If you like mythology, war and beautiful people with no body hair, then Troy may be the movie for you. It recounts the story of the ancient impregnable city that was destroyed partly by its overreaching. The makers of Troy can probably sympathize. The movie was directed by Wolfgang Petersen, a skilled filmmaker who suffers from one fairly serious flaw: he is insane. His insanity is not crippling; since moving from Germany to Hollywood in 1987, Petersen has managed to make such bankable fare as In the Line of Fire, Air Force One and The Perfect Storm. But his condition is chronic, and its occurrences are memorable. "You know, I am amazed a bit by the proportion of Brad Pitt's pectoral muscles," he says, and gives a 10minute soliloquy on Pitt's physique. Petersen also muses at length on the importance of having soup at 11 a.m., the merits of eating at the same restaurant every night while shooting and his belief that Peter O'Toole secretly craves advice on acting. "I nudge him," says Petersen. "I am maybe a little crazy to do so, but I already know that I am a little crazy!"

The only people mad enough to employ Petersen on a regular basis are movie executives, who are trapped in an increasingly illogical if undeniably daring way of doing business. The latest proof is Petersen's loose adaptation of Homer's The Iliad, starring Pitt, Eric Bana and Orlando Bloom. With a budget that Warner Bros. (which, like TIME, is part of Time Warner) puts at $175 million — but that several sources say has crept closer to a quarter of a billion dollars — Troy is one of the biggest, craziest movie gambits since Titanic. It's not just that the film required some 1,500 battle-trained extras or that production was plagued by war, hurricanes and frothing Bulgarian weight lifters or even that Pitt, playing the legendary Achilles, injured his Achilles tendon. It's also that the odds of a movie of Troy's scope making money have never been longer.

A year ago, studios started loading up their summer 2004 blockbusters like bullets in a chamber. Each movie has a one-week shot at grabbing the public's attention before another is fired into multiplexes and scatters the competition. Troy opens in roughly 3,500 locations on May 14, the week after Van Helsing and a week before Shrek 2. If it doesn't open huge or if it dies soon after it opens, it could do untold harm to the careers of Petersen, Pitt and numerous Warner Bros. executives. "On something this big, it'll come down on me and everyone else they're selling it on," says Pitt. "There are people keeping close score, believe me. I just hope they also pay attention to the story."

The story, The Iliad, is the epic poem of the Trojan War, set off when Paris, a Trojan prince, settles a dispute among three goddesses and is rewarded with Helen, the most beautiful woman in the world. The goddesses neglect to inform Paris that Helen is married, and Agamemnon, brother of Helen's husband and king of the Greeks, sends 1,000 ships to Troy to get her back. Paris — a lover not a fighter — asks his noble brother Hector to defend him and the rest of Troy while the Greeks rally behind the demigod Achilles, the world's greatest warrior.

There's a movie in there, but it's buried beneath 24 books of dactylic hexameter and some unfathomably dull speechifying by the gods. David Benioff, the novelist cum screenwriter who sold Warner Bros. on the idea for $150,000, decided early on that the god stuff had to go. "I had this terror of some actor in a toga hurling CGI [computer-generated imagery] thunderbolts from the top of Mount Olympus," Benioff says, in reference to the 1981 Laurence Olivier — as — Zeus camp classic, Clash of the Titans. After dropping the deities and adding the Trojan horse from The Aeneid, Benioff focused his taut 140page script on Hector and the now mortal Achilles. "They're the two great heroes on opposite sides, but it's not a good guy — bad guy story. It's humans vs. humans, and that's what makes it great tragedy."

Petersen saw a Troy draft in early 2002 and signed on immediately. "I was offered Gladiator — before Ridley Scott," he says ruefully. "And I turned it down ... What a fool was I. This time, again I responded to similar material. Great lovers. Great fights. I did not hesitate." Pitt received an early draft too, and over dinner at Petersen's favorite German restaurant ("They brought me out a giant ham hock, extra gristle," Pitt recalls), he committed to doing months of dialect and sword work and putting on the additional 7 lbs. to 10 lbs. of muscle required to play Achilles. "I hadn't worked for two years, so I figured, f___ it," says Pitt. "I got no excuses. Plus, once you've done a few movies, you want to up the ante. I don't know how much was fueled by the story or approaching 40 or what. But I wanted to see — if I wasn't lazy about it, if I really went at the physical and emotional work — where it might end up."

With Pitt on board, Petersen cast the other dozen or so leading roles according to the gospel of David Lean. "I looked at Lawrence of Arabia," says Petersen, "at Peter O'Toole and Omar Sharif. Oh, my God! What attractive guys they were. I think these epic stories need attractive people. So I decided I will go for a high standard of beauty." Eric Bana (last summer's Hulk) was chosen to play Hector; O'Toole snapped up the role of Priam, the Trojan king; Julie Christie took a cameo as Achilles' mother Thetis; and despite rumored interest from Nicole Kidman and Julia Roberts, a worldwide casting call went out for a really pretty Helen of Troy, with German newcomer Diane Kruger landing the role. Finally, Orlando Bloom was cast as Paris. "It was a ferociously good-looking set," says Benioff. "A good way to crush your ego is to walk into a restaurant with Orlando Bloom."

With Troy's pretty people in place, the first hint of the trials to come arrived when production designer Nigel Phelps, who had been researching the architecture of ancient Troy at the British Museum, informed Petersen that the city was kind of a dump. "Going through all these sketches, there was a moment of realization," says Phelps. "Troy just didn't have the size or the spectacle the movie demanded. There was a wall and a gate, but most of the buildings were maybe 10-ft. high and made of mud." To make Troy look like a city worth defending, Phelps had to scramble to put together "an architectural vocabulary from a bunch of ancient cultures that was, you know, made up."

