Those investments have brought the Maktoums just about every prize in Thoroughbred racing, except perhaps the biggest: the Kentucky Derby. No other dirt race attracts crowds as large or delivers such prestige. That’s partly because it’s as hard to buy or raise a winner as it is to pick the right horse to bet on. The field is composed of three-year-old horses, the equine equivalent of teenagers, demonstrating all the physical and mental predictability of your typical high schooler. They must run farther than ever before—1¼ miles—on a track more tightly packed than any they’ve ever experienced. So far, the best a Maktoum entry has finished is sixth. And while the final lineup isn’t set until a few days before the Derby in May, the Maktoums have been prepping about a dozen horses for this year’s starting gate.

Sheik Mohammed has made no secret of his desire to win America’s biggest race. But it’s his battles in the auction ring that really have the horse world’s attention. Over the past few decades, the Maktoums have gone head-to-head for the best horses with a secretive Irish billionaire named John Magnier. Always surrounded by a bevy of advisers, Magnier has long dominated the breeding industry, in which owners pay up to $500,000 to have their mares “covered” by a stallion with the right heritage, looks, and track record. His company, Coolmore, is a brand name in its native Ireland as well as the largest stallion manager in the world. Magnier’s pursuit of horses with the most prized bloodlines for stud income has kept him in heated competition with Sheik Mohammed, who is looking for the best racers. Now the sheik has set his sights on reaching the top of the stallion business in America, and the rivalry between the Irish and the Arabs—as the industry shorthand goes—has grown hostile. Coolmore won’t send its best horses to race in Dubai, and for the past two years, the Maktoums have refused to send their mares to Coolmore stallions or even to buy any horse with Coolmore bloodlines.

“Cold war? This is nuclear,” says Richard Santulli, the C.E.O. of NetJets, who co-owns the Jayeff B Stables in Woodbridge, New Jersey. In 2005, Santulli brought to auction two yearlings sired by a fashionable Coolmore stallion. In the past, either of these young horses would have guaranteed a bidding war between Magnier and the Maktoums. This time, Sheik Mohammed didn’t lift a finger. Magnier ended up buying both horses for a fraction of what Santulli thought they should have brought in. “When you take the Arabs out of the mix, well, you see what happens,” he says.

Of course, every industry has its rivalries. But this one is different. Sheik Mohammed’s desire to dominate the horse industry and fashion Dubai into a global destination for racing is rooted in a time more than 350 years ago, before the Thoroughbred even existed. The wildflower-lined road to his Godolphin stables in Dubai offers telling evidence of the depth of the ruler’s passion: There, a 150-foot-long, 25-foot-high billboard reads, GODOLPHIN: BRINGING THE RACEHORSE HOME.

“DID YOU ASK YOURSELF WHY I named my stables Darley and Godolphin?” Sheik Mohammed asks. He’s sitting on a blue leather couch in a suite at Nad al-Sheba. On the wall is an oil painting of him with two of his seven sons (he also has nine daughters). Crisford takes a seat nearby. A cell phone rings, and the sheik pulls out a beat-up Nokia. He’s a surprisingly down-to-earth guy. He drives himself around Dubai in a white Mercedes G-Class truck (the license plate displays only the numeral 1) and loves to dance, hunt, and write poetry. No bodyguards or assistants trail him. Still, the ruler is comfortable with ceremony. When a waiter comes by, he first drops to a knee and bows his head before offering Sheik Mohammed vegetable soup.

Growing up, the sheik led a life that blended royal and traditional desert lifestyles. Long before the country started pumping out oil in 1969, Dubai was a prosperous port where traders from the Middle East and India came to buy and sell gold. Like its neighbors, it had ceded control of foreign policy and defense to the British Empire in exchange for maritime peace and political support. Sheiks who sided with the empire were paid handsomely for drilling rights and other privileges.

