor shack with his mother, two sisters, an uncle, and his grandfather, a gravedigger at a nearby cemetery. Serendipitously, Trevino's shack was located on the fringe of a Dallas country club. By the time he was 8, he and his friends were out on the golf course hunting for balls. Says Trevino: "If I had been born in the projects-oh, hell, I'd have never known anything about golf.''

Trevino's next big break came when he was 18, a corporal in the Marines on his way to Okinawa. Through a clerical error, he was ordered to pull mess duty on a base instead of being sent to reconnaissance training. As it turned out, there was an opening on the base's golf team. For the next 18 months, Trevino played every afternoon. "If I had ended up in recon where I was supposed to be," he says, "they would have taught me all those mean looks and stuff, and I'd probably be in jail today."

Johnny Barfield, son of an Alabama sharecropper, might never have escaped poverty were it not for one lucky coffee break that led to a great idea. In 1947, "with no formal skills at all," he says, he took a job as a custodian at the University of Michigan for $1.75 an hour. While cleaning the chemistry building one day, he happened to sit down for a rest right next to a pile of magazines. He began browsing through one and came across an article on contract cleaning. "It suddenly dawned on me," he says, "there were lots of people out there willing to pay for something I had become expert at."

In 1954 he and his wife, Betty, loaded up a station wagon with mops, buckets, ladders, and sponges, and built Barfield Cleaning Services, which ITT bought 15 years later for a sum Barfield declines to disclose. From contacts he made cleaning auto plants, Barfield, 68, built a second business, Bartech Staffing Services, which provides companies with temporary technical workers. Today he employs 1,500 people and has $63 million in annual revenues.

While Barfield found luck in a moment's repose, Barnett Helzberg Jr. bumped smack into it on a busy New York City street corner one summer morning in 1994. The well-to-do Kansas City jeweler wasn't exactly looking for opportunity that day. In New York for a meeting, he was actually trying to pick his way through the crowds on 58th Street to get back to his hotel. Just as he passed the Plaza near Fifth Avenue, he heard a woman call out, "Mr. Buffett!" He turned, and sure enough, there was the Omaha billionaire.

HERE'S what flew through Helzberg's mind in the next few seconds: As the owner of four shares of Berkshire Hathaway stock, he knew from the company's annual reports the financial criteria that Buffett insisted upon for any business he might consider purchasing. Helzberg also knew that his business, the third-largest jewelry chain in the U.S., fit the bill. Having turned 60, he was toying with the idea of selling the company. He could think of no one better to buy it. He followed quickly on the woman's heels. Says Helzberg: "I walked over to Buffett, and we had a very detailed 20-second meeting."

In May, Buffett bought Helzberg Diamond Shops, a chain of 164 stores with annual revenues of roughly $300 million. "That deal never would have happened if I hadn't been walking down that street," says Buffett. "I could have been there 30 seconds earlier or 30 seconds later, and I never would have met him." (Of course, had Buffett arrived at a different time or walked down 59th Street instead, he might have been even luckier. "I might have bumped into Bill Gates," he quips, "and bought Microsoft.")

Sometimes one person's misfortune can be another's lucky break. Estee Lauder got lucky--that's all there is to it--when British heartthrob Hugh Grant was arrested with a hooker near Sunset Boulevard last June. Suddenly, Lauder's new spokeswoman--Grant's live-in girlfriend Elizabeth Hurley--was not just another pretty face who wore fabulously tight dresses held together by safety pins. She was someone millions of women could identify with. Vulnerable, down to earth, and accessible was what Lauder wanted when it dumped its former model, the perfect Paulina Porizkova. Now they had her--the wronged woman.

As for Divine Brown, the woman arrested with Grant, luck rained down upon her for a time. Her chance encounter landed her a modeling job in a Brazilian lingerie commercial, for which she was paid some $30,000. She also reportedly earned in excess of $100,000 for telling all to a British tabloid. Not bad, as they say, for a night's work.

Sometimes what seems bad at first can end up being lucky after all. Buffett feels that way about a demoralizing experience he had when he was 20: Harvard business school turned him down. When the letter arrived, Buffett went to the library of the local college where he was taking some business courses and began researching other graduate schools. While looking at Columbia's catalogue, he noticed that both Benjamin Graham and David Dodd, whose book Security Analysis he had recently read and admired, were teaching there. He wrote to Dodd, who was an associate dean, in early August, and enrolled the next month. "Probably the luckiest thing that ever happened to me," Buffett says, "was getting rejected from Harvard." Had he gone to Harvard, he might never have gotten to know Graham, who became his teacher, his mentor, and later his boss. That connection also prompted Buffett to buy into Geico, on whose board Graham served. Today, Geico is a pillar of Berkshire Hathaway's insurance holdings.

Luck never took so many twists and turns as it did on Jim Lovell's attempt to visit the moon 25 years ago. Numerologists had a field day with the mission: Apollo 13 blasted off at 13:13 on 4/11/70 (add 'em up one by one) and ran into "a problem" on the 13th day of April. Lovell doesn't consider it a matter of luck that he and his fellow travelers made it back to earth safely. "That was strictly brainpower, hard work, and motivation," he says. Nothing short of miraculous, though, was the timing of the disabling explosion. "Luck was with me there," says Lovell. "There was a window of only a few hours for that explosion. Had it occurred earlier, we would not have had enough electrical power to go all the way around the moon and get home. If it had happened later, when we were in lunar orbit, we wouldn't have had sufficient fuel to get back." It was also lucky for Lovell that when his book agent sent the proposal for Lost Moon--Lovell's account of the mission--out to Hollywood, it landed on the desk of a guy named Michael Bostick. Says Lovell: "It just so happens that Michael's father, Jerry, was working in the control center when we ran into trouble."

Most people have no idea where to look for luck. Not a problem. Luck--good or bad--finds you when it wants you, whether you're flying to the moon or remembering your ABCs. Vanna White struck it rich flipping letters on Wheel of Fortune, the world's most watched game show. Once a struggling actress, she landed the job 13 years ago in an audition with 200 other women. "I turned letters," she says, "and my knees shook." And dumb luck was on her side.