The casinos’ impact is greatest at the sport’s low end, the so-called claiming races, a world away from the bluegrass pageantry of Saturday’s Kentucky Derby. In the claiming ranks — where some of the cheapest horses fill starting gates at tracks like Aqueduct, Penn National, near Harrisburg, Pa., and Evangeline Downs in Louisiana — the casino money has upset the traditional racetrack balance of risk and reward.

“It’s strictly self-centered greed of not thinking about the horse but thinking about maybe I can get one more race out of him and get a piece of the game,” said Dr. Tom David, until recently the chief veterinarian for the Louisiana Racing Commission.

To better protect the horses, some industry experts say, purses should be limited so the potential winnings in any race do not exceed the value of the horses running in it. That way, the incentive for the owner is to care for the horse over the long haul, rather than risking it for a single payday. A prominent veterinarians group, the American Association of Equine Practitioners, recommends that no purse exceed a horse’s value by more than 50 percent.

Yet that recommendation is widely ignored, The Times found.

At Aqueduct, horses worth $7,500 — at the lowest level of competition — recently raced for a $40,000 purse, nearly four times the recommended maximum. Two of them broke down and had to be euthanized. Both had been given pain medication in the days leading up to the race. In all, 19 of the 30 Aqueduct deaths occurred in races where the veterinarians’ standard was violated.

Nationwide, 57 percent of thoroughbred claiming races at casino tracks exceeded that 50 percent standard, and horses broke down or showed signs of injury at a 29 percent higher rate in those races, according to a Times analysis.

In a statement, the New York Racing Association said “it would be inappropriate and irresponsible of The New York Times to speculate on the reasons for breakdowns and injuries” before the governor’s task force has finished its inquiry.

Big purses have destabilized the racetrack economy in another way. Every claiming race is essentially a marketplace, with all horses for sale at a fixed price. But the casino money has set off a frenzy of horse trading at Aqueduct, with owners eager to buy and also to sell to slake the surging demand. Since the casino opened late last fall, nearly 500 horses and $10.7 million have changed hands, more than double the previous year, records show.