KAILUA-KONA, Hawaii — For Anthony Hsieh and other wealthy big-game fishermen, this is a summer of great expectations. Or maybe grand illusions — it's too early to know.

Mr. Hsieh, the former president of LendingTree.com, and some of the world's best-financed fishermen are flocking to the cobalt blue waters here off the coast of Hawaii to try to catch what many consider the holy grail of trophy fish, the grander — a blue marlin that tops 1,000 pounds.

Not only are these fish prized for their size, beauty, and heroic fighting ability, they have serious literary cachet: the most famous one stars in Ernest Hemingway's classic novel "The Old Man and the Sea." Only 51 granders have been caught and recorded since 1939, according to the International Game Fish Association. Although locals here in Hawaii have a slightly higher tally, one thing is certain: Nearly everyone who has ever set out to catch one has failed.

Though little is known for certain about the current status of the blue marlin population in Hawaii — the only place in the world where the elusive, migratory beasts have been caught year-round — the stars seem to have aligned to produce a bumper crop. Increasing pressure from conservationists as well as new tournament incentives to "catch and release" fish shy of 1,000 pounds may be increasing the ranks of marlins that grow to grander size. A recent ban on long-line commercial fishing, which used to claim hundreds of marlin casualties each year, seems to be helping. What's more, soaring gas prices have cut the local sport-fishing charter business by around 40 percent, leaving the few there who can afford to stay on the water with little competition.

Sure, says Mr. Hsieh, 43, it's a bit of an obsession — and one his Chinese-immigrant parents can't understand. He says he'll spend $1.6 million this year to keep his fishing team at sea trolling for granders, up from $1.2 million last year. Mr. Hsieh left his post at LendingTree in 2007 and founded Granders Inc., which operates a Southern California-based yacht dealership and brokerage.

A fishing addict since his high-school deckhand days in Newport Beach, Calif., he now spends the entire month of July in Kona with his wife and four daughters, fishing nearly every day and logging notes about the moon phase, currents, temperature and tides into his BlackBerry each night.

Mr. Hsieh's team made waves in the fishing world two years ago after winning $3.9 million at Bisbee's Black and Blue fishing tournament in Cabo San Lucas — the largest single payout in sport-fishing history. His multimillion-dollar yachts stir jealousy in the hearts of his neighbors at Kona's 260-slip harbor. Last August, he hooked what he judged to be a 900-pound blue marlin in Kona, and ordered his team to toss it back. Still, the grander eludes him.

Last week, Mr. Hsieh and his team, "Bad Company," were warming up for the annual Skins Marlin Derby, where the first boat to catch a grander would win a Corvette. But after two days on the water with no bites, the crew was getting antsy. Captain Randy Parker suspected someone on board had been eating bananas — considered bad luck in marlin hunting — possibly in muffin form. Deckhand Keith O'Brien killed time slicing up last week's catch into sashimi, after changing the lures fruitlessly for the umpteenth time. Six-year-old Amanda lolled inside the cabin on a leather couch watching "Goonies" on a flat-screen TV, while her father, Mr. Hsieh, implored her to come outside. "I thought you were going to be my good luck charm today," he said.

As sportfishing's demographics have shifted, tournaments have morphed from purely recreational contests to events in which competitors can win more than professional golfers. So while record high fuel prices may be causing most of America's 40 million anglers to jump ship, today's serious big-game fishers aren't letting an extra $20,000 a year on fuel crush their grander dreams. The average marlin hunter earns $445,000 a year, has a net worth of $2.3 million, and spends an average of 84 days a year on the water, says Bisbee's tournament director Wayne Bisbee.

When it comes to granders, hooking one is only half the battle. The fish are so fast they have spurred chases at speeds approaching 50 miles per hour and at other times, have taken the fight to the fishermen. A teenager from Atlanta was hospitalized with broken sinus walls and cheek lacerations three years ago after a 600-pound marlin jumped out of the water and lunged bill-first at his face. A lawyer from Valdosta, Ga., was knocked off his feet recently after his 1,115-pound marlin, bleeding upside down in the water, suddenly sprang to life.

Superstitions rule the day. Hawaiians never utter aloud that they're going fishing for fear their prey will hear. It's also customary in Hawaii to have new boats blessed by an island priest, many of whom charge for the service. The banana curse first seemed silly to Mr. Hsieh and his crew until one day six years ago when, after a hapless day at sea, they discovered a dozen bananas tied under the bow pulpit of the boat, presumably the handiwork of a rival. Mr. Parker, whose brother's name is Marlin, says he doesn't trust the priests who make a living blessing vessels. He relies on a friend, who he says once successfully exorcized an evil spirit hiding in a boat's shower.

Last month, Mr. Parker and his friend performed two ceremonies to cleanse Mr. Hsieh's new boat of its former name, "Amnesia." They wrote the word on a slip of paper, wrapped it in green ti leaves and sent it into the sea at sunset with tropical fruits and flowers. They repeated the ceremony a week later after sensing the vessel was not completely cleansed.