Sheik Mohammed’s father, Sheik Rashid bin Saeed al-Maktoum, was one such ruler. He represented the fourth generation of Maktoums to govern the land, and he made sure his sons—Maktoum, Hamdan, Mohammed, and Ahmed—were grounded in their Bedouin heritage. That included a mastery of horses, which were key to both war and transportation in the desert. Bedouin have a long tradition as expert riders and strict breeders, able to recount the pedigree of each of their animals. Sheik Rashid personally taught his sons how to ride, interrupting his schedule to meet them at the royal stables. The boys’ grandfather Sheik Saeed bin Maktoum al-Maktoum spent hours spinning tales of his equine exploits and recounting the many battles won by mounted Islamic armies. At the end of each school day, the brothers would sprint to their father’s stables, grab a horse, and speed along the beach past fishermen scrambling to get out of the way.

They were master horsemen, but few outside Dubai, as Sheik Mohammed soon learned, were aware of that. In the summer of 1966, Sheik Mohammed’s father sent him to the U.K. to learn En-glish at a language school in Cambridge and to live with a local family. Cambridge is about a half-hour from Newmarket, the birthplace of horse racing in the U.K., and Sheik Mohammed’s host mother would talk constantly about the great British tradition in the sport. The young sheik protested.

“She thought these horses, this magnificent Thoroughbred, belonged to them,” Sheik Mohammed says. His voice is gravelly and strong and his English heavily accented. “So I argued, ‘No, they descended from my horse.’ She couldn’t understand.”

As Sheik Mohammed saw it, the British were just a blip in the history of the racehorse. Every Thoroughbred must be able to trace its lineage back to one of three sires: the Byerly Turk, the Darley Arabian, or the Godolphin Barb. Those horses arrived in England in the late 17th and early 18th centuries as either colonial gifts or war booty from the Middle East and Turkey. Most histories of the Thoroughbred start there. But trace the heritage of those founding sires back even further, insists Sheik Mohammed, and you get to his land. “They are all from Arabia,” he says. “All from the Arabian Peninsula.”

Sheik Mohammed decided to reclaim what he believed was his heritage. After graduating from language school as well as a military training academy in En-gland, he returned to Dubai, where in 1971 his father appointed him minister of defense for the newly formed United Arab Emirates. He was 22. (His eldest brother, Maktoum, secured the prime minister spot and succeeded his father as ruler of Dubai in 1990. When Sheik Maktoum died in 2006, Sheik Mohammed assumed both titles.) Oil money flowed into the ruling family’s coffers, and Sheik Mohammed started steering some of it toward horses. By the late 1970s, he and his brothers were buying, racing, and winning in England and Ireland.

At his brother Maktoum’s urging, Sheik Mohammed decided in the summer of 1979 to join the buyers from around the world who converged annually on Lexington, Kentucky, for the big sale of yearlings at the Keeneland auction house. These horses were being eyed for the racetrack but had yet to be named or even saddled. The sale was the social event of the year for the small city, and when Sheik Mohammed showed up for the first time, he came unprepared. Jumping into a cab after arriving at the airport, he drove around looking for a hotel. All of them were full, so the cabbie recommended a nearby motel. Sheik Mohammed shrugged; it sounded close enough. In his room, as the cars zipped past his window, the sheik picked up the phone and dialed zero. “Can you please send up three coffees?” he asked. “Come and get them yourself!” replied the manager. (“I wrote a poem about that,” notes Sheik Mohammed.)

A couple of years later, the sheik was better prepared, with a room at the Hyatt Regency and a request from his brother Maktoum to bid on a promising yearling, the offspring of a famous Canadian racer named Northern Dancer that had sired many European racetrack winners. Sheik Mohammed spent the morning evaluating the horse, running through the things his father and grandfather had taught him: He stared into the yearling’s eyes; an angry gaze meant the horse might be uncontrollable. He looked at the nostrils; the bigger, the better for taking in air during a run.