The invented Troy, surrounded by a wall 40 ft. by 500 ft. made from 200 tons of plaster, was to be built in Morocco. But shortly before shooting started, the location had to be switched. "The war in Iraq," says Petersen with a shrug. "There were concerns about terrorism in the area. So we go to Mexico." First, however, the production stopped in Malta to shoot scenes that would take place inside the Trojan walls. There were cataclysms — a stuntman hurt himself during shooting and died unexpectedly weeks later, an editor reportedly had his laptop stolen, sparking fears that Troy might be bootlegged before it hit theaters, and paparazzi photos of Pitt in his armor (and on a cell phone) were inspiring jokes around the globe — but on the whole, Petersen moved briskly.

Momentum slowed in Mexico. For the battle scenes, the movie needed an empty beach, and the best one available was a few miles outside Cabo San Lucas. "This beach was fantastic," says Phelps. "Four miles long, very broad, absolutely nothing there. And we found out why." The beach was home to 4,000 protected cacti. Botanists had to be called in to transplant each cactus to a nursery and note its exact location on the beach so it could be returned when production ended. The entire Mexican coast is also part of an endangered-turtle habitat, so 24-hour-a-day specialists were hired to spot turtle eggs and transfer them to incubators.

By the time the roughly 200 tons of props and equipment arrived from Malta on two Russian Antonov air freighters, it was clear that the beach scenes were going to be rough. "The heat was unbearable," says O'Toole, the man who played Lean's T.E. Lawrence. "Why anyone should choose to shoot on a tropic is beyond me."

O'Toole, the king, had it easy. It was the soldiers who truly suffered. Petersen used CGI to fill out the battle scenes — he was known to say, "Same thing, only more expensive," when he wanted to go wider and reveal 50,000 digital fighters — but on any given day, there were some 1,500 battle-trained and costumed extras milling around on the scalding, shadeless beach. About 250 of them were the weight lifters, who were recruited from a sports academy in Sofia and brought in for close-ups. "Those guys were absolutely beating the crap out of each other," says Bana. They went on strike for several days. "I'm not totally into the details, but it had to do with payments and maybe the kind of food they were getting," says Petersen. A few flew home in a rage. Most agreed to stay on.

Meanwhile, the Trojan horse had been broken down into hundreds of pieces for the flight across the Atlantic, the crew awoke one day shocked to discover 150 ft. of beach missing because of the tides, the Greek ships had engine trouble, and nearly everyone battled Montezuma's revenge. "None of this was easy," says Pitt.

Amazingly, the principals remained relatively unscathed until the end. The critical fight between Hector and Achilles was scheduled to be shot just before production wrapped, to give Bana and Pitt extra time to practice their swordsmanship with renowned stunt coordinator Simon Crane (Braveheart, Saving Private Ryan). But a few days before the fight, Pitt damaged his Achilles tendon — an irony he can laugh about now, though only a little. A few days later, Hurricane Marty, the second hurricane to hit the production, blew down the walls of Troy. The walls were rebuilt, and Pitt's leg healed, but shooting was suspended for three months, during which both actors had to stay in peak physical shape. "You could say it was just another one of the challenges," Bana says wryly.

Warner Bros. president and COO Alan Horn insists that none of the chaos or overruns worried him. "We can plan a budget in advance," says Horn, "but it's a little tricky, you know? We're sacking Troy. I had complete faith in Wolfgang. I wouldn't have him do Miss Congeniality, but with this, I was not concerned."

Despite Horn's sangfroid, there is no guarantee that Troy will be a hit. Summer blockbusters have become the riskiest investment in the film business. In his book Hollywood Economics, economist Arthur De Vany analyzed 2,015 movies to determine what succeeds and what fails. The answer, best summarized by screenwriter William Goldman, is that "nobody knows anything." What De Vany did learn is that moviegoers behave according to the principles of Bose-Einstein condensation — a fancy way of saying they are more likely to go to a movie if they receive an "authentic signal" that other people have enjoyed it. Before a movie opens, studios can generate inauthentic signals by securing a star and advertising heavily, creating the impression of a phenomenon. This puts butts in seats on opening weekend and gets the competition out of the way. "You can orchestrate an opening," says De Vany. "What you're doing is briefly dominating supply. That's not demand."

The long-term demand necessary to sustain a blockbuster is still dependent on the authentic signal, word of mouth. Last year's The Matrix: Reloaded took in $91.7 million opening weekend; two weeks later it earned $15.6 million. Word of mouth can just as easily work to a movie's advantage, but not if there are tons of other movies right behind it jamming the signal. "Studios may think that they're reducing risk by having a week to themselves," says De Vany, "but they're wrong. One studio can throw a boulder in the pond and make a splash. If many do, you get turbulence and chaotic audience behavior."

Horn insists Troy is a safe bet when home-video and foreign-box-office revenues are factored in, but even he admits there's risk. So why make such a sprawling hydra of a movie and throw it into Hollywood's most competitive season? In part because no one knows anything. Troy could be a monster hit. But for everyone from Petersen and Horn to the lowliest production assistant, the audacity of the enterprise is, in large part, the point. "As an actor [on a movie like this], you get to feel like you're an explorer," says Bana. "It's completely different from being tucked away in some air-conditioned studio every day. You feel like you're all in."

Petersen naturally puts it in his own unique way. "I have many favorite scenes in the movie," he says. "One, of course, is the scene with Priam and Achilles. In the whole huge movie, it's the smallest scene. Just two guys talking to each other. I also love when Achilles lands on the beach at Troy and calls to all the soldiers, 'Go get your immortality!' You get this sense that this is maybe a dark, kind of crazy guy, right? But he has enormous dreams."

• Josh Tyrangiel