On a stage in a spacious Las Vegas banquet hall sits a nervous-looking, dark-haired Danish woman named Connie Sonne. The 46-year-old retired police officer made a name for herself as a psychic in Europe by claiming she knew the whereabouts of famous missing British toddler Madeleine McCann. Sonne also says she can read playing cards through sealed envelopes using only a crystal. If she can successfully demonstrate her skills in this controlled experiment at the South Point Hotel Casino and Spa, she'll receive $1 million.

A broad-shouldered security guard enters, dressed in a standard-issue black polyester uniform. He walks toward the stage, carrying the precious cargo he's been hired to protect: a large manila envelope sealed with duct tape.

The 700 people in the audience — famous magicians, television personalities, mind readers, scientists, and garden-variety nerds — sit in silence, their eyes fixed on the package. The guard passes VIPs: magicians Penn and Teller, astronomer Phil Plait, psychologist Dr. Ray Hyman — and there, at the end of the first row, with a bald head and a beard as long and white as Darwin's, sits James Randi. For more than 60 years, "The Amazing Randi" has been performing magic, debunking psychics, and discussing the perils of all things paranormal. Now 81, he heads the Fort Lauderdale–based James Randi Educational Foundation.

Across from Sonne on the stage is a magician named Banachek. Back in 1980, with help from Randi, he tricked scientists at Washington University's now-defunct McDonnell Laboratory for Psychical Research in St. Louis into believing he had supernatural powers. He later admitted he had performed an elaborate hoax. Today, Banachek is administering Sonne's test.

The security guard hands the envelope to Banachek. Inside is a 10-sided die and four smaller envelopes. Banachek cuts one open and removes 10 more envelopes. Inside each one is a playing card. Sonne rolls the die. It stops on three. She now must find the envelope containing the three of hearts, plus two other cards. If she can, the money is hers.

Sonne glances at the audience, then back at the envelopes spread before her. With her right hand, she dangles her crystal amulet over the table.

For four minutes, the room is motionless. Sonne's dowsing charm sways like a pendulum over the envelopes. No one speaks — nobody wants to be Sonne's excuse if she later says she was too distracted. Randi watches closely, his bushy eyebrows cocked. It's his foundation's million bucks on the line.

Randi has debunked more than 100 psychics and faith healers in a quest to rid the world of hucksters. It also makes him the subject of scorn among purveyors of the paranormal, true believers who say Randi has made himself rich, pulling in nearly $200,000 a year from his foundation, at the expense of others' careers.

Now, however, Randi's work may be in jeopardy. His foundation has been hemorrhaging money, and Randi, who has spent his career challenging the notion of an afterlife, now faces his own mortality. He has intestinal cancer and may not have long to live. He has been a commanding presence for four decades, but it's unclear who could fill his role as the face of the skeptic community.

Randi still has a loyal group of followers, though, who revere him like a religious leader. Many of them come to Las Vegas every year for his conference, the Amazing Meeting. This July, the weekend of critical thinking culminated in Sonne's dowsing demonstration — the first public attempt at the Million Dollar Paranormal Challenge.

When Sonne indicates she has found the three of hearts, Banachek writes "3" on the sealed envelope. She rolls the die twice more, then searches for a seven and an ace. For the final card, the awkward silence lasts nearly five tedious minutes before Sonne chooses the envelope farthest to the left.

After nearly 20 minutes, it's time to see how she fared. Banachek asks her to cut open the envelope marked "3." She does, and Banachek peeks inside.

The James Randi Foundation put together its first skeptics' conference in 2003. That first year in Fort Lauderdale, the event drew just 150 attendees. In the years since, it has grown to become the largest gathering of critical thinkers, doubters, heretics, and nonbelievers in the world. More than 1,100 conferees paid about $300 each for admission this year. They come to hear some of the most famous voices in critical thinking — Adam Savage, San Francisco–based cohost of the Discovery Channel's MythBusters; Bill Prady, cocreator of CBS' The Big Bang Theory — and to discuss Randi's favorite topic, skeptical inquiry, a discipline devoted to debunking psychics, faith healers, con artists, and ghost whisperers through the holy miracle of old-fashioned science.

The Amazing Meeting attendees are mostly white males with glasses, facial hair, and a healthy appreciation of physics and Monty Python. They come from as far away as Australia and Japan. There are college students, bloggers, and rambunctious computer scientists. In the halls of the conference, they banter about the psychological phenomenon known as "the ideomotor effect," the pseudoscience behind the instant sommelier (a contraption that can supposedly age wine to perfection in 30 minutes), and — a favorite conversation topic — getting wasted at the hotel bar.

The highlight of the weekend for most of the skeptics here is the chance to meet the man dubbed "The King of Debunking." Randi is a 5-foot-5 command performance, with his characteristic white beard and brow, and penchant for zingers. On each morning of the conference, Randi arrives at the main lecture hall in a wheelchair. A slow-moving pack of swooning disciples gathers around him. Pictures are taken. Hands are shaken. A little girl asks him to sign her straitjacket. A booth sells little James Randi dolls with glasses, bushy white beards, and tiny handcuffs. Some conferees come with questions they've been dying to ask for years ("Mr. Randi, when you flew in upside down over Japan, did you have any plan in the event of an autorotation ditch?"). But most want to give thanks to the man who got them sober to the ways of the world: "Hi, I saw you speak in Toronto, and you changed my life." "You let me know it was okay to question my own beliefs."