Instead, the Mount Airy resident is selling the $2 win tickets on eBay, along with programs and collectible Kentucky Derby drinking glasses.
"It's kind of my way of gambling," Jensen, 38, said.
The hope that Big Brown will win the Belmont Stakes today and become a Triple Crown winner has spurred the dreams of fans of thoroughbred racing - as well as those in the collectibles industry.
As of last night, various sellers had bids of more than $90 for a Derby and Preakness ticket combo.
Mementos from Triple Crown winners are the most popular racing items collected and sold, auction leaders and other experts say, because the achievement is so rare. Only 11 horses have held the title since the races began in the 1800s, and there hasn't been once since Affirmed in 1978.
"That's the thing that resonates most with the public. Even nonhorse-racing fans can relate to a Kentucky Derby winner," and a Triple Crown favorite has even more recognition, said Brian Marren, vice president of acquisitions for Mastro Auctions in Illinois.
Already, hopeful sellers have posted items on eBay such as programs, tickets to races and unclaimed betting slips from the Preakness and Kentucky Derby, as well as manufactured keepsakes such as T-shirts, glasses and even stuffed horses.
A similar excitement stirred in 2004, when Smarty Jones won the first two legs of the Triple Crown, according to Mike Gathagan, spokesman for the Maryland Jockey Club.
"Smarty Jones mania ran wild," he wrote in an e-mail. "It seemed crazier than this year."
He suspects that some people buy tickets for all the top horses at the derby, assuming that one of them might also win Preakness. "If all goes well, it's only another $2 investment in New York," Gathagan said.
There definitely is a market for these items, said T.S. O'Connell, editor of Sports Collectors Digest. For years, people have hung on to betting slips rather than cash them in.
"A lot of people have determined that such things may have greater artifact or - at the very least - sentimental value than getting your 20 cents return. ... I'm sure the New York State Racing Commission doesn't mind that foible one bit," he said.
But betting tickets and programs are not necessarily investments, he said.
"Because they're printed in large numbers and now saved in large numbers, the value is probably not that great," O'Connell said.
The nature of the sport also restricts what's available for sale. Attention usually remains focused on the horses. "As far as I know, I don't think Big Brown signs any autographs," said Mike Heffner, president of lelands.com, a Massachusetts-based auctioneer.
There's a limited supply of what are considered the most valuable items: race-worn material like jockeys' silks or horseshoes. For example, items connected to Seattle Slew, who won the Triple Crown in 1977, have sold at auction for as much as $80,000, Marren said.
But most racehorse owners don't have much incentive to sell race-worn items.
"A lot of the families that own horses at that level are not facing the temptation or economic pressure to sell artifacts," O'Connell said.
Jensen, who works in financial services, has sold collectibles on eBay for eight years and works with a partner who is a bigger horse-racing fan, he said. They started working together in 2004, when Smarty Jones was a contender. "We didn't do too well with that," he said.
This year they are pitching a package deal: a pair of $2 win tickets - one from Preakness as well as a "pre-paid" ticket from the Belmont Stakes.
"A lot of people that can't go to the races, they enjoy having a piece of memorabilia," Jensen said. "They still have a piece of something that was there the day he won the race."
The two hope to sell their slips for $10 to $20 apiece. Given the odds, they would only make an additional 40 cents if they cashed in the tickets at the track - which is where they will go if Big Brown doesn't win. He packages them in protective sleeves made for sports cards.
Jensen has several auctions poised to start right before and after the race itself. He plans to spend the afternoon monitoring the race on television and his auctions via the Internet.
"If he wins, I want to be right there to capture everyone's excitement - and their money," he said.